7.13/3.04 WORST_CASE(Omega(n^1), O(n^1)) 7.13/3.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.13/3.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.13/3.05 7.13/3.05 7.13/3.05 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 7.13/3.05 7.13/3.05 (0) CpxIntTrs 7.13/3.05 (1) Koat Proof [FINISHED, 716 ms] 7.13/3.05 (2) BOUNDS(1, n^1) 7.13/3.05 (3) Loat Proof [FINISHED, 1412 ms] 7.13/3.05 (4) BOUNDS(n^1, INF) 7.13/3.05 7.13/3.05 7.13/3.05 ---------------------------------------- 7.13/3.05 7.13/3.05 (0) 7.13/3.05 Obligation: 7.13/3.05 Complexity Int TRS consisting of the following rules: 7.13/3.05 f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f17(0, K, L, 0, E, F, G, H, I, J)) :|: TRUE 7.13/3.05 f17(A, B, C, D, E, F, G, H, I, J) -> Com_1(f17(A, B, C, D + 1, E, F, G, H, I, J)) :|: E >= D + 1 7.13/3.05 f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, B, C, D, E, F - 1, G, H, I, J)) :|: F >= 0 7.13/3.05 f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, G + 1, H, I, J)) :|: E >= G + 1 7.13/3.05 f45(A, B, C, D, E, F, G, H, I, J) -> Com_1(f45(A + 1, B, C, D, E, F, G, H, I, J)) :|: E >= A + 1 7.13/3.05 f55(A, B, C, D, E, F, G, H, I, J) -> Com_1(f55(A, B, C, D, E, F, G, H + 1, I, J)) :|: E >= H + 1 7.13/3.05 f65(A, B, C, D, E, F, G, H, I, J) -> Com_1(f65(A, B, C, D, E, F, G, H, I - 1, J)) :|: I >= 0 7.13/3.05 f75(A, B, C, D, E, F, G, H, I, J) -> Com_1(f75(A, B, C, D, E, F, G, H, I, J + 1)) :|: E >= J + 1 7.13/3.05 f83(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(A - 1, B, C, D, E, F, G, H, I, J)) :|: A >= 0 7.13/3.05 f83(A, B, C, D, E, F, G, H, I, J) -> Com_1(f93(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= A + 1 7.13/3.05 f75(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(E - 1, B, C, D, E, F, G, H, I, J)) :|: J >= E 7.13/3.05 f65(A, B, C, D, E, F, G, H, I, J) -> Com_1(f75(A, B, C, D, E, F, G, H, I, 0)) :|: 0 >= I + 1 7.13/3.05 f55(A, B, C, D, E, F, G, H, I, J) -> Com_1(f65(A, B, C, D, E, F, G, H, E - 1, J)) :|: H >= E 7.13/3.05 f45(A, B, C, D, E, F, G, H, I, J) -> Com_1(f55(A, B, C, D, E, F, G, 0, I, J)) :|: A >= E 7.13/3.05 f37(A, B, C, D, E, F, G, H, I, J) -> Com_1(f45(0, B, C, D, E, F, G, H, I, J)) :|: G >= E 7.13/3.05 f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, 0, H, I, J)) :|: 0 >= F + 1 7.13/3.05 f17(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, B, C, D, E, E - 1, G, H, I, J)) :|: D >= E 7.13/3.05 7.13/3.05 The start-symbols are:[f0_10] 7.13/3.05 7.13/3.05 7.13/3.05 ---------------------------------------- 7.13/3.05 7.13/3.05 (1) Koat Proof (FINISHED) 7.13/3.05 YES(?, 15*ar_4 + 65) 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Initial complexity problem: 7.13/3.05 7.13/3.05 1: T: 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, k, l, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9]. 7.13/3.05 7.13/3.05 We thus obtain the following problem: 7.13/3.05 7.13/3.05 2: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Repeatedly propagating knowledge in problem 2 produces the following problem: 7.13/3.05 7.13/3.05 3: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = 8 7.13/3.05 7.13/3.05 Pol(f0) = 8 7.13/3.05 7.13/3.05 Pol(f17) = 8 7.13/3.05 7.13/3.05 Pol(f27) = 7 7.13/3.05 7.13/3.05 Pol(f37) = 6 7.13/3.05 7.13/3.05 Pol(f45) = 5 7.13/3.05 7.13/3.05 Pol(f55) = 4 7.13/3.05 7.13/3.05 Pol(f65) = 3 7.13/3.05 7.13/3.05 Pol(f75) = 2 7.13/3.05 7.13/3.05 Pol(f83) = 1 7.13/3.05 7.13/3.05 Pol(f93) = 0 7.13/3.05 7.13/3.05 orients all transitions weakly and the transitions 7.13/3.05 7.13/3.05 f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 4: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = V_3 7.13/3.05 7.13/3.05 Pol(f27) = V_3 7.13/3.05 7.13/3.05 Pol(f37) = V_3 7.13/3.05 7.13/3.05 Pol(f45) = V_3 7.13/3.05 7.13/3.05 Pol(f55) = V_3 7.13/3.05 7.13/3.05 Pol(f65) = V_3 7.13/3.05 7.13/3.05 Pol(f75) = V_3 7.13/3.05 7.13/3.05 Pol(f83) = V_1 + 1 7.13/3.05 7.13/3.05 Pol(f93) = V_1 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 5: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = V_3 7.13/3.05 7.13/3.05 Pol(f27) = V_3 7.13/3.05 7.13/3.05 Pol(f37) = V_3 7.13/3.05 7.13/3.05 Pol(f45) = V_3 