WORST_CASE(Omega(1),?) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: l10 0: l0 -> l1 : acc12^0'=acc12^post_1, acc_length11^0'=acc_length11^post_1, coef_len210^0'=coef_len210^post_1, coef_len6^0'=coef_len6^post_1, i8^0'=i8^post_1, in_len4^0'=in_len4^post_1, j9^0'=j9^post_1, scale7^0'=scale7^post_1, [ acc12^0==acc12^post_1 && acc_length11^0==acc_length11^post_1 && coef_len210^0==coef_len210^post_1 && coef_len6^0==coef_len6^post_1 && i8^0==i8^post_1 && in_len4^0==in_len4^post_1 && j9^0==j9^post_1 && scale7^0==scale7^post_1 ], cost: 1 3: l1 -> l3 : acc12^0'=acc12^post_4, acc_length11^0'=acc_length11^post_4, coef_len210^0'=coef_len210^post_4, coef_len6^0'=coef_len6^post_4, i8^0'=i8^post_4, in_len4^0'=in_len4^post_4, j9^0'=j9^post_4, scale7^0'=scale7^post_4, [ i8^post_4==1+i8^0 && acc12^0==acc12^post_4 && acc_length11^0==acc_length11^post_4 && coef_len210^0==coef_len210^post_4 && coef_len6^0==coef_len6^post_4 && in_len4^0==in_len4^post_4 && j9^0==j9^post_4 && scale7^0==scale7^post_4 ], cost: 1 1: l2 -> l0 : acc12^0'=acc12^post_2, acc_length11^0'=acc_length11^post_2, coef_len210^0'=coef_len210^post_2, coef_len6^0'=coef_len6^post_2, i8^0'=i8^post_2, in_len4^0'=in_len4^post_2, j9^0'=j9^post_2, scale7^0'=scale7^post_2, [ coef_len6^0<=acc_length11^0 && acc12^0==acc12^post_2 && acc_length11^0==acc_length11^post_2 && coef_len210^0==coef_len210^post_2 && coef_len6^0==coef_len6^post_2 && i8^0==i8^post_2 && in_len4^0==in_len4^post_2 && j9^0==j9^post_2 && scale7^0==scale7^post_2 ], cost: 1 2: l2 -> l0 : acc12^0'=acc12^post_3, acc_length11^0'=acc_length11^post_3, coef_len210^0'=coef_len210^post_3, coef_len6^0'=coef_len6^post_3, i8^0'=i8^post_3, in_len4^0'=in_len4^post_3, j9^0'=j9^post_3, scale7^0'=scale7^post_3, [ 1+acc_length11^0<=coef_len6^0 && acc_length11^post_3==1+acc_length11^0 && acc12^0==acc12^post_3 && coef_len210^0==coef_len210^post_3 && coef_len6^0==coef_len6^post_3 && i8^0==i8^post_3 && in_len4^0==in_len4^post_3 && j9^0==j9^post_3 && scale7^0==scale7^post_3 ], cost: 1 7: l3 -> l5 : acc12^0'=acc12^post_8, acc_length11^0'=acc_length11^post_8, coef_len210^0'=coef_len210^post_8, coef_len6^0'=coef_len6^post_8, i8^0'=i8^post_8, in_len4^0'=in_len4^post_8, j9^0'=j9^post_8, scale7^0'=scale7^post_8, [ acc12^0==acc12^post_8 && acc_length11^0==acc_length11^post_8 && coef_len210^0==coef_len210^post_8 && coef_len6^0==coef_len6^post_8 && i8^0==i8^post_8 && in_len4^0==in_len4^post_8 && j9^0==j9^post_8 && scale7^0==scale7^post_8 ], cost: 1 4: l4 -> l2 : acc12^0'=acc12^post_5, acc_length11^0'=acc_length11^post_5, coef_len210^0'=coef_len210^post_5, coef_len6^0'=coef_len6^post_5, i8^0'=i8^post_5, in_len4^0'=in_len4^post_5, j9^0'=j9^post_5, scale7^0'=scale7^post_5, [ acc12^0==acc12^post_5 && acc_length11^0==acc_length11^post_5 && coef_len210^0==coef_len210^post_5 && coef_len6^0==coef_len6^post_5 && i8^0==i8^post_5 && in_len4^0==in_len4^post_5 && j9^0==j9^post_5 && scale7^0==scale7^post_5 ], cost: 1 5: l4 -> l1 : acc12^0'=acc12^post_6, acc_length11^0'=acc_length11^post_6, coef_len210^0'=coef_len210^post_6, coef_len6^0'=coef_len6^post_6, i8^0'=i8^post_6, in_len4^0'=in_len4^post_6, j9^0'=j9^post_6, scale7^0'=scale7^post_6, [ acc_length11^post_6==-1+acc_length11^0 && acc12^0==acc12^post_6 && coef_len210^0==coef_len210^post_6 && coef_len6^0==coef_len6^post_6 && i8^0==i8^post_6 && in_len4^0==in_len4^post_6 && j9^0==j9^post_6 && scale7^0==scale7^post_6 ], cost: 1 6: l4 -> l2 : acc12^0'=acc12^post_7, acc_length11^0'=acc_length11^post_7, coef_len210^0'=coef_len210^post_7, coef_len6^0'=coef_len6^post_7, i8^0'=i8^post_7, in_len4^0'=in_len4^post_7, j9^0'=j9^post_7, scale7^0'=scale7^post_7, [ acc12^0==acc12^post_7 && acc_length11^0==acc_length11^post_7 && coef_len210^0==coef_len210^post_7 && coef_len6^0==coef_len6^post_7 && i8^0==i8^post_7 && in_len4^0==in_len4^post_7 && j9^0==j9^post_7 && scale7^0==scale7^post_7 ], cost: 1 11: l5 -> l8 : acc12^0'=acc12^post_12, acc_length11^0'=acc_length11^post_12, coef_len210^0'=coef_len210^post_12, coef_len6^0'=coef_len6^post_12, i8^0'=i8^post_12, in_len4^0'=in_len4^post_12, j9^0'=j9^post_12, scale7^0'=scale7^post_12, [ in_len4^0<=i8^0 && acc12^0==acc12^post_12 && acc_length11^0==acc_length11^post_12 && coef_len210^0==coef_len210^post_12 && coef_len6^0==coef_len6^post_12 && i8^0==i8^post_12 && in_len4^0==in_len4^post_12 && j9^0==j9^post_12 && scale7^0==scale7^post_12 ], cost: 1 12: l5 -> l7 : acc12^0'=acc12^post_13, acc_length11^0'=acc_length11^post_13, coef_len210^0'=coef_len210^post_13, coef_len6^0'=coef_len6^post_13, i8^0'=i8^post_13, in_len4^0'=in_len4^post_13, j9^0'=j9^post_13, scale7^0'=scale7^post_13, [ 1+i8^0<=in_len4^0 && acc12^post_13==acc12^post_13 && j9^post_13==1 && acc_length11^0==acc_length11^post_13 && coef_len210^0==coef_len210^post_13 && coef_len6^0==coef_len6^post_13 && i8^0==i8^post_13 && in_len4^0==in_len4^post_13 && scale7^0==scale7^post_13 ], cost: 1 8: l6 -> l4 : acc12^0'=acc12^post_9, acc_length11^0'=acc_length11^post_9, coef_len210^0'=coef_len210^post_9, coef_len6^0'=coef_len6^post_9, i8^0'=i8^post_9, in_len4^0'=in_len4^post_9, j9^0'=j9^post_9, scale7^0'=scale7^post_9, [ acc_length11^0<=j9^0 && acc12^0==acc12^post_9 && acc_length11^0==acc_length11^post_9 && coef_len210^0==coef_len210^post_9 && coef_len6^0==coef_len6^post_9 && i8^0==i8^post_9 && in_len4^0==in_len4^post_9 && j9^0==j9^post_9 && scale7^0==scale7^post_9 ], cost: 1 9: l6 -> l7 : acc12^0'=acc12^post_10, acc_length11^0'=acc_length11^post_10, coef_len210^0'=coef_len210^post_10, coef_len6^0'=coef_len6^post_10, i8^0'=i8^post_10, in_len4^0'=in_len4^post_10, j9^0'=j9^post_10, scale7^0'=scale7^post_10, [ 1+j9^0<=acc_length11^0 && acc12^post_10==acc12^post_10 && j9^post_10==1+j9^0 && acc_length11^0==acc_length11^post_10 && coef_len210^0==coef_len210^post_10 && coef_len6^0==coef_len6^post_10 && i8^0==i8^post_10 && in_len4^0==in_len4^post_10 && scale7^0==scale7^post_10 ], cost: 1 10: l7 -> l6 : acc12^0'=acc12^post_11, acc_length11^0'=acc_length11^post_11, coef_len210^0'=coef_len210^post_11, coef_len6^0'=coef_len6^post_11, i8^0'=i8^post_11, in_len4^0'=in_len4^post_11, j9^0'=j9^post_11, scale7^0'=scale7^post_11, [ acc12^0==acc12^post_11 && acc_length11^0==acc_length11^post_11 && coef_len210^0==coef_len210^post_11 && coef_len6^0==coef_len6^post_11 && i8^0==i8^post_11 && in_len4^0==in_len4^post_11 && j9^0==j9^post_11 && scale7^0==scale7^post_11 ], cost: 1 13: l9 -> l3 : acc12^0'=acc12^post_14, acc_length11^0'=acc_length11^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=coef_len6^post_14, i8^0'=i8^post_14, in_len4^0'=in_len4^post_14, j9^0'=j9^post_14, scale7^0'=scale7^post_14, [ in_len4^post_14==10 && coef_len6^post_14==35 && scale7^post_14==285 && coef_len210^post_14==coef_len210^post_14 && acc_length11^post_14==coef_len210^post_14 && i8^post_14==0 && acc12^0==acc12^post_14 && j9^0==j9^post_14 ], cost: 1 14: l10 -> l9 : acc12^0'=acc12^post_15, acc_length11^0'=acc_length11^post_15, coef_len210^0'=coef_len210^post_15, coef_len6^0'=coef_len6^post_15, i8^0'=i8^post_15, in_len4^0'=in_len4^post_15, j9^0'=j9^post_15, scale7^0'=scale7^post_15, [ acc12^0==acc12^post_15 && acc_length11^0==acc_length11^post_15 && coef_len210^0==coef_len210^post_15 && coef_len6^0==coef_len6^post_15 && i8^0==i8^post_15 && in_len4^0==in_len4^post_15 && j9^0==j9^post_15 && scale7^0==scale7^post_15 ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 14: l10 -> l9 : acc12^0'=acc12^post_15, acc_length11^0'=acc_length11^post_15, coef_len210^0'=coef_len210^post_15, coef_len6^0'=coef_len6^post_15, i8^0'=i8^post_15, in_len4^0'=in_len4^post_15, j9^0'=j9^post_15, scale7^0'=scale7^post_15, [ acc12^0==acc12^post_15 && acc_length11^0==acc_length11^post_15 && coef_len210^0==coef_len210^post_15 && coef_len6^0==coef_len6^post_15 && i8^0==i8^post_15 && in_len4^0==in_len4^post_15 && j9^0==j9^post_15 && scale7^0==scale7^post_15 ], cost: 1 Removed unreachable and leaf rules: Start location: l10 0: l0 -> l1 : acc12^0'=acc12^post_1, acc_length11^0'=acc_length11^post_1, coef_len210^0'=coef_len210^post_1, coef_len6^0'=coef_len6^post_1, i8^0'=i8^post_1, in_len4^0'=in_len4^post_1, j9^0'=j9^post_1, scale7^0'=scale7^post_1, [ acc12^0==acc12^post_1 && acc_length11^0==acc_length11^post_1 && coef_len210^0==coef_len210^post_1 && coef_len6^0==coef_len6^post_1 && i8^0==i8^post_1 && in_len4^0==in_len4^post_1 && j9^0==j9^post_1 && scale7^0==scale7^post_1 ], cost: 1 3: l1 -> l3 : acc12^0'=acc12^post_4, acc_length11^0'=acc_length11^post_4, coef_len210^0'=coef_len210^post_4, coef_len6^0'=coef_len6^post_4, i8^0'=i8^post_4, in_len4^0'=in_len4^post_4, j9^0'=j9^post_4, scale7^0'=scale7^post_4, [ i8^post_4==1+i8^0 && acc12^0==acc12^post_4 && acc_length11^0==acc_length11^post_4 && coef_len210^0==coef_len210^post_4 && coef_len6^0==coef_len6^post_4 && in_len4^0==in_len4^post_4 && j9^0==j9^post_4 && scale7^0==scale7^post_4 ], cost: 1 1: l2 -> l0 : acc12^0'=acc12^post_2, acc_length11^0'=acc_length11^post_2, coef_len210^0'=coef_len210^post_2, coef_len6^0'=coef_len6^post_2, i8^0'=i8^post_2, in_len4^0'=in_len4^post_2, j9^0'=j9^post_2, scale7^0'=scale7^post_2, [ coef_len6^0<=acc_length11^0 && acc12^0==acc12^post_2 && acc_length11^0==acc_length11^post_2 && coef_len210^0==coef_len210^post_2 && coef_len6^0==coef_len6^post_2 && i8^0==i8^post_2 && in_len4^0==in_len4^post_2 && j9^0==j9^post_2 && scale7^0==scale7^post_2 ], cost: 1 2: l2 -> l0 : acc12^0'=acc12^post_3, acc_length11^0'=acc_length11^post_3, coef_len210^0'=coef_len210^post_3, coef_len6^0'=coef_len6^post_3, i8^0'=i8^post_3, in_len4^0'=in_len4^post_3, j9^0'=j9^post_3, scale7^0'=scale7^post_3, [ 1+acc_length11^0<=coef_len6^0 && acc_length11^post_3==1+acc_length11^0 && acc12^0==acc12^post_3 && coef_len210^0==coef_len210^post_3 && coef_len6^0==coef_len6^post_3 && i8^0==i8^post_3 && in_len4^0==in_len4^post_3 && j9^0==j9^post_3 && scale7^0==scale7^post_3 ], cost: 1 7: l3 -> l5 : acc12^0'=acc12^post_8, acc_length11^0'=acc_length11^post_8, coef_len210^0'=coef_len210^post_8, coef_len6^0'=coef_len6^post_8, i8^0'=i8^post_8, in_len4^0'=in_len4^post_8, j9^0'=j9^post_8, scale7^0'=scale7^post_8, [ acc12^0==acc12^post_8 && acc_length11^0==acc_length11^post_8 && coef_len210^0==coef_len210^post_8 && coef_len6^0==coef_len6^post_8 && i8^0==i8^post_8 && in_len4^0==in_len4^post_8 && j9^0==j9^post_8 && scale7^0==scale7^post_8 ], cost: 1 4: l4 -> l2 : acc12^0'=acc12^post_5, acc_length11^0'=acc_length11^post_5, coef_len210^0'=coef_len210^post_5, coef_len6^0'=coef_len6^post_5, i8^0'=i8^post_5, in_len4^0'=in_len4^post_5, j9^0'=j9^post_5, scale7^0'=scale7^post_5, [ acc12^0==acc12^post_5 && acc_length11^0==acc_length11^post_5 && coef_len210^0==coef_len210^post_5 && coef_len6^0==coef_len6^post_5 && i8^0==i8^post_5 && in_len4^0==in_len4^post_5 && j9^0==j9^post_5 && scale7^0==scale7^post_5 ], cost: 1 5: l4 -> l1 : acc12^0'=acc12^post_6, acc_length11^0'=acc_length11^post_6, coef_len210^0'=coef_len210^post_6, coef_len6^0'=coef_len6^post_6, i8^0'=i8^post_6, in_len4^0'=in_len4^post_6, j9^0'=j9^post_6, scale7^0'=scale7^post_6, [ acc_length11^post_6==-1+acc_length11^0 && acc12^0==acc12^post_6 && coef_len210^0==coef_len210^post_6 && coef_len6^0==coef_len6^post_6 && i8^0==i8^post_6 && in_len4^0==in_len4^post_6 && j9^0==j9^post_6 && scale7^0==scale7^post_6 ], cost: 1 6: l4 -> l2 : acc12^0'=acc12^post_7, acc_length11^0'=acc_length11^post_7, coef_len210^0'=coef_len210^post_7, coef_len6^0'=coef_len6^post_7, i8^0'=i8^post_7, in_len4^0'=in_len4^post_7, j9^0'=j9^post_7, scale7^0'=scale7^post_7, [ acc12^0==acc12^post_7 && acc_length11^0==acc_length11^post_7 && coef_len210^0==coef_len210^post_7 && coef_len6^0==coef_len6^post_7 && i8^0==i8^post_7 && in_len4^0==in_len4^post_7 && j9^0==j9^post_7 && scale7^0==scale7^post_7 ], cost: 1 12: l5 -> l7 : acc12^0'=acc12^post_13, acc_length11^0'=acc_length11^post_13, coef_len210^0'=coef_len210^post_13, coef_len6^0'=coef_len6^post_13, i8^0'=i8^post_13, in_len4^0'=in_len4^post_13, j9^0'=j9^post_13, scale7^0'=scale7^post_13, [ 1+i8^0<=in_len4^0 && acc12^post_13==acc12^post_13 && j9^post_13==1 && acc_length11^0==acc_length11^post_13 && coef_len210^0==coef_len210^post_13 && coef_len6^0==coef_len6^post_13 && i8^0==i8^post_13 && in_len4^0==in_len4^post_13 && scale7^0==scale7^post_13 ], cost: 1 8: l6 -> l4 : acc12^0'=acc12^post_9, acc_length11^0'=acc_length11^post_9, coef_len210^0'=coef_len210^post_9, coef_len6^0'=coef_len6^post_9, i8^0'=i8^post_9, in_len4^0'=in_len4^post_9, j9^0'=j9^post_9, scale7^0'=scale7^post_9, [ acc_length11^0<=j9^0 && acc12^0==acc12^post_9 && acc_length11^0==acc_length11^post_9 && coef_len210^0==coef_len210^post_9 && coef_len6^0==coef_len6^post_9 && i8^0==i8^post_9 && in_len4^0==in_len4^post_9 && j9^0==j9^post_9 && scale7^0==scale7^post_9 ], cost: 1 9: l6 -> l7 : acc12^0'=acc12^post_10, acc_length11^0'=acc_length11^post_10, coef_len210^0'=coef_len210^post_10, coef_len6^0'=coef_len6^post_10, i8^0'=i8^post_10, in_len4^0'=in_len4^post_10, j9^0'=j9^post_10, scale7^0'=scale7^post_10, [ 1+j9^0<=acc_length11^0 && acc12^post_10==acc12^post_10 && j9^post_10==1+j9^0 && acc_length11^0==acc_length11^post_10 && coef_len210^0==coef_len210^post_10 && coef_len6^0==coef_len6^post_10 && i8^0==i8^post_10 && in_len4^0==in_len4^post_10 && scale7^0==scale7^post_10 ], cost: 1 10: l7 -> l6 : acc12^0'=acc12^post_11, acc_length11^0'=acc_length11^post_11, coef_len210^0'=coef_len210^post_11, coef_len6^0'=coef_len6^post_11, i8^0'=i8^post_11, in_len4^0'=in_len4^post_11, j9^0'=j9^post_11, scale7^0'=scale7^post_11, [ acc12^0==acc12^post_11 && acc_length11^0==acc_length11^post_11 && coef_len210^0==coef_len210^post_11 && coef_len6^0==coef_len6^post_11 && i8^0==i8^post_11 && in_len4^0==in_len4^post_11 && j9^0==j9^post_11 && scale7^0==scale7^post_11 ], cost: 1 13: l9 -> l3 : acc12^0'=acc12^post_14, acc_length11^0'=acc_length11^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=coef_len6^post_14, i8^0'=i8^post_14, in_len4^0'=in_len4^post_14, j9^0'=j9^post_14, scale7^0'=scale7^post_14, [ in_len4^post_14==10 && coef_len6^post_14==35 && scale7^post_14==285 && coef_len210^post_14==coef_len210^post_14 && acc_length11^post_14==coef_len210^post_14 && i8^post_14==0 && acc12^0==acc12^post_14 && j9^0==j9^post_14 ], cost: 1 14: l10 -> l9 : acc12^0'=acc12^post_15, acc_length11^0'=acc_length11^post_15, coef_len210^0'=coef_len210^post_15, coef_len6^0'=coef_len6^post_15, i8^0'=i8^post_15, in_len4^0'=in_len4^post_15, j9^0'=j9^post_15, scale7^0'=scale7^post_15, [ acc12^0==acc12^post_15 && acc_length11^0==acc_length11^post_15 && coef_len210^0==coef_len210^post_15 && coef_len6^0==coef_len6^post_15 && i8^0==i8^post_15 && in_len4^0==in_len4^post_15 && j9^0==j9^post_15 && scale7^0==scale7^post_15 ], cost: 1 Simplified all rules, resulting in: Start location: l10 0: l0 -> l1 : [], cost: 1 3: l1 -> l3 : i8^0'=1+i8^0, [], cost: 1 1: l2 -> l0 : [ coef_len6^0<=acc_length11^0 ], cost: 1 2: l2 -> l0 : acc_length11^0'=1+acc_length11^0, [ 1+acc_length11^0<=coef_len6^0 ], cost: 1 7: l3 -> l5 : [], cost: 1 5: l4 -> l1 : acc_length11^0'=-1+acc_length11^0, [], cost: 1 6: l4 -> l2 : [], cost: 1 12: l5 -> l7 : acc12^0'=acc12^post_13, j9^0'=1, [ 1+i8^0<=in_len4^0 ], cost: 1 8: l6 -> l4 : [ acc_length11^0<=j9^0 ], cost: 1 9: l6 -> l7 : acc12^0'=acc12^post_10, j9^0'=1+j9^0, [ 1+j9^0<=acc_length11^0 ], cost: 1 10: l7 -> l6 : [], cost: 1 13: l9 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 1 14: l10 -> l9 : [], cost: 1 ### Simplification by acceleration and chaining ### Eliminated locations (on linear paths): Start location: l10 0: l0 -> l1 : [], cost: 1 3: l1 -> l3 : i8^0'=1+i8^0, [], cost: 1 1: l2 -> l0 : [ coef_len6^0<=acc_length11^0 ], cost: 1 2: l2 -> l0 : acc_length11^0'=1+acc_length11^0, [ 1+acc_length11^0<=coef_len6^0 ], cost: 1 16: l3 -> l7 : acc12^0'=acc12^post_13, j9^0'=1, [ 1+i8^0<=in_len4^0 ], cost: 2 5: l4 -> l1 : acc_length11^0'=-1+acc_length11^0, [], cost: 1 6: l4 -> l2 : [], cost: 1 8: l6 -> l4 : [ acc_length11^0<=j9^0 ], cost: 1 9: l6 -> l7 : acc12^0'=acc12^post_10, j9^0'=1+j9^0, [ 1+j9^0<=acc_length11^0 ], cost: 1 10: l7 -> l6 : [], cost: 1 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 0: l0 -> l1 : [], cost: 1 3: l1 -> l3 : i8^0'=1+i8^0, [], cost: 1 16: l3 -> l7 : acc12^0'=acc12^post_13, j9^0'=1, [ 1+i8^0<=in_len4^0 ], cost: 2 5: l4 -> l1 : acc_length11^0'=-1+acc_length11^0, [], cost: 1 19: l4 -> l0 : [ coef_len6^0<=acc_length11^0 ], cost: 2 20: l4 -> l0 : acc_length11^0'=1+acc_length11^0, [ 1+acc_length11^0<=coef_len6^0 ], cost: 2 17: l7 -> l4 : [ acc_length11^0<=j9^0 ], cost: 2 18: l7 -> l7 : acc12^0'=acc12^post_10, j9^0'=1+j9^0, [ 1+j9^0<=acc_length11^0 ], cost: 2 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Accelerating simple loops of location 7. Accelerating the following rules: 18: l7 -> l7 : acc12^0'=acc12^post_10, j9^0'=1+j9^0, [ 1+j9^0<=acc_length11^0 ], cost: 2 Accelerated rule 18 with backward acceleration, yielding the new rule 21. [accelerate] Nesting with 1 inner and 1 outer candidates Removing the simple loops: 18. Accelerated all simple loops using metering functions (where possible): Start location: l10 0: l0 -> l1 : [], cost: 1 3: l1 -> l3 : i8^0'=1+i8^0, [], cost: 1 16: l3 -> l7 : acc12^0'=acc12^post_13, j9^0'=1, [ 1+i8^0<=in_len4^0 ], cost: 2 5: l4 -> l1 : acc_length11^0'=-1+acc_length11^0, [], cost: 1 19: l4 -> l0 : [ coef_len6^0<=acc_length11^0 ], cost: 2 20: l4 -> l0 : acc_length11^0'=1+acc_length11^0, [ 1+acc_length11^0<=coef_len6^0 ], cost: 2 17: l7 -> l4 : [ acc_length11^0<=j9^0 ], cost: 2 21: l7 -> l7 : acc12^0'=acc12^post_10, j9^0'=acc_length11^0, [ acc_length11^0-j9^0>=1 ], cost: 2*acc_length11^0-2*j9^0 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l10 0: l0 -> l1 : [], cost: 1 3: l1 -> l3 : i8^0'=1+i8^0, [], cost: 1 16: l3 -> l7 : acc12^0'=acc12^post_13, j9^0'=1, [ 1+i8^0<=in_len4^0 ], cost: 2 22: l3 -> l7 : acc12^0'=acc12^post_10, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 ], cost: 2*acc_length11^0 5: l4 -> l1 : acc_length11^0'=-1+acc_length11^0, [], cost: 1 19: l4 -> l0 : [ coef_len6^0<=acc_length11^0 ], cost: 2 20: l4 -> l0 : acc_length11^0'=1+acc_length11^0, [ 1+acc_length11^0<=coef_len6^0 ], cost: 2 17: l7 -> l4 : [ acc_length11^0<=j9^0 ], cost: 2 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 23: l3 -> l4 : acc12^0'=acc12^post_13, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 ], cost: 4 24: l3 -> l4 : acc12^0'=acc12^post_10, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 ], cost: 2+2*acc_length11^0 27: l4 -> l3 : acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, [], cost: 2 28: l4 -> l3 : i8^0'=1+i8^0, [ coef_len6^0<=acc_length11^0 ], cost: 4 29: l4 -> l3 : acc_length11^0'=1+acc_length11^0, i8^0'=1+i8^0, [ 1+acc_length11^0<=coef_len6^0 ], cost: 4 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Eliminated locations (on tree-shaped paths): Start location: l10 30: l3 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 ], cost: 6 31: l3 -> l3 : acc12^0'=acc12^post_13, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 && coef_len6^0<=acc_length11^0 ], cost: 8 32: l3 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=1+acc_length11^0, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 && 1+acc_length11^0<=coef_len6^0 ], cost: 8 33: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 ], cost: 4+2*acc_length11^0 34: l3 -> l3 : acc12^0'=acc12^post_10, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 && coef_len6^0<=acc_length11^0 ], cost: 6+2*acc_length11^0 35: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1+acc_length11^0, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Applied pruning (of leafs and parallel rules): Start location: l10 30: l3 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 ], cost: 6 31: l3 -> l3 : acc12^0'=acc12^post_13, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 && coef_len6^0<=acc_length11^0 ], cost: 8 33: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 ], cost: 4+2*acc_length11^0 34: l3 -> l3 : acc12^0'=acc12^post_10, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 && coef_len6^0<=acc_length11^0 ], cost: 6+2*acc_length11^0 35: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1+acc_length11^0, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Accelerating simple loops of location 3. Accelerating the following rules: 30: l3 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 ], cost: 6 31: l3 -> l3 : acc12^0'=acc12^post_13, i8^0'=1+i8^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 && coef_len6^0<=acc_length11^0 ], cost: 8 33: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-1+acc_length11^0, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 ], cost: 4+2*acc_length11^0 34: l3 -> l3 : acc12^0'=acc12^post_10, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 && coef_len6^0<=acc_length11^0 ], cost: 6+2*acc_length11^0 35: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1+acc_length11^0, i8^0'=1+i8^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && -1+acc_length11^0>=1 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 Accelerated rule 30 with backward acceleration, yielding the new rule 36. Accelerated rule 31 with backward acceleration, yielding the new rule 37. Accelerated rule 33 with