WORST_CASE(INF,?) ### 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'=coef_len210^post_14, coef_len210^0'=coef_len210^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'=coef_len210^post_14, coef_len210^0'=coef_len210^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'=coef_len210^post_14, coef_len210^0'=coef_len210^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 metering function -j9^0+acc_length11^0, yielding the new rule 21. 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, [ 1+j9^0<=acc_length11^0 ], cost: -2*j9^0+2*acc_length11^0 15: l10 -> l3 : acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^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 && 2<=acc_length11^0 ], 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'=coef_len210^post_14, coef_len210^0'=coef_len210^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 && 2<=acc_length11^0 ], 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'=coef_len210^post_14, coef_len210^0'=coef_len210^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 && 2<=acc_length11^0 ], 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 && 2<=acc_length11^0 && 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 && 2<=acc_length11^0 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 15: l10 -> l3 : acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^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 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 && 2<=acc_length11^0 ], 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 && 2<=acc_length11^0 && 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 && 2<=acc_length11^0 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 15: l10 -> l3 : acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^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: 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 && 2<=acc_length11^0 ], 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 && 2<=acc_length11^0 && 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 && 2<=acc_length11^0 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 Accelerated rule 31 with metering function in_len4^0-i8^0, yielding the new rule 36. Found no metering function for rule 32. Found no metering function for rule 33. Accelerated rule 34 with metering function in_len4^0-i8^0, yielding the new rule 37. Found no metering function for rule 35. Nested simple loops 33 (outer loop) and 36 (inner loop) with metering function -2+acc_length11^0, resulting in the new rules: 38. Removing the simple loops: 31 33 34. Accelerated all simple loops using metering functions (where possible): Start location: l10 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 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 && 2<=acc_length11^0 && 1+acc_length11^0<=coef_len6^0 ], cost: 6+2*acc_length11^0 36: l3 -> l3 : acc12^0'=acc12^post_13, i8^0'=in_len4^0, j9^0'=1, [ 1+i8^0<=in_len4^0 && acc_length11^0<=1 && coef_len6^0<=acc_length11^0 ], cost: 8*in_len4^0-8*i8^0 37: l3 -> l3 : acc12^0'=acc12^post_10, i8^0'=in_len4^0, j9^0'=acc_length11^0, [ 1+i8^0<=in_len4^0 && 2<=acc_length11^0 && coef_len6^0<=acc_length11^0 ], cost: 6*in_len4^0+2*(in_len4^0-i8^0)*acc_length11^0-6*i8^0 38: l3 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=2, i8^0'=in_len4^0, j9^0'=1, [ 2-acc_length11^0==0 && 2+i8^0<=in_len4^0 && coef_len6^0<=-1+acc_length11^0 && -2+acc_length11^0>=1 ], cost: 6+2*acc_length11^0*(-2+acc_length11^0)-(-2+acc_length11^0)^2-3*acc_length11^0 15: l10 -> l3 : acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^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'=coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=0, in_len4^0'=10, scale7^0'=285, [], cost: 2 39: l10 -> l3 : acc12^0'=acc12^post_13, acc_length11^0'=1+coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=1, in_len4^0'=10, j9^0'=1, scale7^0'=285, [ coef_len210^post_14<=1 ], cost: 10 40: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1+coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=1, in_len4^0'=10, j9^0'=coef_len210^post_14, scale7^0'=285, [ 2<=coef_len210^post_14 && 1+coef_len210^post_14<=35 ], cost: 8+2*coef_len210^post_14 41: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=coef_len210^post_14, scale7^0'=285, [ 35<=coef_len210^post_14 ], cost: 62+20*coef_len210^post_14 Removed unreachable locations (and leaf rules with constant cost): Start location: l10 40: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1+coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=1, in_len4^0'=10, j9^0'=coef_len210^post_14, scale7^0'=285, [ 2<=coef_len210^post_14 && 1+coef_len210^post_14<=35 ], cost: 8+2*coef_len210^post_14 41: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=coef_len210^post_14, scale7^0'=285, [ 35<=coef_len210^post_14 ], cost: 62+20*coef_len210^post_14 ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: l10 40: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=1+coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=1, in_len4^0'=10, j9^0'=coef_len210^post_14, scale7^0'=285, [ 2<=coef_len210^post_14 && 1+coef_len210^post_14<=35 ], cost: 8+2*coef_len210^post_14 41: l10 -> l3 : acc12^0'=acc12^post_10, acc_length11^0'=coef_len210^post_14, coef_len210^0'=coef_len210^post_14, coef_len6^0'=35, i8^0'=10, in_len4^0'=10, j9^0'=coef_len210^post_14, scale7^0'=285, [ 35<=coef_len210^post_14 ], cost: 62+20*coef_len210^post_14 Computing asymptotic complexity for rule 40 Could not solve the limit problem. Resulting cost 0 has complexity: Unknown Computing asymptotic complexity for rule 41 Solved the limit problem by the following transformations: Created initial limit problem: -34+coef_len210^post_14 (+/+!), 62+20*coef_len210^post_14 (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {coef_len210^post_14==n} resulting limit problem: [solved] Solution: coef_len210^post_14 / n Resulting cost 62+20*n has complexity: Unbounded Found new complexity Unbounded. Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Unbounded Cpx degree: Unbounded Solved cost: 62+20*n Rule cost: 62+20*coef_len210^post_14 Rule guard: [ 35<=coef_len210^post_14 ] WORST_CASE(INF,?)