[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (20.12,180.02) – (19.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (99.91,180.09) – (99.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (59.95,280) – (59.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (89.95,160.07) .. controls (99.77,170.17) and (99.77,170.17) .. (99.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.95,160.07) .. controls (99.81,150.01) and (99.81,150.01) .. (100,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (29.95,160) .. controls (20.26,170.11) and (20.26,170.11) .. (20.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (20.09,139.93) .. controls (20.01,150.08) and (19.94,150.02) .. (29.95,160) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (39.95,20) .. controls (40.05,30.15) and (40.08,30.09) .. (29.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.95,40) .. controls (86.47,36.51) and (84.19,34.24) .. (82.71,32.34) .. controls (79.95,28.78) and (79.95,26.51) .. (79.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (39.95,60) – (39.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (79.95,60) – (79.95,140) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.91,40) .. controls (360.22,50.11) and (360.22,50.11) .. (360.07,60.02) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.95,160) .. controls (360.12,149.92) and (360.12,149.92) .. (359.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (309.95,160) .. controls (319.79,149.92) and (319.79,149.92) .. (319.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (310,39.98) .. controls (319.81,50.08) and (319.81,50.08) .. (319.95,60) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (309.95,40) .. controls (300.12,29.92) and (300.12,29.92) .. (299.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.95,40) .. controls (379.79,29.92) and (379.79,29.92) .. (379.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (309.95,40) .. controls (300.12,50.08) and (300.12,50.08) .. (299.95,60) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (369.95,40) .. controls (379.87,50.14) and (379.87,50.14) .. (379.98,60.06) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (299.95,60) – (300.09,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (379.98,60.06) – (380,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (300.12,180.02) – (299.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (379.91,180.09) – (379.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.95,140) – (339.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.95,160.07) .. controls (379.77,170.17) and (379.77,170.17) .. (379.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (369.95,160.07) .. controls (379.81,150.01) and (379.81,150.01) .. (380,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (309.95,160) .. controls (300.26,170.11) and (300.26,170.11) .. (300.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (300.09,139.93) .. controls (300.01,150.08) and (299.94,150.02) .. (309.95,160) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.89,190) – (369.95,160.07) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.89,190) – (331.45,181.52) – (309.95,159.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (319.95,20) .. controls (320.05,30.15) and (320.08,30.09) .. (309.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (369.95,40) .. controls (366.47,36.51) and (364.19,34.24) .. (362.71,32.34) .. controls (359.95,28.78) and (359.95,26.51) .. (359.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (319.95,60) – (319.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (359.95,60) – (359.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (199.95,70) – (199.95,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,40) – (199.95,70) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,40) – (199.95,70) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,40) .. controls (160.12,29.92) and (160.12,29.92) .. (159.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,40) .. controls (239.79,29.92) and (239.79,29.92) .. (239.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (169.95,40) .. controls (160.12,50.08) and (160.12,50.08) .. (159.95,60) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.95,40) .. controls (239.87,50.14) and (239.87,50.14) .. (239.98,60.06) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (159.95,60) – (160.09,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (239.98,60.06) – (240,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,160.07) – (200.02,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,159.93) – (200.02,130) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (199.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (179.95,20) .. controls (180.05,30.15) and (180.08,30.09) .. (169.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.95,40) .. controls (226.47,36.51) and (224.19,34.24) .. (222.71,32.34) .. controls (219.95,28.78) and (219.95,26.51) .. (219.95,20) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (200,40) – (200,20) ;
[shift=(200,40), rotate = 270] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (30,160) .. controls (39.81,170.11) and (39.81,170.11) .. (39.95,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (39.95,180.02) – (39.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.91,160) .. controls (80.22,170.11) and (80.22,170.11) .. (80.07,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (79.95,180) – (79.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (160.12,180.02) – (159.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (239.91,180.09) – (239.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (199.95,280) – (200,170) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,160.07) .. controls (239.77,170.17) and (239.77,170.17) .. (239.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.95,160.07) .. controls (239.81,150.01) and (239.81,150.01) .. (240,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,160) .. controls (160.26,170.11) and (160.26,170.11) .. (160.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (160.09,139.93) .. controls (160.01,150.08) and (159.94,150.02) .. (169.95,160) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (170,160) .. controls (179.81,170.11) and (179.81,170.11) .. (179.95,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (179.95,180.02) – (179.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.91,160) .. controls (220.22,170.11) and (220.22,170.11) .. (220.07,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (219.95,180) – (219.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (199.95,160) – (200,170) ;
[shift=(199.95,160), rotate = 89.74] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (348.37,258.46) .. controls (358.29,268.6) and (359.84,270.08) .. (359.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.91,250) – (348.37,258.46) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.91,250) – (331.24,258.67) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (331.24,258.67) .. controls (321.41,268.75) and (320.12,270.08) .. (319.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.91,190) – (339.91,250) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.86,270.09) – (339.91,280) ;
[shift=(339.86,270.09), rotate = 89.74] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.95,160) – (339.95,140) ;
[shift=(339.95,160), rotate = 270] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,149.91) – (480,140) ;
[shift=(479.95,149.91), rotate = 270.26] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (479.95,230) – (479.95,170) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,260) – (479.95,230) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,260) – (479.95,230) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,260) .. controls (440.12,270.08) and (440.12,270.08) .. (439.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,260) .. controls (519.79,270.08) and (519.79,270.08) .. (519.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (449.95,260) .. controls (440.12,249.92) and (440.12,249.92) .. (439.95,240) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (509.95,260) .. controls (519.87,249.86) and (519.87,249.86) .. (519.98,239.94) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (439.95,240) – (440.09,160.07) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (519.98,239.94) – (520,159.91) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (440.12,119.98) – (439.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (519.91,119.91) – (519.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,139.93) – (480.02,170) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,140.07) – (480.02,170) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,139.93) .. controls (519.77,129.83) and (519.77,129.83) .. (519.91,119.91) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (509.95,139.93) .. controls (519.81,149.99) and (519.81,149.99) .. (520,159.91) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,140) .. controls (440.26,129.89) and (440.26,129.89) .. (440.12,119.98) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (440.09,160.07) .. controls (440.01,149.92) and (439.94,149.98) .. (449.95,140) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (488.41,41.54) .. controls (498.33,31.4) and (499.89,29.92) .. (500,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.95,50) – (488.41,41.54) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.95,50) – (471.29,41.33) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (471.29,41.33) .. controls (461.45,31.25) and (460.17,29.92) .. (460,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.95,110) – (479.95,50) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.89,110) – (509.95,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.89,110) – (471.45,118.48) – (449.95,140.07) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (459.95,280) .. controls (460.05,269.85) and (460.08,269.91) .. (449.95,260) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (509.95,260) .. controls (506.47,263.49) and (504.19,265.76) .. (502.71,267.66) .. controls (499.95,271.22) and (499.95,273.49) .. (499.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (480,260) – (480,280) ;
[shift=(480,260), rotate = 90] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,129.91) – (479.95,149.91) ;
[shift=(479.95,129.91), rotate = 90] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.91,29.91) – (479.95,20) ;
[shift=(479.91,29.91), rotate = 270.26] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