backward acceleration, yielding the new rule 38. Accelerated rule 33 with backward acceleration, yielding the new rule 39. Accelerated rule 34 with backward acceleration, yielding the new rule 40. Accelerated rule 35 with backward acceleration, yielding the new rule 41. Accelerated rule 35 with backward acceleration, yielding the new rule 42. [accelerate] Nesting with 7 inner and 5 outer candidates Removing the simple loops: 30 31 33 34 35. Accelerated all simple loops using metering functions (where possible): Start location: l10 36: l3 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=i8^0+acc_length11^0-in_len4^0, i8^0'=in_len4^0, j9^0'=1, [ acc_length11^0<=1 && -i8^0+in_len4^0>=1 ], cost: -6*i8^0+6*in_len4^0 37: l3 -> l3 : acc12^0'=acc12^post_13, i8^0'=in_len4^0, j9^0'=1, [ acc_length11^0<=1 && coef_len6^0<=acc_length11^0 && -i8^0+in_len4^0>=1 ], cost: -8*i8^0+8*in_len4^0 38: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=i8^0+acc_length11^0-in_len4^0, i8^0'=in_len4^0, j9^0'=1+i8^0+acc_length11^0-in_len4^0, [ -i8^0+in_len4^0>=1 && i8^0+acc_length11^0-in_len4^0>=1 ], cost: -5*i8^0+5*in_len4^0-2*acc_length11^0*(i8^0-in_len4^0)-(i8^0-in_len4^0)^2 39: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1, i8^0'=-1+i8^0+acc_length11^0, j9^0'=2, [ -1+acc_length11^0>=1 && -1+i8^0+acc_length11^0<=in_len4^0 ], cost: -5+5*acc_length11^0-(-1+acc_length11^0)^2+2*(-1+acc_length11^0)*acc_length11^0 40: l3 -> l3 : acc12^0'=acc12^post_10, i8^0'=in_len4^0, j9^0'=acc_length11^0, [ -1+acc_length11^0>=1 && coef_len6^0<=acc_length11^0 && -i8^0+in_len4^0>=1 ], cost: -6*i8^0+6*in_len4^0-2*acc_length11^0*(i8^0-in_len4^0) 41: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-i8^0+acc_length11^0+in_len4^0, i8^0'=in_len4^0, j9^0'=-1-i8^0+acc_length11^0+in_len4^0, [ -1+acc_length11^0>=1 && -i8^0+in_len4^0>=1 && -i8^0+acc_length11^0+in_len4^0<=coef_len6^0 ], cost: -5*i8^0+5*in_len4^0-2*acc_length11^0*(i8^0-in_len4^0)+(i8^0-in_len4^0)^2 42: l3 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=coef_len6^0, i8^0'=i8^0-acc_length11^0+coef_len6^0, j9^0'=-1+coef_len6^0, [ -1+acc_length11^0>=1 && -acc_length11^0+coef_len6^0>=1 && i8^0-acc_length11^0+coef_len6^0<=in_len4^0 ], cost: -5*acc_length11^0-2*acc_length11^0*(acc_length11^0-coef_len6^0)+5*coef_len6^0+(acc_length11^0-coef_len6^0)^2 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 Chained accelerated rules (with incoming rules): Start location: l10 15: l10 -> l3 : acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 43: l10 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=-10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=1, scale7^0'=285, [ acc_length11^post_14<=1 ], cost: 62 44: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=-9+acc_length11^post_14, scale7^0'=285, [ -10+acc_length11^post_14>=1 ], cost: -48+20*acc_length11^post_14 45: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=-1+acc_length11^post_14, in_len4^0'=10, j9^0'=2, scale7^0'=285, [ -1+acc_length11^post_14>=1 && -1+acc_length11^post_14<=10 ], cost: -3+2*acc_length11^post_14*(-1+acc_length11^post_14)-(-1+acc_length11^post_14)^2+5*acc_length11^post_14 46: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=acc_length11^post_14, scale7^0'=285, [ 35<=acc_length11^post_14 ], cost: 62+20*acc_length11^post_14 47: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=9+acc_length11^post_14, scale7^0'=285, [ -1+acc_length11^post_14>=1 && 10+acc_length11^post_14<=35 ], cost: 152+20*acc_length11^post_14 