WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l7 0: l0 -> l1 : Result_6^0'=Result_6^post_1, _^0'=_^post_1, a_128^0'=a_128^post_1, a_243^0'=a_243^post_1, c_15^0'=c_15^post_1, elem_16^0'=elem_16^post_1, head_9^0'=head_9^post_1, i_8^0'=i_8^post_1, k_296^0'=k_296^post_1, len_246^0'=len_246^post_1, len_48^0'=len_48^post_1, length_7^0'=length_7^post_1, lt_18^0'=lt_18^post_1, lt_19^0'=lt_19^post_1, lt_20^0'=lt_20^post_1, lt_21^0'=lt_21^post_1, prev_17^0'=prev_17^post_1, x_13^0'=x_13^post_1, x_23^0'=x_23^post_1, y_110^0'=y_110^post_1, y_14^0'=y_14^post_1, y_158^0'=y_158^post_1, y_259^0'=y_259^post_1, y_309^0'=y_309^post_1, y_80^0'=y_80^post_1, [ 0<=len_48^0 && -i_8^0+length_7^0<=0 && Result_6^post_1==head_9^0 && 0<=len_48^0 && 0<=len_48^0 && x_13^1_1==Result_6^post_1 && c_15^1_1==x_13^1_1 && x_13^2_1==0 && 0<=len_48^0 && y_14^1_1==c_15^1_1 && lt_21^1_1==y_80^0 && c_15^2_1==lt_21^1_1 && lt_21^2_1==lt_21^2_1 && elem_16^1_1==x_13^2_1 && prev_17^1_1==0 && 0<=-1+len_48^0 && elem_16^1_1<=0 && 0<=elem_16^1_1 && prev_17^1_1<=0 && 0<=prev_17^1_1 && x_13^3_1==y_14^1_1 && 0<=-1+len_48^0 && a_128^post_1==-2+len_48^0 && y_14^2_1==c_15^2_1 && lt_21^3_1==y_110^0 && c_15^3_1==lt_21^3_1 && lt_21^4_1==lt_21^4_1 && elem_16^2_1==x_13^3_1 && prev_17^2_1==0 && 0<=a_128^post_1 && lt_19^1_1==lt_19^1_1 && lt_20^1_1==lt_20^1_1 && 0<=lt_19^1_1-lt_20^1_1 && lt_19^post_1==lt_19^post_1 && lt_20^post_1==lt_20^post_1 && prev_17^2_1<=0 && 0<=prev_17^2_1 && x_13^post_1==y_14^2_1 && 0<=a_128^post_1 && len_246^post_1==1 && a_243^post_1==-1+a_128^post_1+_^0 && y_14^post_1==c_15^3_1 && lt_21^5_1==y_158^0 && c_15^post_1==lt_21^5_1 && lt_21^post_1==lt_21^post_1 && elem_16^post_1==x_13^post_1 && prev_17^post_1==0 && _^0==_^post_1 && head_9^0==head_9^post_1 && i_8^0==i_8^post_1 && k_296^0==k_296^post_1 && len_48^0==len_48^post_1 && length_7^0==length_7^post_1 && lt_18^0==lt_18^post_1 && x_23^0==x_23^post_1 && y_110^0==y_110^post_1 && y_158^0==y_158^post_1 && y_259^0==y_259^post_1 && y_309^0==y_309^post_1 && y_80^0==y_80^post_1 ], cost: 1 1: l0 -> l2 : Result_6^0'=Result_6^post_2, _^0'=_^post_2, a_128^0'=a_128^post_2, a_243^0'=a_243^post_2, c_15^0'=c_15^post_2, elem_16^0'=elem_16^post_2, head_9^0'=head_9^post_2, i_8^0'=i_8^post_2, k_296^0'=k_296^post_2, len_246^0'=len_246^post_2, len_48^0'=len_48^post_2, length_7^0'=length_7^post_2, lt_18^0'=lt_18^post_2, lt_19^0'=lt_19^post_2, lt_20^0'=lt_20^post_2, lt_21^0'=lt_21^post_2, prev_17^0'=prev_17^post_2, x_13^0'=x_13^post_2, x_23^0'=x_23^post_2, y_110^0'=y_110^post_2, y_14^0'=y_14^post_2, y_158^0'=y_158^post_2, y_259^0'=y_259^post_2, y_309^0'=y_309^post_2, y_80^0'=y_80^post_2, [ 0<=len_48^0 && len_48^post_2==1+len_48^0 && 0<=-1-i_8^0+length_7^0 && head_9^post_2==head_9^post_2 && i_8^post_2==1+i_8^0 && Result_6^0==Result_6^post_2 && _^0==_^post_2 && a_128^0==a_128^post_2 && a_243^0==a_243^post_2 && c_15^0==c_15^post_2 && elem_16^0==elem_16^post_2 && k_296^0==k_296^post_2 && len_246^0==len_246^post_2 && length_7^0==length_7^post_2 && lt_18^0==lt_18^post_2 && lt_19^0==lt_19^post_2 && lt_20^0==lt_20^post_2 && lt_21^0==lt_21^post_2 && prev_17^0==prev_17^post_2 && x_13^0==x_13^post_2 && x_23^0==x_23^post_2 && y_110^0==y_110^post_2 && y_14^0==y_14^post_2 && y_158^0==y_158^post_2 && y_259^0==y_259^post_2 && y_309^0==y_309^post_2 && y_80^0==y_80^post_2 ], cost: 1 4: l1 -> l4 : Result_6^0'=Result_6^post_5, _^0'=_^post_5, a_128^0'=a_128^post_5, a_243^0'=a_243^post_5, c_15^0'=c_15^post_5, elem_16^0'=elem_16^post_5, head_9^0'=head_9^post_5, i_8^0'=i_8^post_5, k_296^0'=k_296^post_5, len_246^0'=len_246^post_5, len_48^0'=len_48^post_5, length_7^0'=length_7^post_5, lt_18^0'=lt_18^post_5, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_5, prev_17^0'=prev_17^post_5, x_13^0'=x_13^post_5, x_23^0'=x_23^post_5, y_110^0'=y_110^post_5, y_14^0'=y_14^post_5, y_158^0'=y_158^post_5, y_259^0'=y_259^post_5, y_309^0'=y_309^post_5, y_80^0'=y_80^post_5, [ 