7.07/3.15 WORST_CASE(Omega(n^1), O(n^1)) 7.07/3.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 7.07/3.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 7.07/3.17 7.07/3.17 7.07/3.17 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 7.07/3.17 7.07/3.17 (0) CpxIntTrs 7.07/3.17 (1) Koat Proof [FINISHED, 616 ms] 7.07/3.17 (2) BOUNDS(1, n^1) 7.07/3.17 (3) Loat Proof [FINISHED, 1434 ms] 7.07/3.17 (4) BOUNDS(n^1, INF) 7.07/3.17 7.07/3.17 7.07/3.17 ---------------------------------------- 7.07/3.17 7.07/3.17 (0) 7.07/3.17 Obligation: 7.07/3.17 Complexity Int TRS consisting of the following rules: 7.07/3.17 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 7.07/3.17 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 7.07/3.17 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)) :|: E >= F + 1 7.07/3.17 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 7.07/3.17 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 7.07/3.17 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 7.07/3.17 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)) :|: E >= I + 1 7.07/3.17 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 7.07/3.17 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)) :|: E >= A + 1 7.07/3.17 f83(A, B, C, D, E, F, G, H, I, J) -> Com_1(f93(A, B, C, D, E, F, G, H, I, J)) :|: A >= E 7.07/3.17 f75(A, B, C, D, E, F, G, H, I, J) -> Com_1(f83(0, B, C, D, E, F, G, H, I, J)) :|: J >= E 7.07/3.17 f65(A, B, C, D, E, F, G, H, I, J) -> Com_1(f75(A, B, C, D, E, F, G, H, I, 0)) :|: I >= E 7.07/3.17 f55(A, B, C, D, E, F, G, H, I, J) -> Com_1(f65(A, B, C, D, E, F, G, H, 0, J)) :|: H >= E 7.07/3.17 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 7.07/3.17 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 7.07/3.17 f27(A, B, C, D, E, F, G, H, I, J) -> Com_1(f37(A, B, C, D, E, F, 0, H, I, J)) :|: F >= E 7.07/3.17 f17(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, B, C, D, E, 0, G, H, I, J)) :|: D >= E 7.07/3.17 7.07/3.17 The start-symbols are:[f0_10] 7.07/3.17 7.07/3.17 7.07/3.17 ---------------------------------------- 7.07/3.17 7.07/3.17 (1) Koat Proof (FINISHED) 7.07/3.17 YES(?, 15*ar_4 + 65) 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 Initial complexity problem: 7.07/3.17 7.07/3.17 1: T: 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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(0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 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]. 7.07/3.17 7.07/3.17 We thus obtain the following problem: 7.07/3.17 7.07/3.17 2: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 Repeatedly propagating knowledge in problem 2 produces the following problem: 7.07/3.17 7.07/3.17 3: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: ?, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = 8 7.07/3.17 7.07/3.17 Pol(f0) = 8 7.07/3.17 7.07/3.17 Pol(f17) = 8 7.07/3.17 7.07/3.17 Pol(f27) = 7 7.07/3.17 7.07/3.17 Pol(f37) = 6 7.07/3.17 7.07/3.17 Pol(f45) = 5 7.07/3.17 7.07/3.17 Pol(f55) = 4 7.07/3.17 7.07/3.17 Pol(f65) = 3 7.07/3.17 7.07/3.17 Pol(f75) = 2 7.07/3.17 7.07/3.17 Pol(f83) = 1 7.07/3.17 7.07/3.17 Pol(f93) = 0 7.07/3.17 7.07/3.17 orients all transitions weakly and the transitions 7.07/3.17 7.07/3.17 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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 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 ] 7.07/3.17 7.07/3.17 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 ] 7.07/3.17 7.07/3.17 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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 4: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = V_3 7.07/3.17 7.07/3.17 Pol(f27) = V_3 7.07/3.17 7.07/3.17 Pol(f37) = V_3 7.07/3.17 7.07/3.17 Pol(f45) = V_3 7.07/3.17 7.07/3.17 Pol(f55) = V_3 7.07/3.17 7.07/3.17 Pol(f65) = V_3 7.07/3.17 7.07/3.17 Pol(f75) = V_3 7.07/3.17 7.07/3.17 Pol(f83) = -V_1 + V_3 7.07/3.17 7.07/3.17 Pol(f93) = -V_1 + V_3 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 5: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = V_3 7.07/3.17 7.07/3.17 Pol(f27) = V_3 7.07/3.17 7.07/3.17 Pol(f37) = V_3 7.07/3.17 7.07/3.17 Pol(f45) = V_3 7.07/3.17 7.07/3.17 Pol(f55) = V_3 7.07/3.17 7.07/3.17 Pol(f65) = V_3 7.07/3.17 7.07/3.17 Pol(f75) = V_3 - V_8 7.07/3.17 7.07/3.17 Pol(f83) = V_3 - V_8 7.07/3.17 7.07/3.17 Pol(f93) = V_3 - V_8 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 6: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = V_3 7.07/3.17 7.07/3.17 Pol(f27) = V_3 7.07/3.17 7.07/3.17 Pol(f37) = V_3 7.07/3.17 7.07/3.17 Pol(f45) = V_3 7.07/3.17 7.07/3.17 Pol(f55) = V_3 7.07/3.17 7.07/3.17 Pol(f65) = V_3 - V_7 7.07/3.17 7.07/3.17 Pol(f75) = V_3 - V_7 7.07/3.17 7.07/3.17 Pol(f83) = V_3 - V_7 7.07/3.17 7.07/3.17 Pol(f93) = V_3 - V_7 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 