(115,130) node [anchor=north west][inner sep=0.75pt]    $+$;

(255,130) node [anchor=north west][inner sep=0.75pt]    $+$;

(395,130) node [anchor=north west][inner sep=0.75pt]    $+$;

Decomposition of $f(v_1)$.

every picture/.style=line width=0.75pt

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,150.09) – (480,160) ;
[shift=(479.95,150.09), rotate = 89.74] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (89.91,40) .. controls (80.22,50.11) and (80.22,50.11) .. (80.07,60.02) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (89.95,160) .. controls (80.12,149.92) and (80.12,149.92) .. (79.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (29.95,160) .. controls (39.79,149.92) and (39.79,149.92) .. (39.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (30,39.98) .. controls (39.81,50.08) and (39.81,50.08) .. (39.95,60) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (29.95,40) .. controls (20.12,29.92) and (20.12,29.92) .. (19.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (89.95,40) .. controls (99.79,29.92) and (99.79,29.92) .. (99.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (29.95,40) .. controls (20.12,50.08) and (20.12,50.08) .. (19.95,60) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.95,40) .. controls (99.87,50.14) and (99.87,50.14) .. (99.98,60.06) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (19.95,60) – (20.09,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (99.98,60.06) – (100,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (20.12,180.02) – (19.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (99.91,180.09) – (99.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (59.95,280) – (59.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (89.95,160.07) .. controls (99.77,170.17) and (99.77,170.17) .. (99.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.95,160.07) .. controls (99.81,150.01) and (99.81,150.01) .. (100,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (29.95,160) .. controls (20.26,170.11) and (20.26,170.11) .. (20.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (20.09,139.93) .. controls (20.01,150.08) and (19.94,150.02) .. (29.95,160) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (39.95,20) .. controls (40.05,30.15) and (40.08,30.09) .. (29.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.95,40) .. controls (86.47,36.51) and (84.19,34.24) .. (82.71,32.34) .. controls (79.95,28.78) and (79.95,26.51) .. (79.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (39.95,60) – (39.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (79.95,60) – (79.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (479.95,70) – (479.95,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,40) – (479.95,70) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,40) – (479.95,70) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,40) .. controls (440.12,29.92) and (440.12,29.92) .. (439.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,40) .. controls (519.79,29.92) and (519.79,29.92) .. (519.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (449.95,40) .. controls (440.12,50.08) and (440.12,50.08) .. (439.95,60) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (509.95,40) .. controls (519.87,50.14) and (519.87,50.14) .. (519.98,60.06) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (439.95,60) – (440.09,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (519.98,60.06) – (520,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (440.12,180.02) – (439.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (519.91,180.09) – (519.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,160.07) – (480.02,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,159.93) – (480.02,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (509.95,160.07) .. controls (519.77,170.17) and (519.77,170.17) .. (519.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (509.95,160.07) .. controls (519.81,150.01) and (519.81,150.01) .. (520,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (449.95,160) .. controls (440.26,170.11) and (440.26,170.11) .. (440.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (440.09,139.93) .. controls (440.01,150.08) and (439.94,150.02) .. (449.95,160) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (488.41,258.46) .. controls (498.33,268.6) and (499.89,270.08) .. (500,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.95,250) – (488.41,258.46) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.95,250) – (471.29,258.67) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (471.29,258.67) .. controls (461.45,268.75) and (460.17,270.08) .. (460,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.95,190) – (479.95,250) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.89,190) – (509.95,160.07) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (479.89,190) – (471.45,181.52) – (449.95,159.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (459.95,20) .. controls (460.05,30.15) and (460.08,30.09) .. (449.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (509.95,40) .. controls (506.47,36.51) and (504.19,34.24) .. (502.71,32.34) .. controls (499.95,28.78) and (499.95,26.51) .. (499.95,20) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (480,40) – (480,20) ;