7.13/3.05 7.13/3.05 Pol(f55) = V_3 7.13/3.05 7.13/3.05 Pol(f65) = V_3 7.13/3.05 7.13/3.05 Pol(f75) = V_3 - V_8 7.13/3.05 7.13/3.05 Pol(f83) = V_3 - V_8 7.13/3.05 7.13/3.05 Pol(f93) = V_3 - V_8 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 6: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = V_3 7.13/3.05 7.13/3.05 Pol(f27) = V_3 7.13/3.05 7.13/3.05 Pol(f37) = V_3 7.13/3.05 7.13/3.05 Pol(f45) = V_3 7.13/3.05 7.13/3.05 Pol(f55) = V_3 7.13/3.05 7.13/3.05 Pol(f65) = V_7 + 1 7.13/3.05 7.13/3.05 Pol(f75) = V_7 7.13/3.05 7.13/3.05 Pol(f83) = V_7 7.13/3.05 7.13/3.05 Pol(f93) = V_7 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 7: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = V_3 7.13/3.05 7.13/3.05 Pol(f27) = V_3 7.13/3.05 7.13/3.05 Pol(f37) = V_3 7.13/3.05 7.13/3.05 Pol(f45) = V_3 7.13/3.05 7.13/3.05 Pol(f55) = V_3 - V_6 7.13/3.05 7.13/3.05 Pol(f65) = V_3 - V_6 7.13/3.05 7.13/3.05 Pol(f75) = V_3 - V_6 7.13/3.05 7.13/3.05 Pol(f83) = V_3 - V_6 7.13/3.05 7.13/3.05 Pol(f93) = V_3 - V_6 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 8: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = V_3 7.13/3.05 7.13/3.05 Pol(f27) = V_3 7.13/3.05 7.13/3.05 Pol(f37) = V_3 - V_5 7.13/3.05 7.13/3.05 Pol(f45) = V_3 - V_5 7.13/3.05 7.13/3.05 Pol(f55) = V_3 - V_5 7.13/3.05 7.13/3.05 Pol(f65) = -V_5 + V_7 7.13/3.05 7.13/3.05 Pol(f75) = -V_5 + V_7 7.13/3.05 7.13/3.05 Pol(f83) = -V_5 + V_7 7.13/3.05 7.13/3.05 Pol(f93) = -V_5 + V_7 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 9: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = V_3 7.13/3.05 7.13/3.05 Pol(f27) = V_4 + 1 7.13/3.05 7.13/3.05 Pol(f37) = V_4 7.13/3.05 7.13/3.05 Pol(f45) = V_4 7.13/3.05 7.13/3.05 Pol(f55) = V_4 7.13/3.05 7.13/3.05 Pol(f65) = V_4 7.13/3.05 7.13/3.05 Pol(f75) = V_4 7.13/3.05 7.13/3.05 Pol(f83) = V_4 7.13/3.05 7.13/3.05 Pol(f93) = V_4 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 10: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(koat_start) = V_3 7.13/3.05 7.13/3.05 Pol(f0) = V_3 7.13/3.05 7.13/3.05 Pol(f17) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f27) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f37) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f45) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f55) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f65) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f75) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f83) = -V_2 + V_3 7.13/3.05 7.13/3.05 Pol(f93) = -V_2 + V_3 7.13/3.05 7.13/3.05 orients all transitions weakly and the transition 7.13/3.05 7.13/3.05 f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 11: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ?, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 A polynomial rank function with 7.13/3.05 7.13/3.05 Pol(f45) = -V_1 + V_3 7.13/3.05 7.13/3.05 and size complexities 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-0) = 0 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-1) = 0 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-3) = ar_5 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-4) = ar_6 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-0) = 0 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-3) = ar_5 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-4) = ar_6 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-0) = 0 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-4) = ar_6 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-0) = 0 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-6) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-6) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ]", 0-7) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-0) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-6) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ]", 0-7) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-6) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ]", 0-7) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-0) = ar_4 + 1 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-6) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-7) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-6) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ]", 0-7) = 0 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-5) = ar_4 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-6) = ar_4 + 1 7.13/3.05 7.13/3.05 S("f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-0) = ? 