7: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = V_3 7.07/3.17 7.07/3.17 Pol(f27) = V_3 7.07/3.17 7.07/3.17 Pol(f37) = V_3 7.07/3.17 7.07/3.17 Pol(f45) = V_3 7.07/3.17 7.07/3.17 Pol(f55) = V_3 - V_6 7.07/3.17 7.07/3.17 Pol(f65) = V_3 - V_6 7.07/3.17 7.07/3.17 Pol(f75) = V_3 - V_6 7.07/3.17 7.07/3.17 Pol(f83) = V_3 - V_6 7.07/3.17 7.07/3.17 Pol(f93) = V_3 - V_6 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 8: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = V_3 7.07/3.17 7.07/3.17 Pol(f27) = V_3 7.07/3.17 7.07/3.17 Pol(f37) = V_3 - V_5 7.07/3.17 7.07/3.17 Pol(f45) = V_3 - V_5 7.07/3.17 7.07/3.17 Pol(f55) = V_3 - V_5 7.07/3.17 7.07/3.17 Pol(f65) = V_3 - V_5 7.07/3.17 7.07/3.17 Pol(f75) = V_3 - V_5 7.07/3.17 7.07/3.17 Pol(f83) = V_3 - V_5 7.07/3.17 7.07/3.17 Pol(f93) = V_3 - V_5 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 9: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = V_3 7.07/3.17 7.07/3.17 Pol(f27) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f37) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f45) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f55) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f65) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f75) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f83) = V_3 - V_4 7.07/3.17 7.07/3.17 Pol(f93) = V_3 - V_4 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 10: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(koat_start) = V_3 7.07/3.17 7.07/3.17 Pol(f0) = V_3 7.07/3.17 7.07/3.17 Pol(f17) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f27) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f37) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f45) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f55) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f65) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f75) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f83) = -V_2 + V_3 7.07/3.17 7.07/3.17 Pol(f93) = -V_2 + V_3 7.07/3.17 7.07/3.17 orients all transitions weakly and the transition 7.07/3.17 7.07/3.17 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 ] 7.07/3.17 7.07/3.17 strictly and produces the following problem: 7.07/3.17 7.07/3.17 11: T: 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_5 >= ar_4 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_8 >= ar_4 ] 7.07/3.17 7.07/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.07/3.17 7.07/3.17 (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)) [ ar_0 >= ar_4 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_0 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_8 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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_4 >= ar_5 + 1 ] 7.07/3.17 7.07/3.17 (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 ] 7.07/3.17 7.07/3.17 (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)) 7.07/3.17 7.07/3.17 start location: koat_start 7.07/3.17 7.07/3.17 leaf cost: 0 7.07/3.17 7.07/3.17 7.07/3.17 7.07/3.17 A polynomial rank function with 7.07/3.17 7.07/3.17 Pol(f45) = -V_1 + V_3 7.07/3.17 7.07/3.17 and size complexities 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.07/3.17 7.07/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-0) = 0 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-4) = ar_6 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-5) = ar_7 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-6) = ar_8 7.27/3.17 7.27/3.17 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_4 >= ar_5 + 1 ]", 0-7) = ar_9 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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) = ? 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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) = ? 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-0) = ? 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-4) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-5) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-6) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_8 + 1 ]", 0-7) = ar_9 7.27/3.17 7.27/3.17 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) = ? 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-0) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-4) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-5) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-6) = ar_4 7.27/3.17 7.27/3.17 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_4 >= ar_0 + 1 ]", 0-7) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-0) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-4) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-5) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-6) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_0 >= ar_4 ]", 0-7) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-0) = 0 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-4) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-5) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-6) = ar_4 7.27/3.17 7.27/3.17 S("f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ]", 0-7) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-0) = ? 