48: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=35, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=35-acc_length11^post_14, in_len4^0'=10, j9^0'=34, scale7^0'=285, [ 35-acc_length11^post_14>=1 && 35-acc_length11^post_14<=10 ], cost: 177-2*(-35+acc_length11^post_14)*acc_length11^post_14-5*acc_length11^post_14+(-35+acc_length11^post_14)^2 Removed unreachable locations (and leaf rules with constant cost): Start location: l10 44: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=-9+acc_length11^post_14, scale7^0'=285, [ -10+acc_length11^post_14>=1 ], cost: -48+20*acc_length11^post_14 45: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=-1+acc_length11^post_14, in_len4^0'=10, j9^0'=2, scale7^0'=285, [ -1+acc_length11^post_14>=1 && -1+acc_length11^post_14<=10 ], cost: -3+2*acc_length11^post_14*(-1+acc_length11^post_14)-(-1+acc_length11^post_14)^2+5*acc_length11^post_14 46: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=acc_length11^post_14, scale7^0'=285, [ 35<=acc_length11^post_14 ], cost: 62+20*acc_length11^post_14 47: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=9+acc_length11^post_14, scale7^0'=285, [ -1+acc_length11^post_14>=1 && 10+acc_length11^post_14<=35 ], cost: 152+20*acc_length11^post_14 48: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=35, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=35-acc_length11^post_14, in_len4^0'=10, j9^0'=34, scale7^0'=285, [ 35-acc_length11^post_14>=1 && 35-acc_length11^post_14<=10 ], cost: 177-2*(-35+acc_length11^post_14)*acc_length11^post_14-5*acc_length11^post_14+(-35+acc_length11^post_14)^2 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l10 44: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=-10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=-9+acc_length11^post_14, scale7^0'=285, [ -10+acc_length11^post_14>=1 ], cost: -48+20*acc_length11^post_14 45: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=-1+acc_length11^post_14, in_len4^0'=10, j9^0'=2, scale7^0'=285, [ -1+acc_length11^post_14>=1 && -1+acc_length11^post_14<=10 ], cost: -3+2*acc_length11^post_14*(-1+acc_length11^post_14)-(-1+acc_length11^post_14)^2+5*acc_length11^post_14 46: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=acc_length11^post_14, scale7^0'=285, [ 35<=acc_length11^post_14 ], cost: 62+20*acc_length11^post_14 47: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=10+acc_length11^post_14, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=9+acc_length11^post_14, scale7^0'=285, [ -1+acc_length11^post_14>=1 && 10+acc_length11^post_14<=35 ], cost: 152+20*acc_length11^post_14 48: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=35, coef_len210^0'=acc_length11^post_14, coef_len6^0'=35, i8^0'=35-acc_length11^post_14, in_len4^0'=10, j9^0'=34, scale7^0'=285, [ 35-acc_length11^post_14>=1 && 35-acc_length11^post_14<=10 ], cost: 177-2*(-35+acc_length11^post_14)*acc_length11^post_14-5*acc_length11^post_14+(-35+acc_length11^post_14)^2 Computing asymptotic complexity for rule 45 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 48 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 44 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 46 Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 47 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: [ acc12^0==acc12^post_15 && acc_length11^0==acc_length11^post_15 && coef_len210^0==coef_len210^post_15 && coef_len6^0==coef_len6^post_15 && i8^0==i8^post_15 && in_len4^0==in_len4^post_15 && j9^0==j9^post_15 && scale7^0==scale7^post_15 ] WORST_CASE(Omega(1),?)