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-5) = 0 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-0) = 0 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-4) = ar_4 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-0) = 0 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-3) = ar_4 + 2 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-4) = 0 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-0) = 0 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-1) = ar_4 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-3) = ar_4 + 1 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-4) = ar_6 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-0) = ar_0 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-1) = ar_3 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-2) = ar_4 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-3) = ar_5 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-4) = ar_6 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-5) = ar_7 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-6) = ar_8 7.13/3.05 7.13/3.05 S("koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]", 0-7) = ar_9 7.13/3.05 7.13/3.05 orients the transitions 7.13/3.05 7.13/3.05 f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 weakly and the transition 7.13/3.05 7.13/3.05 f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 strictly and produces the following problem: 7.13/3.05 7.13/3.05 12: T: 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 0) koat_start(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_4 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, 0, ar_7, ar_8, ar_9)) [ 0 >= ar_5 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_6 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, 0, ar_8, ar_9)) [ ar_0 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_4 - 1, ar_9)) [ ar_7 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, 0)) [ 0 >= ar_8 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_4 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.13/3.05 7.13/3.05 (Comp: 8, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f93(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f83(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(ar_0 - 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1)) [ ar_4 >= ar_9 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f65(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8 - 1, ar_9)) [ ar_8 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f55(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7 + 1, ar_8, ar_9)) [ ar_4 >= ar_7 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 8*ar_4, Cost: 1) f45(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f45(ar_0 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_0 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f37(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f37(ar_0, ar_3, ar_4, ar_5, ar_6 + 1, ar_7, ar_8, ar_9)) [ ar_4 >= ar_6 + 1 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f27(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f27(ar_0, ar_3, ar_4, ar_5 - 1, ar_6, ar_7, ar_8, ar_9)) [ ar_5 >= 0 ] 7.13/3.05 7.13/3.05 (Comp: ar_4, Cost: 1) f17(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(ar_0, ar_3 + 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_4 >= ar_3 + 1 ] 7.13/3.05 7.13/3.05 (Comp: 1, Cost: 1) f0(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f17(0, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) 7.13/3.05 7.13/3.05 start location: koat_start 7.13/3.05 7.13/3.05 leaf cost: 0 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Complexity upper bound 15*ar_4 + 65 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Time: 0.702 sec (SMT: 0.405 sec) 7.13/3.05 7.13/3.05 7.13/3.05 ---------------------------------------- 7.13/3.05 7.13/3.05 (2) 7.13/3.05 BOUNDS(1, n^1) 7.13/3.05 7.13/3.05 ---------------------------------------- 7.13/3.05 7.13/3.05 (3) Loat Proof (FINISHED) 7.13/3.05 7.13/3.05 7.13/3.05 ### Pre-processing the ITS problem ### 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Initial linear ITS problem 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.13/3.05 7.13/3.05 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 7.13/3.05 7.13/3.05 16: f17 -> f27 : F'=-1+E, [ D>=E ], cost: 1 7.13/3.05 7.13/3.05 2: f27 -> f27 : F'=-1+F, [ F>=0 ], cost: 1 7.13/3.05 7.13/3.05 15: f27 -> f37 : G'=0, [ 0>=1+F ], cost: 1 7.13/3.05 7.13/3.05 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 7.13/3.05 7.13/3.05 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.13/3.05 7.13/3.05 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 7.13/3.05 7.13/3.05 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.13/3.05 7.13/3.05 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 7.13/3.05 7.13/3.05 12: f55 -> f65 : Q'=-1+E, [ H>=E ], cost: 1 7.13/3.05 7.13/3.05 6: f65 -> f65 : Q'=-1+Q, [ Q>=0 ], cost: 1 7.13/3.05 7.13/3.05 11: f65 -> f75 : J'=0, [ 0>=1+Q ], cost: 1 7.13/3.05 7.13/3.05 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 7.13/3.05 7.13/3.05 10: f75 -> f83 : A'=-1+E, [ J>=E ], cost: 1 7.13/3.05 7.13/3.05 8: f83 -> f83 : A'=-1+A, [ A>=0 ], cost: 1 7.13/3.05 7.13/3.05 9: f83 -> f93 : [ 0>=1+A ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Removed unreachable and leaf rules: 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.13/3.05 7.13/3.05 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 7.13/3.05 7.13/3.05 16: f17 -> f27 : F'=-1+E, [ D>=E ], cost: 1 7.13/3.05 7.13/3.05 2: f27 -> f27 : F'=-1+F, [ F>=0 ], cost: 1 7.13/3.05 7.13/3.05 15: f27 -> f37 : G'=0, [ 0>=1+F ], cost: 1 7.13/3.05 7.13/3.05 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 7.13/3.05 7.13/3.05 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.13/3.05 7.13/3.05 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 7.13/3.05 7.13/3.05 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.13/3.05 7.13/3.05 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 7.13/3.05 7.13/3.05 12: f55 -> f65 : Q'=-1+E, [ H>=E ], cost: 1 7.13/3.05 7.13/3.05 6: f65 -> f65 : Q'=-1+Q, [ Q>=0 ], cost: 1 7.13/3.05 7.13/3.05 11: f65 -> f75 : J'=0, [ 0>=1+Q ], cost: 1 7.13/3.05 7.13/3.05 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 7.13/3.05 7.13/3.05 10: f75 -> f83 : A'=-1+E, [ J>=E ], cost: 1 7.13/3.05 7.13/3.05 8: f83 -> f83 : A'=-1+A, [ A>=0 ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 ### Simplification by acceleration and chaining ### 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 1. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 1 with metering function -D+E, yielding the new rule 17. 7.13/3.05 7.13/3.05 Removing the simple loops: 1. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 2. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 2: f27 -> f27 : F'=-1+F, [ F>=0 ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 2 with metering function 1+F, yielding the new rule 18. 7.13/3.05 7.13/3.05 Removing the simple loops: 2. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 3. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 3 with metering function -G+E, yielding the new rule 19. 7.13/3.05 7.13/3.05 Removing the simple loops: 3. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 4. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 4 with metering function -A+E, yielding the new rule 20. 7.13/3.05 7.13/3.05 Removing the simple loops: 4. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 5. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 5 with metering function -H+E, yielding the new rule 21. 7.13/3.05 7.13/3.05 Removing the simple loops: 5. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 6. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 6: f65 -> f65 : Q'=-1+Q, [ Q>=0 ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 6 with metering function 1+Q, yielding the new rule 22. 7.13/3.05 7.13/3.05 Removing the simple loops: 6. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 7. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 7 with metering function -J+E, yielding the new rule 23. 7.13/3.05 7.13/3.05 Removing the simple loops: 7. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerating simple loops of location 8. 7.13/3.05 7.13/3.05 Accelerating the following rules: 7.13/3.05 7.13/3.05 8: f83 -> f83 : A'=-1+A, [ A>=0 ], cost: 1 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated rule 8 with metering function 1+A, yielding the new rule 24. 7.13/3.05 7.13/3.05 Removing the simple loops: 8. 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Accelerated all simple loops using metering functions (where possible): 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.13/3.05 7.13/3.05 16: f17 -> f27 : F'=-1+E, [ D>=E ], cost: 1 7.13/3.05 7.13/3.05 17: f17 -> f17 : D'=E, [ E>=1+D ], cost: -D+E 7.13/3.05 7.13/3.05 15: f27 -> f37 : G'=0, [ 0>=1+F ], cost: 1 7.13/3.05 7.13/3.05 18: f27 -> f27 : F'=-1, [ F>=0 ], cost: 1+F 7.13/3.05 7.13/3.05 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.13/3.05 7.13/3.05 19: f37 -> f37 : G'=E, [ E>=1+G ], cost: -G+E 7.13/3.05 7.13/3.05 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.13/3.05 7.13/3.05 20: f45 -> f45 : A'=E, [ E>=1+A ], cost: -A+E 7.13/3.05 7.13/3.05 12: f55 -> f65 : Q'=-1+E, [ H>=E ], cost: 1 7.13/3.05 7.13/3.05 21: f55 -> f55 : H'=E, [ E>=1+H ], cost: -H+E 7.13/3.05 7.13/3.05 11: f65 -> f75 : J'=0, [ 0>=1+Q ], cost: 1 7.13/3.05 7.13/3.05 22: f65 -> f65 : Q'=-1, [ Q>=0 ], cost: 1+Q 7.13/3.05 7.13/3.05 10: f75 -> f83 : A'=-1+E, [ J>=E ], cost: 1 7.13/3.05 7.13/3.05 23: f75 -> f75 : J'=E, [ E>=1+J ], cost: -J+E 7.13/3.05 7.13/3.05 24: f83 -> f83 : A'=-1, [ A>=0 ], cost: 1+A 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Chained accelerated rules (with incoming rules): 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.13/3.05 7.13/3.05 25: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=E, [ E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 16: f17 -> f27 : F'=-1+E, [ D>=E ], cost: 1 7.13/3.05 7.13/3.05 26: f17 -> f27 : F'=-1, [ D>=E && -1+E>=0 ], cost: 1+E 7.13/3.05 7.13/3.05 15: f27 -> f37 : G'=0, [ 0>=1+F ], cost: 1 7.13/3.05 7.13/3.05 27: f27 -> f37 : G'=E, [ 0>=1+F && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.13/3.05 7.13/3.05 28: f37 -> f45 : A'=E, [ G>=E && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.13/3.05 7.13/3.05 29: f45 -> f55 : H'=E, [ A>=E && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 12: f55 -> f65 : Q'=-1+E, [ H>=E ], cost: 1 7.13/3.05 7.13/3.05 30: f55 -> f65 : Q'=-1, [ H>=E && -1+E>=0 ], cost: 1+E 7.13/3.05 7.13/3.05 11: f65 -> f75 : J'=0, [ 0>=1+Q ], cost: 1 7.13/3.05 7.13/3.05 31: f65 -> f75 : J'=E, [ 0>=1+Q && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 10: f75 -> f83 : A'=-1+E, [ J>=E ], cost: 1 7.13/3.05 7.13/3.05 32: f75 -> f83 : A'=-1, [ J>=E && -1+E>=0 ], cost: 1+E 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Removed unreachable locations (and leaf rules with constant cost): 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.13/3.05 7.13/3.05 25: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=E, [ E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 16: f17 -> f27 : F'=-1+E, [ D>=E ], cost: 1 7.13/3.05 7.13/3.05 26: f17 -> f27 : F'=-1, [ D>=E && -1+E>=0 ], cost: 1+E 7.13/3.05 7.13/3.05 15: f27 -> f37 : G'=0, [ 0>=1+F ], cost: 1 7.13/3.05 7.13/3.05 27: f27 -> f37 : G'=E, [ 0>=1+F && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.13/3.05 7.13/3.05 28: f37 -> f45 : A'=E, [ G>=E && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.13/3.05 7.13/3.05 29: f45 -> f55 : H'=E, [ A>=E && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 12: f55 -> f65 : Q'=-1+E, [ H>=E ], cost: 1 7.13/3.05 7.13/3.05 30: f55 -> f65 : Q'=-1, [ H>=E && -1+E>=0 ], cost: 1+E 7.13/3.05 7.13/3.05 11: f65 -> f75 : J'=0, [ 0>=1+Q ], cost: 1 7.13/3.05 7.13/3.05 31: f65 -> f75 : J'=E, [ 0>=1+Q && E>=1 ], cost: 1+E 7.13/3.05 7.13/3.05 32: f75 -> f83 : A'=-1, [ J>=E && -1+E>=0 ], cost: 1+E 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Eliminated