[shift=(480,40), rotate = 270] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.91,40) .. controls (360.22,50.11) and (360.22,50.11) .. (360.07,60.02) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.95,160) .. controls (360.12,149.92) and (360.12,149.92) .. (359.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (309.95,160) .. controls (319.79,149.92) and (319.79,149.92) .. (319.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (310,39.98) .. controls (319.81,50.08) and (319.81,50.08) .. (319.95,60) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (309.95,40) .. controls (300.12,29.92) and (300.12,29.92) .. (299.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.95,40) .. controls (379.79,29.92) and (379.79,29.92) .. (379.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (309.95,40) .. controls (300.12,50.08) and (300.12,50.08) .. (299.95,60) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (369.95,40) .. controls (379.87,50.14) and (379.87,50.14) .. (379.98,60.06) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (299.95,60) – (300.09,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (379.98,60.06) – (380,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (300.12,180.02) – (299.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (379.91,180.09) – (379.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.95,140) – (339.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (369.95,160.07) .. controls (379.77,170.17) and (379.77,170.17) .. (379.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (369.95,160.07) .. controls (379.81,150.01) and (379.81,150.01) .. (380,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (309.95,160) .. controls (300.26,170.11) and (300.26,170.11) .. (300.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (300.09,139.93) .. controls (300.01,150.08) and (299.94,150.02) .. (309.95,160) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.89,190) – (369.95,160.07) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.89,190) – (331.45,181.52) – (309.95,159.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (319.95,20) .. controls (320.05,30.15) and (320.08,30.09) .. (309.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (369.95,40) .. controls (366.47,36.51) and (364.19,34.24) .. (362.71,32.34) .. controls (359.95,28.78) and (359.95,26.51) .. (359.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (319.95,60) – (319.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (359.95,60) – (359.95,140) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (199.95,70) – (199.95,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,40) – (199.95,70) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,40) – (199.95,70) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,40) .. controls (160.12,29.92) and (160.12,29.92) .. (159.95,20) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,40) .. controls (239.79,29.92) and (239.79,29.92) .. (239.95,20) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (169.95,40) .. controls (160.12,50.08) and (160.12,50.08) .. (159.95,60) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.95,40) .. controls (239.87,50.14) and (239.87,50.14) .. (239.98,60.06) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (159.95,60) – (160.09,139.93) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (239.98,60.06) – (240,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,160.07) – (200.02,130) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,159.93) – (200.02,130) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (199.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (179.95,20) .. controls (180.05,30.15) and (180.08,30.09) .. (169.95,40) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.95,40) .. controls (226.47,36.51) and (224.19,34.24) .. (222.71,32.34) .. controls (219.95,28.78) and (219.95,26.51) .. (219.95,20) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (200,40) – (200,20) ;
[shift=(200,40), rotate = 270] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (30,160) .. controls (39.81,170.11) and (39.81,170.11) .. (39.95,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (39.95,180.02) – (39.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (89.91,160) .. controls (80.22,170.11) and (80.22,170.11) .. (80.07,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (79.95,180) – (79.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.95,170.09) – (479.95,150.09) ;
[shift=(479.95,170.09), rotate = 270] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (479.91,270.09) – (479.95,280) ;
[shift=(479.91,270.09), rotate = 89.74] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (160.12,180.02) – (159.95,280) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (239.91,180.09) – (239.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (199.95,280) – (200,170) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (229.95,160.07) .. controls (239.77,170.17) and (239.77,170.17) .. (239.91,180.09) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.95,160.07) .. controls (239.81,150.01) and (239.81,150.01) .. (240,140.09) ;