0<=a_243^0 && 0<=len_246^0 && k_296^post_5==len_246^0 && lt_19^1_2==lt_19^1_2 && lt_20^1_2_1==lt_20^1_2_1 && 0<=-lt_20^1_2_1+lt_19^1_2 && lt_19^post_5==lt_19^post_5 && lt_20^post_5==lt_20^post_5 && prev_17^0<=0 && 0<=prev_17^0 && x_13^post_5==y_14^0 && Result_6^0==Result_6^post_5 && _^0==_^post_5 && a_128^0==a_128^post_5 && a_243^0==a_243^post_5 && c_15^0==c_15^post_5 && elem_16^0==elem_16^post_5 && head_9^0==head_9^post_5 && i_8^0==i_8^post_5 && len_246^0==len_246^post_5 && len_48^0==len_48^post_5 && length_7^0==length_7^post_5 && lt_18^0==lt_18^post_5 && lt_21^0==lt_21^post_5 && prev_17^0==prev_17^post_5 && x_23^0==x_23^post_5 && y_110^0==y_110^post_5 && y_14^0==y_14^post_5 && y_158^0==y_158^post_5 && y_259^0==y_259^post_5 && y_309^0==y_309^post_5 && y_80^0==y_80^post_5 ], cost: 1 5: l1 -> l5 : Result_6^0'=Result_6^post_6, _^0'=_^post_6, a_128^0'=a_128^post_6, a_243^0'=a_243^post_6, c_15^0'=c_15^post_6, elem_16^0'=elem_16^post_6, head_9^0'=head_9^post_6, i_8^0'=i_8^post_6, k_296^0'=k_296^post_6, len_246^0'=len_246^post_6, len_48^0'=len_48^post_6, length_7^0'=length_7^post_6, lt_18^0'=lt_18^post_6, lt_19^0'=lt_19^post_6, lt_20^0'=lt_20^post_6, lt_21^0'=lt_21^post_6, prev_17^0'=prev_17^post_6, x_13^0'=x_13^post_6, x_23^0'=x_23^post_6, y_110^0'=y_110^post_6, y_14^0'=y_14^post_6, y_158^0'=y_158^post_6, y_259^0'=y_259^post_6, y_309^0'=y_309^post_6, y_80^0'=y_80^post_6, [ 0<=a_243^0 && 0<=len_246^0 && lt_19^1_3_1==lt_19^1_3_1 && lt_20^1_3_1==lt_20^1_3_1 && 1-lt_20^1_3_1+lt_19^1_3_1<=0 && lt_19^post_6==lt_19^post_6 && lt_20^post_6==lt_20^post_6 && prev_17^post_6==elem_16^0 && lt_18^1_1==y_259^0 && elem_16^post_6==lt_18^1_1 && lt_18^post_6==lt_18^post_6 && 0<=a_243^0 && 0<=-1+len_246^0 && Result_6^0==Result_6^post_6 && _^0==_^post_6 && a_128^0==a_128^post_6 && a_243^0==a_243^post_6 && c_15^0==c_15^post_6 && head_9^0==head_9^post_6 && i_8^0==i_8^post_6 && k_296^0==k_296^post_6 && len_246^0==len_246^post_6 && len_48^0==len_48^post_6 && length_7^0==length_7^post_6 && lt_21^0==lt_21^post_6 && x_13^0==x_13^post_6 && x_23^0==x_23^post_6 && y_110^0==y_110^post_6 && y_14^0==y_14^post_6 && y_158^0==y_158^post_6 && y_259^0==y_259^post_6 && y_309^0==y_309^post_6 && y_80^0==y_80^post_6 ], cost: 1 2: l2 -> l0 : Result_6^0'=Result_6^post_3, _^0'=_^post_3, a_128^0'=a_128^post_3, a_243^0'=a_243^post_3, c_15^0'=c_15^post_3, elem_16^0'=elem_16^post_3, head_9^0'=head_9^post_3, i_8^0'=i_8^post_3, k_296^0'=k_296^post_3, len_246^0'=len_246^post_3, len_48^0'=len_48^post_3, length_7^0'=length_7^post_3, lt_18^0'=lt_18^post_3, lt_19^0'=lt_19^post_3, lt_20^0'=lt_20^post_3, lt_21^0'=lt_21^post_3, prev_17^0'=prev_17^post_3, x_13^0'=x_13^post_3, x_23^0'=x_23^post_3, y_110^0'=y_110^post_3, y_14^0'=y_14^post_3, y_158^0'=y_158^post_3, y_259^0'=y_259^post_3, y_309^0'=y_309^post_3, y_80^0'=y_80^post_3, [ Result_6^0==Result_6^post_3 && _^0==_^post_3 && a_128^0==a_128^post_3 && a_243^0==a_243^post_3 && c_15^0==c_15^post_3 && elem_16^0==elem_16^post_3 && head_9^0==head_9^post_3 && i_8^0==i_8^post_3 && k_296^0==k_296^post_3 && len_246^0==len_246^post_3 && len_48^0==len_48^post_3 && length_7^0==length_7^post_3 && lt_18^0==lt_18^post_3 && lt_19^0==lt_19^post_3 && lt_20^0==lt_20^post_3 && lt_21^0==lt_21^post_3 && prev_17^0==prev_17^post_3 && x_13^0==x_13^post_3 && x_23^0==x_23^post_3 && y_110^0==y_110^post_3 && y_14^0==y_14^post_3 && y_158^0==y_158^post_3 && y_259^0==y_259^post_3 && y_309^0==y_309^post_3 && y_80^0==y_80^post_3 ], cost: 1 3: l3 -> l0 : Result_6^0'=Result_6^post_4, _^0'=_^post_4, a_128^0'=a_128^post_4, a_243^0'=a_243^post_4, c_15^0'=c_15^post_4, elem_16^0'=elem_16^post_4, head_9^0'=head_9^post_4, i_8^0'=i_8^post_4, k_296^0'=k_296^post_4, len_246^0'=len_246^post_4, len_48^0'=len_48^post_4, length_7^0'=length_7^post_4, lt_18^0'=lt_18^post_4, lt_19^0'=lt_19^post_4, lt_20^0'=lt_20^post_4, lt_21^0'=lt_21^post_4, prev_17^0'=prev_17^post_4, x_13^0'=x_13^post_4, x_23^0'=x_23^post_4, y_110^0'=y_110^post_4, y_14^0'=y_14^post_4, y_158^0'=y_158^post_4, y_259^0'=y_259^post_4, y_309^0'=y_309^post_4, y_80^0'=y_80^post_4, [ x_13^1_2_1==0 && length_7^post_4==17 && x_13^post_4==x_23^0 && head_9^1_1==0 && i_8^1_1==0 && len_48^post_4==i_8^1_1 && 0<=-1+length_7^post_4-i_8^1_1 && head_9^post_4==head_9^post_4 && i_8^post_4==1+i_8^1_1 && Result_6^0==Result_6^post_4 && _^0==_^post_4 && a_128^0==a_128^post_4 && a_243^0==a_243^post_4 && c_15^0==c_15^post_4 && elem_16^0==elem_16^post_4 && k_296^0==k_296^post_4 && len_246^0==len_246^post_4 && lt_18^0==lt_18^post_4 && lt_19^0==lt_19^post_4 && lt_20^0==lt_20^post_4 && lt_21^0==lt_21^post_4 && prev_17^0==prev_17^post_4 && x_23^0==x_23^post_4 && y_110^0==y_110^post_4 && y_14^0==y_14^post_4 && y_158^0==y_158^post_4 && y_259^0==y_259^post_4 && y_309^0==y_309^post_4 && y_80^0==y_80^post_4 ], cost: 1 6: l4 -> l6 : Result_6^0'=Result_6^post_7, _^0'=_^post_7, a_128^0'=a_128^post_7, a_243^0'=a_243^post_7, c_15^0'=c_15^post_7, elem_16^0'=elem_16^post_7, head_9^0'=head_9^post_7, i_8^0'=i_8^post_7, k_296^0'=k_296^post_7, len_246^0'=len_246^post_7, len_48^0'=len_48^post_7, length_7^0'=length_7^post_7, lt_18^0'=lt_18^post_7, lt_19^0'=lt_19^post_7, lt_20^0'=lt_20^post_7, lt_21^0'=lt_21^post_7, prev_17^0'=prev_17^post_7, x_13^0'=x_13^post_7, x_23^0'=x_23^post_7, y_110^0'=y_110^post_7, y_14^0'=y_14^post_7, y_158^0'=y_158^post_7, y_259^0'=y_259^post_7, y_309^0'=y_309^post_7, y_80^0'=y_80^post_7, [ 0<=a_243^0 && 0<=k_296^0 && c_15^0<=0 && 0<=c_15^0 && Result_6^post_7==Result_6^post_7 && _^0==_^post_7 && a_128^0==a_128^post_7 && a_243^0==a_243^post_7 && c_15^0==c_15^post_7 && elem_16^0==elem_16^post_7 && head_9^0==head_9^post_7 && i_8^0==i_8^post_7 && k_296^0==k_296^post_7 && len_246^0==len_246^post_7 && len_48^0==len_48^post_7 && length_7^0==length_7^post_7 && lt_18^0==lt_18^post_7 && lt_19^0==lt_19^post_7 && lt_20^0==lt_20^post_7 && lt_21^0==lt_21^post_7 && prev_17^0==prev_17^post_7 && x_13^0==x_13^post_7 && x_23^0==x_23^post_7 && y_110^0==y_110^post_7 && y_14^0==y_14^post_7 && y_158^0==y_158^post_7 && y_259^0==y_259^post_7 && y_309^0==y_309^post_7 && y_80^0==y_80^post_7 ], cost: 1 7: l4 -> l1 : Result_6^0'=Result_6^post_8, _^0'=_^post_8, a_128^0'=a_128^post_8, a_243^0'=a_243^post_8, c_15^0'=c_15^post_8, elem_16^0'=elem_16^post_8, head_9^0'=head_9^post_8, i_8^0'=i_8^post_8, k_296^0'=k_296^post_8, len_246^0'=len_246^post_8, len_48^0'=len_48^post_8, length_7^0'=length_7^post_8, lt_18^0'=lt_18^post_8, lt_19^0'=lt_19^post_8, lt_20^0'=lt_20^post_8, lt_21^0'=lt_21^post_8, prev_17^0'=prev_17^post_8, x_13^0'=x_13^post_8, x_23^0'=x_23^post_8, y_110^0'=y_110^post_8, y_14^0'=y_14^post_8, y_158^0'=y_158^post_8, y_259^0'=y_259^post_8, y_309^0'=y_309^post_8, y_80^0'=y_80^post_8, [ 0<=a_243^0 && 0<=k_296^0 && len_246^post_8==1+k_296^0 && a_243^post_8==-1+a_243^0 && y_14^post_8==c_15^0 && lt_21^1_2==y_309^0 && c_15^post_8==lt_21^1_2 && lt_21^post_8==lt_21^post_8 && elem_16^post_8==x_13^0 && prev_17^post_8==0 && Result_6^0==Result_6^post_8 && _^0==_^post_8 && a_128^0==a_128^post_8 && head_9^0==head_9^post_8 && i_8^0==i_8^post_8 && k_296^0==k_296^post_8 && len_48^0==len_48^post_8 && length_7^0==length_7^post_8 && lt_18^0==lt_18^post_8 && lt_19^0==lt_19^post_8 && lt_20^0==lt_20^post_8 && x_13^0==x_13^post_8 && x_23^0==x_23^post_8 && y_110^0==y_110^post_8 && y_158^0==y_158^post_8 && y_259^0==y_259^post_8 && y_309^0==y_309^post_8 && y_80^0==y_80^post_8 ], cost: 1 8: l7 -> l3 : Result_6^0'=Result_6^post_9, _^0'=_^post_9, a_128^0'=a_128^post_9, a_243^0'=a_243^post_9, c_15^0'=c_15^post_9, elem_16^0'=elem_16^post_9, head_9^0'=head_9^post_9, i_8^0'=i_8^post_9, k_296^0'=k_296^post_9, len_246^0'=len_246^post_9, len_48^0'=len_48^post_9, length_7^0'=length_7^post_9, lt_18^0'=lt_18^post_9, lt_19^0'=lt_19^post_9, lt_20^0'=lt_20^post_9, lt_21^0'=lt_21^post_9, prev_17^0'=prev_17^post_9, x_13^0'=x_13^post_9, x_23^0'=x_23^post_9, y_110^0'=y_110^post_9, y_14^0'=y_14^post_9, y_158^0'=y_158^post_9, y_259^0'=y_259^post_9, y_309^0'=y_309^post_9, y_80^0'=y_80^post_9, [ Result_6^0==Result_6^post_9 && _^0==_^post_9 && a_128^0==a_128^post_9 && a_243^0==a_243^post_9 && c_15^0==c_15^post_9 && elem_16^0==elem_16^post_9 && head_9^0==head_9^post_9 && i_8^0==i_8^post_9 && k_296^0==k_296^post_9 && len_246^0==len_246^post_9 && len_48^0==len_48^post_9 && length_7^0==length_7^post_9 && lt_18^0==lt_18^post_9 && lt_19^0==lt_19^post_9 && lt_20^0==lt_20^post_9 && lt_21^0==lt_21^post_9 && prev_17^0==prev_17^post_9 && x_13^0==x_13^post_9 && x_23^0==x_23^post_9 && y_110^0==y_110^post_9 && y_14^0==y_14^post_9 && y_158^0==y_158^post_9 && y_259^0==y_259^post_9 && y_309^0==y_309^post_9 && y_80^0==y_80^post_9 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 8: l7 -> l3 : Result_6^0'=Result_6^post_9, _^0'=_^post_9, a_128^0'=a_128^post_9, a_243^0'=a_243^post_9, c_15^0'=c_15^post_9, elem_16^0'=elem_16^post_9, head_9^0'=head_9^post_9, i_8^0'=i_8^post_9, k_296^0'=k_296^post_9, len_246^0'=len_246^post_9, len_48^0'=len_48^post_9, length_7^0'=length_7^post_9, lt_18^0'=lt_18^post_9, lt_19^0'=lt_19^post_9, lt_20^0'=lt_20^post_9, lt_21^0'=lt_21^post_9, prev_17^0'=prev_17^post_9, x_13^0'=x_13^post_9, x_23^0'=x_23^post_9, y_110^0'=y_110^post_9, y_14^0'=y_14^post_9, y_158^0'=y_158^post_9, y_259^0'=y_259^post_9, y_309^0'=y_309^post_9, y_80^0'=y_80^post_9, [ Result_6^0==Result_6^post_9 && _^0==_^post_9 && a_128^0==a_128^post_9 && a_243^0==a_243^post_9 && c_15^0==c_15^post_9 && elem_16^0==elem_16^post_9 && head_9^0==head_9^post_9 && i_8^0==i_8^post_9 && k_296^0==k_296^post_9 && len_246^0==len_246^post_9 && len_48^0==len_48^post_9 && length_7^0==length_7^post_9 && lt_18^0==lt_18^post_9 && lt_19^0==lt_19^post_9 && lt_20^0==lt_20^post_9 && lt_21^0==lt_21^post_9 && prev_17^0==prev_17^post_9 && x_13^0==x_13^post_9 && x_23^0==x_23^post_9 && y_110^0==y_110^post_9 && y_14^0==y_14^post_9 && y_158^0==y_158^post_9 && y_259^0==y_259^post_9 && y_309^0==y_309^post_9 && y_80^0==y_80^post_9 ], cost: 1 Removed unreachable and leaf rules: Start location: l7 0: l0 -> l1 : Result_6^0'=Result_6^post_1, _^0'=_^post_1, a_128^0'=a_128^post_1, a_243^0'=a_243^post_1, c_15^0'=c_15^post_1, elem_16^0'=elem_16^post_1, head_9^0'=head_9^post_1, i_8^0'=i_8^post_1, k_296^0'=k_296^post_1, len_246^0'=len_246^post_1, len_48^0'=len_48^post_1, length_7^0'=length_7^post_1, lt_18^0'=lt_18^post_1, lt_19^0'=lt_19^post_1, lt_20^0'=lt_20^post_1, lt_21^0'=lt_21^post_1, prev_17^0'=prev_17^post_1, x_13^0'=x_13^post_1, x_23^0'=x_23^post_1, y_110^0'=y_110^post_1, y_14^0'=y_14^post_1, y_158^0'=y_158^post_1, y_259^0'=y_259^post_1, y_309^0'=y_309^post_1, y_80^0'=y_80^post_1, [ 0<=len_48^0 && -i_8^0+length_7^0<=0 && Result_6^post_1==head_9^0 && 0<=len_48^0 && 0<=len_48^0 && x_13^1_1==Result_6^post_1 && c_15^1_1==x_13^1_1 && x_13^2_1==0 && 0<=len_48^0 && y_14^1_1==c_15^1_1 && lt_21^1_1==y_80^0 && c_15^2_1==lt_21^1_1 && lt_21^2_1==lt_21^2_1 && elem_16^1_1==x_13^2_1 && prev_17^1_1==0 && 0<=-1+len_48^0 && elem_16^1_1<=0 && 0<=elem_16^1_1 && prev_17^1_1<=0 && 0<=prev_17^1_1 && x_13^3_1==y_14^1_1 && 0<=-1+len_48^0 && a_128^post_1==-2+len_48^0 && y_14^2_1==c_15^2_1 && lt_21^3_1==y_110^0 && c_15^3_1==lt_21^3_1 && lt_21^4_1==lt_21^4_1 && elem_16^2_1==x_13^3_1 && prev_17^2_1==0 && 0<=a_128^post_1 && lt_19^1_1==lt_19^1_1 && lt_20^1_1==lt_20^1_1 && 0<=lt_19^1_1-lt_20^1_1 && lt_19^post_1==lt_19^post_1 && lt_20^post_1==lt_20^post_1 && prev_17^2_1<=0 && 0<=prev_17^2_1 && x_13^post_1==y_14^2_1 && 0<=a_128^post_1 && len_246^post_1==1 && a_243^post_1==-1+a_128^post_1+_^0 && y_14^post_1==c_15^3_1 && lt_21^5_1==y_158^0 && c_15^post_1==lt_21^5_1 && lt_21^post_1==lt_21^post_1 && elem_16^post_1==x_13^post_1 && prev_17^post_1==0 && _^0==_^post_1 && head_9^0==head_9^post_1 && i_8^0==i_8^post_1 && k_296^0==k_296^post_1 && len_48^0==len_48^post_1 && length_7^0==length_7^post_1 && lt_18^0==lt_18^post_1 && x_23^0==x_23^post_1 && y_110^0==y_110^post_1 && y_158^0==y_158^post_1 && y_259^0==y_259^post_1 && y_309^0==y_309^post_1 && y_80^0==y_80^post_1 ], cost: 1 1: l0 -> l2 : Result_6^0'=Result_6^post_2, _^0'=_^post_2, a_128^0'=a_128^post_2, a_243^0'=a_243^post_2, c_15^0'=c_15^post_2, elem_16^0'=elem_16^post_2, head_9^0'=head_9^post_2, i_8^0'=i_8^post_2, k_296^0'=k_296^post_2, len_246^0'=len_246^post_2, len_48^0'=len_48^post_2, length_7^0'=length_7^post_2, lt_18^0'=lt_18^post_2, lt_19^0'=lt_19^post_2, lt_20^0'=lt_20^post_2, lt_21^0'=lt_21^post_2, prev_17^0'=prev_17^post_2, x_13^0'=x_13^post_2, x_23^0'=x_23^post_2, y_110^0'=y_110^post_2, y_14^0'=y_14^post_2, y_158^0'=y_158^post_2, y_259^0'=y_259^post_2, y_309^0'=y_309^post_2, y_80^0'=y_80^post_2, [ 0<=len_48^0 && len_48^post_2==1+len_48^0 && 0<=-1-i_8^0+length_7^0 && head_9^post_2==head_9^post_2 && i_8^post_2==1+i_8^0 && Result_6^0==Result_6^post_2 && _^0==_^post_2 && a_128^0==a_128^post_2 && a_243^0==a_243^post_2 && c_15^0==c_15^post_2 && elem_16^0==elem_16^post_2 && k_296^0==k_296^post_2 && len_246^0==len_246^post_2 && length_7^0==length_7^post_2 && lt_18^0==lt_18^post_2 && lt_19^0==lt_19^post_2 && lt_20^0==lt_20^post_2 && lt_21^0==lt_21^post_2 && prev_17^0==prev_17^post_2 && x_13^0==x_13^post_2 && x_23^0==x_23^post_2 && y_110^0==y_110^post_2 && y_14^0==y_14^post_2 && y_158^0==y_158^post_2 && y_259^0==y_259^post_2 && y_309^0==y_309^post_2 && y_80^0==y_80^post_2 ], cost: 1 4: l1 -> l4 : Result_6^0'=Result_6^post_5, _^0'=_^post_5, a_128^0'=a_128^post_5, a_243^0'=a_243^post_5, c_15^0'=c_15^post_5, elem_16^0'=elem_16^post_5, head_9^0'=head_9^post_5, i_8^0'=i_8^post_5, k_296^0'=k_296^post_5, len_246^0'=len_246^post_5, len_48^0'=len_48^post_5, length_7^0'=length_7^post_5, lt_18^0'=lt_18^post_5, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_5, prev_17^0'=prev_17^post_5, x_13^0'=x_13^post_5, x_23^0'=x_23^post_5, y_110^0'=y_110^post_5, y_14^0'=y_14^post_5, y_158^0'=y_158^post_5, y_259^0'=y_259^post_5, y_309^0'=y_309^post_5, y_80^0'=y_80^post_5, [ 0<=a_243^0 && 0<=len_246^0 && k_296^post_5==len_246^0 && lt_19^1_2==lt_19^1_2 && lt_20^1_2_1==lt_20^1_2_1 && 0<=-lt_20^1_2_1+lt_19^1_2 && lt_19^post_5==lt_19^post_5 && lt_20^post_5==lt_20^post_5 && prev_17^0<=0 && 0<=prev_17^0 && x_13^post_5==y_14^0 && Result_6^0==Result_6^post_5 && _^0==_^post_5 && a_128^0==a_128^post_5 && a_243^0==a_243^post_5 && c_15^0==c_15^post_5 && elem_16^0==elem_16^post_5 && head_9^0==head_9^post_5 && i_8^0==i_8^post_5 && len_246^0==len_246^post_5 && len_48^0==len_48^post_5 && length_7^0==length_7^post_5 && lt_18^0==lt_18^post_5 && lt_21^0==lt_21^post_5 && prev_17^0==prev_17^post_5 && x_23^0==x_23^post_5 && y_110^0==y_110^post_5 && y_14^0==y_14^post_5 && y_158^0==y_158^post_5 && y_259^0==y_259^post_5 && y_309^0==y_309^post_5 && y_80^0==y_80^post_5 ], cost: 1 2: l2 -> l0 : Result_6^0'=Result_6^post_3, _^0'=_^post_3, a_128^0'=a_128^post_3, a_243^0'=a_243^post_3, c_15^0'=c_15^post_3, elem_16^0'=elem_16^post_3, head_9^0'=head_9^post_3, i_8^0'=i_8^post_3, k_296^0'=k_296^post_3, len_246^0'=len_246^post_3, len_48^0'=len_48^post_3, length_7^0'=length_7^post_3, lt_18^0'=lt_18^post_3, lt_19^0'=lt_19^post_3, lt_20^0'=lt_20^post_3, lt_21^0'=lt_21^post_3, prev_17^0'=prev_17^post_3, x_13^0'=x_13^post_3, x_23^0'=x_23^post_3, y_110^0'=y_110^post_3, y_14^0'=y_14^post_3, y_158^0'=y_158^post_3, y_259^0'=y_259^post_3, y_309^0'=y_309^post_3, y_80^0'=y_80^post_3, [ Result_6^0==Result_6^post_3 && _^0==_^post_3 && a_128^0==a_128^post_3 && a_243^0==a_243^post_3 && c_15^0==c_15^post_3 && elem_16^0==elem_16^post_3 && head_9^0==head_9^post_3 && i_8^0==i_8^post_3 && k_296^0==k_296^post_3 && len_246^0==len_246^post_3 && len_48^0==len_48^post_3 && length_7^0==length_7^post_3 && lt_18^0==lt_18^post_3 && lt_19^0==lt_19^post_3 && lt_20^0==lt_20^post_3 && lt_21^0==lt_21^post_3 && prev_17^0==prev_17^post_3 && x_13^0==x_13^post_3 && x_23^0==x_23^post_3 && y_110^0==y_110^post_3 && y_14^0==y_14^post_3 && y_158^0==y_158^post_3 && y_259^0==y_259^post_3 && y_309^0==y_309^post_3 && y_80^0==y_80^post_3 ], cost: 1 3: l3 -> l0 : Result_6^0'=Result_6^post_4, _^0'=_^post_4, a_128^0'=a_128^post_4, a_243^0'=a_243^post_4, c_15^0'=c_15^post_4, elem_16^0'=elem_16^post_4, head_9^0'=head_9^post_4, i_8^0'=i_8^post_4, k_296^0'=k_296^post_4, len_246^0'=len_246^post_4, len_48^0'=len_48^post_4, length_7^0'=length_7^post_4, lt_18^0'=lt_18^post_4, lt_19^0'=lt_19^post_4, lt_20^0'=lt_20^post_4, lt_21^0'=lt_21^post_4, prev_17^0'=prev_17^post_4, x_13^0'=x_13^post_4, x_23^0'=x_23^post_4, y_110^0'=y_110^post_4, y_14^0'=y_14^post_4, y_158^0'=y_158^post_4, y_259^0'=y_259^post_4, y_309^0'=y_309^post_4, y_80^0'=y_80^post_4, [ x_13^1_2_1==0 && length_7^post_4==17 && x_13^post_4==x_23^0 && head_9^1_1==0 && i_8^1_1==0 && len_48^post_4==i_8^1_1 && 0<=-1+length_7^post_4-i_8^1_1 && head_9^post_4==head_9^post_4 && i_8^post_4==1+i_8^1_1 && Result_6^0==Result_6^post_4 && _^0==_^post_4 && a_128^0==a_128^post_4 && a_243^0==a_243^post_4 && c_15^0==c_15^post_4 && elem_16^0==elem_16^post_4 && k_296^0==k_296^post_4 && len_246^0==len_246^post_4 && lt_18^0==lt_18^post_4 && lt_19^0==lt_19^post_4 && lt_20^0==lt_20^post_4 && lt_21^0==lt_21^post_4 && prev_17^0==prev_17^post_4 && x_23^0==x_23^post_4 && y_110^0==y_110^post_4 && y_14^0==y_14^post_4 && y_158^0==y_158^post_4 && y_259^0==y_259^post_4 && y_309^0==y_309^post_4 && y_80^0==y_80^post_4 ], cost: 1 7: l4 -> l1 : Result_6^0'=Result_6^post_8, _^0'=_^post_8, a_128^0'=a_128^post_8, a_243^0'=a_243^post_8, c_15^0'=c_15^post_8, elem_16^0'=elem_16^post_8, head_9^0'=head_9^post_8, i_8^0'=i_8^post_8, k_296^0'=k_296^post_8, len_246^0'=len_246^post_8, len_48^0'=len_48^post_8, length_7^0'=length_7^post_8, lt_18^0'=lt_18^post_8, lt_19^0'=lt_19^post_8, lt_20^0'=lt_20^post_8, lt_21^0'=lt_21^post_8, prev_17^0'=prev_17^post_8, x_13^0'=x_13^post_8, x_23^0'=x_23^post_8, y_110^0'=y_110^post_8, y_14^0'=y_14^post_8, y_158^0'=y_158^post_8, y_259^0'=y_259^post_8, y_309^0'=y_309^post_8, y_80^0'=y_80^post_8, [ 0<=a_243^0 && 0<=k_296^0 && len_246^post_8==1+k_296^0 && a_243^post_8==-1+a_243^0 && y_14^post_8==c_15^0 && lt_21^1_2==y_309^0 && c_15^post_8==lt_21^1_2 && lt_21^post_8==lt_21^post_8 && elem_16^post_8==x_13^0 && prev_17^post_8==0 && Result_6^0==Result_6^post_8 && _^0==_^post_8 && a_128^0==a_128^post_8 && head_9^0==head_9^post_8 && i_8^0==i_8^post_8 && k_296^0==k_296^post_8 && len_48^0==len_48^post_8 && length_7^0==length_7^post_8 && lt_18^0==lt_18^post_8 && lt_19^0==lt_19^post_8 && lt_20^0==lt_20^post_8 && x_13^0==x_13^post_8 && x_23^0==x_23^post_8 && y_110^0==y_110^post_8 && y_158^0==y_158^post_8 && y_259^0==y_259^post_8 && y_309^0==y_309^post_8 && y_80^0==y_80^post_8 ], cost: 1 8: l7 -> l3 : Result_6^0'=Result_6^post_9, _^0'=_^post_9, a_128^0'=a_128^post_9, a_243^0'=a_243^post_9, c_15^0'=c_15^post_9, elem_16^0'=elem_16^post_9, head_9^0'=head_9^post_9, i_8^0'=i_8^post_9, k_296^0'=k_296^post_9, len_246^0'=len_246^post_9, len_48^0'=len_48^post_9, length_7^0'=length_7^post_9, lt_18^0'=lt_18^post_9, lt_19^0'=lt_19^post_9, lt_20^0'=lt_20^post_9, lt_21^0'=lt_21^post_9, prev_17^0'=prev_17^post_9, x_13^0'=x_13^post_9, x_23^0'=x_23^post_9, y_110^0'=y_110^post_9, y_14^0'=y_14^post_9, y_158^0'=y_158^post_9, y_259^0'=y_259^post_9, y_309^0'=y_309^post_9, y_80^0'=y_80^post_9, [ Result_6^0==Result_6^post_9 && _^0==_^post_9 && a_128^0==a_128^post_9 && a_243^0==a_243^post_9 && c_15^0==c_15^post_9 && elem_16^0==elem_16^post_9 && head_9^0==head_9^post_9 && i_8^0==i_8^post_9 && k_296^0==k_296^post_9 && len_246^0==len_246^post_9 && len_48^0==len_48^post_9 && length_7^0==length_7^post_9 && lt_18^0==lt_18^post_9 && lt_19^0==lt_19^post_9 && lt_20^0==lt_20^post_9 && lt_21^0==lt_21^post_9 && prev_17^0==prev_17^post_9 && x_13^0==x_13^post_9 && x_23^0==x_23^post_9 && y_110^0==y_110^post_9 && y_14^0==y_14^post_9 && y_158^0==y_158^post_9 && y_259^0==y_259^post_9 && y_309^0==y_309^post_9 && y_80^0==y_80^post_9 ], cost: 1 Simplified all rules, resulting in: Start location: l7 0: l0 -> l1 : Result_6^0'=head_9^0, a_128^0'=-2+len_48^0, a_243^0'=-3+_^0+len_48^0, c_15^0'=y_158^0, elem_16^0'=y_80^0, len_246^0'=1, lt_19^0'=lt_19^post_1, lt_20^0'=lt_20^post_1, lt_21^0'=lt_21^post_1, prev_17^0'=0, x_13^0'=y_80^0, y_14^0'=y_110^0, [ -i_8^0+length_7^0<=0 && 0<=-2+len_48^0 ], cost: 1 1: l0 -> l2 : head_9^0'=head_9^post_2, i_8^0'=1+i_8^0, len_48^0'=1+len_48^0, [ 0<=len_48^0 && 0<=-1-i_8^0+length_7^0 ], cost: 1 4: l1 -> l4 : k_296^0'=len_246^0, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, x_13^0'=y_14^0, [ 0<=a_243^0 && 0<=len_246^0 && prev_17^0==0 ], cost: 1 2: l2 -> l0 : [], cost: 1 3: l3 -> l0 : head_9^0'=head_9^post_4, i_8^0'=1, len_48^0'=0, length_7^0'=17, x_13^0'=x_23^0, [], cost: 1 7: l4 -> l1 : a_243^0'=-1+a_243^0, c_15^0'=y_309^0, elem_16^0'=x_13^0, len_246^0'=1+k_296^0, lt_21^0'=lt_21^post_8, prev_17^0'=0, y_14^0'=c_15^0, [ 0<=a_243^0 && 0<=k_296^0 ], cost: 1 8: l7 -> l3 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l7 0: l0 -> l1 : Result_6^0'=head_9^0, a_128^0'=-2+len_48^0, a_243^0'=-3+_^0+len_48^0, c_15^0'=y_158^0, elem_16^0'=y_80^0, len_246^0'=1, lt_19^0'=lt_19^post_1, lt_20^0'=lt_20^post_1, lt_21^0'=lt_21^post_1, prev_17^0'=0, x_13^0'=y_80^0, y_14^0'=y_110^0, [ -i_8^0+length_7^0<=0 && 0<=-2+len_48^0 ], cost: 1 10: l0 -> l0 : head_9^0'=head_9^post_2, i_8^0'=1+i_8^0, len_48^0'=1+len_48^0, [ 0<=len_48^0 && 0<=-1-i_8^0+length_7^0 ], cost: 2 11: l1 -> l1 : a_243^0'=-1+a_243^0, c_15^0'=y_309^0, elem_16^0'=y_14^0, k_296^0'=len_246^0, len_246^0'=1+len_246^0, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_14^0, y_14^0'=c_15^0, [ 0<=a_243^0 && 0<=len_246^0 && prev_17^0==0 ], cost: 2 9: l7 -> l0 : head_9^0'=head_9^post_4, i_8^0'=1, len_48^0'=0, length_7^0'=17, x_13^0'=x_23^0, [], cost: 2 Accelerating simple loops of location 0. Accelerating the following rules: 10: l0 -> l0 : head_9^0'=head_9^post_2, i_8^0'=1+i_8^0, len_48^0'=1+len_48^0, [ 0<=len_48^0 && 0<=-1-i_8^0+length_7^0 ], cost: 2 Accelerated rule 10 with backward acceleration, yielding the new rule 12. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 10. Accelerating simple loops of location 1. Accelerating the following rules: 11: l1 -> l1 : a_243^0'=-1+a_243^0, c_15^0'=y_309^0, elem_16^0'=y_14^0, k_296^0'=len_246^0, len_246^0'=1+len_246^0, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_14^0, y_14^0'=c_15^0, [ 0<=a_243^0 && 0<=len_246^0 && prev_17^0==0 ], cost: 2 Accelerated rule 11 with backward acceleration, yielding the new rule 13. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 11. Accelerated all simple loops using metering functions (where possible): Start location: l7 0: l0 -> l1 : Result_6^0'=head_9^0, a_128^0'=-2+len_48^0, a_243^0'=-3+_^0+len_48^0, c_15^0'=y_158^0, elem_16^0'=y_80^0, len_246^0'=1, lt_19^0'=lt_19^post_1, lt_20^0'=lt_20^post_1, lt_21^0'=lt_21^post_1, prev_17^0'=0, x_13^0'=y_80^0, y_14^0'=y_110^0, [ -i_8^0+length_7^0<=0 && 0<=-2+len_48^0 ], cost: 1 12: l0 -> l0 : head_9^0'=head_9^post_2, i_8^0'=length_7^0, len_48^0'=-i_8^0+length_7^0+len_48^0, [ 0<=len_48^0 && -i_8^0+length_7^0>=1 ], cost: -2*i_8^0+2*length_7^0 13: l1 -> l1 : a_243^0'=-1, c_15^0'=y_309^0, elem_16^0'=y_309^0, k_296^0'=len_246^0+a_243^0, len_246^0'=1+len_246^0+a_243^0, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_309^0, y_14^0'=y_309^0, [ 0<=len_246^0 && prev_17^0==0 && 1+a_243^0>=1 ], cost: 2+2*a_243^0 9: l7 -> l0 : head_9^0'=head_9^post_4, i_8^0'=1, len_48^0'=0, length_7^0'=17, x_13^0'=x_23^0, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l7 0: l0 -> l1 : Result_6^0'=head_9^0, a_128^0'=-2+len_48^0, a_243^0'=-3+_^0+len_48^0, c_15^0'=y_158^0, elem_16^0'=y_80^0, len_246^0'=1, lt_19^0'=lt_19^post_1, lt_20^0'=lt_20^post_1, lt_21^0'=lt_21^post_1, prev_17^0'=0, x_13^0'=y_80^0, y_14^0'=y_110^0, [ -i_8^0+length_7^0<=0 && 0<=-2+len_48^0 ], cost: 1 15: l0 -> l1 : Result_6^0'=head_9^0, a_128^0'=-2+len_48^0, a_243^0'=-1, c_15^0'=y_309^0, elem_16^0'=y_309^0, k_296^0'=-2+_^0+len_48^0, len_246^0'=-1+_^0+len_48^0, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_309^0, y_14^0'=y_309^0, [ -i_8^0+length_7^0<=0 && 0<=-2+len_48^0 && -2+_^0+len_48^0>=1 ], cost: -3+2*_^0+2*len_48^0 9: l7 -> l0 : head_9^0'=head_9^post_4, i_8^0'=1, len_48^0'=0, length_7^0'=17, x_13^0'=x_23^0, [], cost: 2 14: l7 -> l0 : head_9^0'=head_9^post_2, i_8^0'=17, len_48^0'=16, length_7^0'=17, x_13^0'=x_23^0, [], cost: 34 Removed unreachable locations (and leaf rules with constant cost): Start location: l7 15: l0 -> l1 : Result_6^0'=head_9^0, a_128^0'=-2+len_48^0, a_243^0'=-1, c_15^0'=y_309^0, elem_16^0'=y_309^0, k_296^0'=-2+_^0+len_48^0, len_246^0'=-1+_^0+len_48^0, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_309^0, y_14^0'=y_309^0, [ -i_8^0+length_7^0<=0 && 0<=-2+len_48^0 && -2+_^0+len_48^0>=1 ], cost: -3+2*_^0+2*len_48^0 9: l7 -> l0 : head_9^0'=head_9^post_4, i_8^0'=1, len_48^0'=0, length_7^0'=17, x_13^0'=x_23^0, [], cost: 2 14: l7 -> l0 : head_9^0'=head_9^post_2, i_8^0'=17, len_48^0'=16, length_7^0'=17, x_13^0'=x_23^0, [], cost: 34 Eliminated locations (on tree-shaped paths): Start location: l7 16: l7 -> l1 : Result_6^0'=head_9^post_2, a_128^0'=14, a_243^0'=-1, c_15^0'=y_309^0, elem_16^0'=y_309^0, head_9^0'=head_9^post_2, i_8^0'=17, k_296^0'=14+_^0, len_246^0'=15+_^0, len_48^0'=16, length_7^0'=17, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_309^0, y_14^0'=y_309^0, [ 14+_^0>=1 ], cost: 63+2*_^0 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l7 16: l7 -> l1 : Result_6^0'=head_9^post_2, a_128^0'=14, a_243^0'=-1, c_15^0'=y_309^0, elem_16^0'=y_309^0, head_9^0'=head_9^post_2, i_8^0'=17, k_296^0'=14+_^0, len_246^0'=15+_^0, len_48^0'=16, length_7^0'=17, lt_19^0'=lt_19^post_5, lt_20^0'=lt_20^post_5, lt_21^0'=lt_21^post_8, prev_17^0'=0, x_13^0'=y_309^0, y_14^0'=y_309^0, [ 14+_^0>=1 ], cost: 63+2*_^0 Computing asymptotic complexity for rule 16 Resulting cost 0 has complexity: Unknown Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Constant Cpx degree: 0 Solved cost: 1 Rule cost: 1 Rule guard: [ Result_6^0==Result_6^post_9 && _^0==_^post_9 && a_128^0==a_128^post_9 && a_243^0==a_243^post_9 && c_15^0==c_15^post_9 && elem_16^0==elem_16^post_9 && head_9^0==head_9^post_9 && i_8^0==i_8^post_9 && k_296^0==k_296^post_9 && len_246^0==len_246^post_9 && len_48^0==len_48^post_9 && length_7^0==length_7^post_9 && lt_18^0==lt_18^post_9 && lt_19^0==lt_19^post_9 && lt_20^0==lt_20^post_9 && lt_21^0==lt_21^post_9 && prev_17^0==prev_17^post_9 && x_13^0==x_13^post_9 && x_23^0==x_23^post_9 && y_110^0==y_110^post_9 && y_14^0==y_14^post_9 && y_158^0==y_158^post_9 && y_259^0==y_259^post_9 && y_309^0==y_309^post_9 && y_80^0==y_80^post_9 ] WORST_CASE(Omega(1),?)