locations (on tree-shaped paths): 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 33: f0 -> f27 : A'=0, B'=free_1, C'=free, D'=0, F'=-1+E, [ 0>=E ], cost: 2 7.13/3.05 7.13/3.05 34: f0 -> f27 : A'=0, B'=free_1, C'=free, D'=E, F'=-1+E, [ E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 35: f0 -> f27 : A'=0, B'=free_1, C'=free, D'=E, F'=-1, [ E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 36: f27 -> f45 : A'=0, G'=0, [ 0>=1+F && 0>=E ], cost: 2 7.13/3.05 7.13/3.05 37: f27 -> f45 : A'=0, G'=E, [ 0>=1+F && E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 38: f27 -> f45 : A'=E, G'=E, [ 0>=1+F && E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 39: f45 -> f65 : H'=0, Q'=-1+E, [ A>=E && 0>=E ], cost: 2 7.13/3.05 7.13/3.05 40: f45 -> f65 : H'=E, Q'=-1+E, [ A>=E && E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 41: f45 -> f65 : H'=E, Q'=-1, [ A>=E && E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 42: f65 -> f83 : A'=-1, J'=E, [ 0>=1+Q && E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Eliminated locations (on tree-shaped paths): 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 43: f0 -> f45 : A'=0, B'=free_1, C'=free, D'=0, F'=-1+E, G'=0, [ 0>=E ], cost: 4 7.13/3.05 7.13/3.05 44: f0 -> f45 : A'=0, B'=free_1, C'=free, D'=E, F'=-1, G'=E, [ E>=1 ], cost: 4+3*E 7.13/3.05 7.13/3.05 45: f0 -> f45 : A'=E, B'=free_1, C'=free, D'=E, F'=-1, G'=E, [ E>=1 ], cost: 4+4*E 7.13/3.05 7.13/3.05 46: f0 -> [18] : [ E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 48: f45 -> f83 : A'=-1, H'=E, Q'=-1, J'=E, [ A>=E && E>=1 ], cost: 4+4*E 7.13/3.05 7.13/3.05 49: f45 -> [19] : [ A>=E && E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Eliminated locations (on tree-shaped paths): 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 46: f0 -> [18] : [ E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 50: f0 -> f83 : A'=-1, B'=free_1, C'=free, D'=E, F'=-1, G'=E, H'=E, Q'=-1, J'=E, [ E>=1 ], cost: 8+8*E 7.13/3.05 7.13/3.05 51: f0 -> [19] : A'=E, B'=free_1, C'=free, D'=E, F'=-1, G'=E, [ E>=1 ], cost: 6+5*E 7.13/3.05 7.13/3.05 52: f0 -> [20] : [ E>=1 ], cost: 4+3*E 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 ### Computing asymptotic complexity ### 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Fully simplified ITS problem 7.13/3.05 7.13/3.05 Start location: f0 7.13/3.05 7.13/3.05 46: f0 -> [18] : [ E>=1 ], cost: 2+E 7.13/3.05 7.13/3.05 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 7.13/3.05 7.13/3.05 50: f0 -> f83 : A'=-1, B'=free_1, C'=free, D'=E, F'=-1, G'=E, H'=E, Q'=-1, J'=E, [ E>=1 ], cost: 8+8*E 7.13/3.05 7.13/3.05 51: f0 -> [19] : A'=E, B'=free_1, C'=free, D'=E, F'=-1, G'=E, [ E>=1 ], cost: 6+5*E 7.13/3.05 7.13/3.05 52: f0 -> [20] : [ E>=1 ], cost: 4+3*E 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Computing asymptotic complexity for rule 46 7.13/3.05 7.13/3.05 Solved the limit problem by the following transformations: 7.13/3.05 7.13/3.05 Created initial limit problem: 7.13/3.05 7.13/3.05 2+E (+), E (+/+!) [not solved] 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 removing all constraints (solved by SMT) 7.13/3.05 7.13/3.05 resulting limit problem: [solved] 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 applying transformation rule (C) using substitution {E==n} 7.13/3.05 7.13/3.05 resulting limit problem: 7.13/3.05 7.13/3.05 [solved] 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Solution: 7.13/3.05 7.13/3.05 E / n 7.13/3.05 7.13/3.05 Resulting cost 2+n has complexity: Poly(n^1) 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Found new complexity Poly(n^1). 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 Obtained the following overall complexity (w.r.t. the length of the input n): 7.13/3.05 7.13/3.05 Complexity: Poly(n^1) 7.13/3.05 7.13/3.05 Cpx degree: 1 7.13/3.05 7.13/3.05 Solved cost: 2+n 7.13/3.05 7.13/3.05 Rule cost: 2+E 7.13/3.05 7.13/3.05 Rule guard: [ E>=1 ] 7.13/3.05 7.13/3.05 7.13/3.05 7.13/3.05 WORST_CASE(Omega(n^1),?) 7.13/3.05 7.13/3.05 7.13/3.05 ---------------------------------------- 7.13/3.05 7.13/3.05 (4) 7.13/3.05 BOUNDS(n^1, INF) 7.13/3.07 EOF