[color=rgb, 255:red, 6; green, 86; blue, 179   ,draw opacity=1 ][line width=1.75]    (169.95,160) .. controls (160.26,170.11) and (160.26,170.11) .. (160.12,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (160.09,139.93) .. controls (160.01,150.08) and (159.94,150.02) .. (169.95,160) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (170,160) .. controls (179.81,170.11) and (179.81,170.11) .. (179.95,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (179.95,180.02) – (179.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (229.91,160) .. controls (220.22,170.11) and (220.22,170.11) .. (220.07,180.02) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (219.95,180) – (219.95,280) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (199.95,160) – (200,170) ;
[shift=(199.95,160), rotate = 89.74] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (348.37,258.46) .. controls (358.29,268.6) and (359.84,270.08) .. (359.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.91,250) – (348.37,258.46) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.91,250) – (331.24,258.67) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (331.24,258.67) .. controls (321.41,268.75) and (320.12,270.08) .. (319.95,280) ;

[color=rgb, 255:red, 126; green, 211; blue, 33   ,draw opacity=1 ][line width=1.75]    (339.91,190) – (339.91,250) ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.86,270.09) – (339.91,280) ;
[shift=(339.86,270.09), rotate = 89.74] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

[color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][line width=1.75]    (339.95,160) – (339.95,140) ;
[shift=(339.95,160), rotate = 270] [color=rgb, 255:red, 255; green, 0; blue, 0    ,draw opacity=1 ][fill=rgb, 255:red, 255; green, 0; blue, 0    ,fill opacity=1 ][line width=1.75]      (0, 0) circle [x radius= 4.62, y radius= 4.62]   ;

(115,130) node [anchor=north west][inner sep=0.75pt]    $+$;

(255,130) node [anchor=north west][inner sep=0.75pt]    $+$;

(395,130) node [anchor=north west][inner sep=0.75pt]    $+$;

Decomposition of $f(v_2)$.

This allowed us to find the correct element to find the counterexample. Repeating the same idea, we see that the elements of the form $12\ldots (n-1)n(n-1)\ldots 21$ have a line as conflated expression graph. Let's say this line is the following figure.

every picture/.style=line width=0.75pt

[line width=0.75]    (30,10) – (60,10) ;

[line width=0.75]    (90,10) – (120,10) ;

[line width=0.75]    (210,10) – (240,10) ;

[line width=0.75]    (290,10) – (320,10) ;

[line width=0.75]    (150,10) – (180,10) ;

(9,2.4) node [anchor=north west][inner sep=0.75pt]  [font=]  $E_{1}$;

(69,2.4) node [anchor=north west][inner sep=0.75pt]  [font=]  $E_{2}$;

(129,2.4) node [anchor=north west][inner sep=0.75pt]  [font=]  $E_{3}$;

(183,8) node [anchor=north west][inner sep=0.75pt]    $\dotsc $;

(249,2.4) node [anchor=north west][inner sep=0.75pt]  [font=]  $E_{n-1}$;

(329,2.4) node [anchor=north west][inner sep=0.75pt]  [font=]  $E_{n}$;

Considering $p$ the path $[E_2, E_1, E_2, E_3, \ldots, E_n, E_{n-1}, \ldots, E_2]$ and $q$ the path $[E_2, E_3, \ldots, E_n, E_{n-1}, \ldots, E_1, E_2]$. We can check in general that $f(p)\neq f(q)$ by evaluating these path morphisms in particular elements. We will not give a rigorous proof of this fact, but the general strategy can be inferred from Figure <ref>. The purple strand is related to the index $4$. The black, to the index $5$.

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