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-4) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-5) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-6) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_8 >= ar_4 ]", 0-7) = 0 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-0) = ? 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-4) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-5) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-6) = 0 7.27/3.17 7.27/3.17 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, 0, ar_9)) [ ar_7 >= ar_4 ]", 0-7) = ar_9 7.27/3.17 7.27/3.17 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) = ? 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-0) = 0 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-3) = ar_4 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-4) = 0 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-5) = ar_7 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-6) = ar_8 7.27/3.17 7.27/3.17 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)) [ ar_5 >= ar_4 ]", 0-7) = ar_9 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-0) = 0 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-1) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-2) = ar_4 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-3) = 0 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-4) = ar_6 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-5) = ar_7 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-6) = ar_8 7.27/3.17 7.27/3.17 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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ]", 0-7) = ar_9 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 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 7.27/3.17 7.27/3.17 orients the transitions 7.27/3.17 7.27/3.17 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 ] 7.27/3.17 7.27/3.17 weakly and the transition 7.27/3.17 7.27/3.17 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 ] 7.27/3.17 7.27/3.17 strictly and produces the following problem: 7.27/3.17 7.27/3.17 12: T: 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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, 0, ar_6, ar_7, ar_8, ar_9)) [ ar_3 >= ar_4 ] 7.27/3.17 7.27/3.17 (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)) [ ar_5 >= ar_4 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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, 0, ar_9)) [ ar_7 >= ar_4 ] 7.27/3.17 7.27/3.17 (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)) [ ar_8 >= ar_4 ] 7.27/3.17 7.27/3.17 (Comp: 8, Cost: 1) f75(ar_0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f83(0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_9 >= ar_4 ] 7.27/3.17 7.27/3.17 (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)) [ ar_0 >= ar_4 ] 7.27/3.17 7.27/3.17 (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_4 >= ar_0 + 1 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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_4 >= ar_8 + 1 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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_4 >= ar_5 + 1 ] 7.27/3.17 7.27/3.17 (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 ] 7.27/3.17 7.27/3.17 (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)) 7.27/3.17 7.27/3.17 start location: koat_start 7.27/3.17 7.27/3.17 leaf cost: 0 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Complexity upper bound 15*ar_4 + 65 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Time: 0.661 sec (SMT: 0.362 sec) 7.27/3.17 7.27/3.17 7.27/3.17 ---------------------------------------- 7.27/3.17 7.27/3.17 (2) 7.27/3.17 BOUNDS(1, n^1) 7.27/3.17 7.27/3.17 ---------------------------------------- 7.27/3.17 7.27/3.17 (3) Loat Proof (FINISHED) 7.27/3.17 7.27/3.17 7.27/3.17 ### Pre-processing the ITS problem ### 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Initial linear ITS problem 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.27/3.17 7.27/3.17 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 7.27/3.17 7.27/3.17 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 7.27/3.17 7.27/3.17 2: f27 -> f27 : F'=1+F, [ E>=1+F ], cost: 1 7.27/3.17 7.27/3.17 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 7.27/3.17 7.27/3.17 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 7.27/3.17 7.27/3.17 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.27/3.17 7.27/3.17 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 7.27/3.17 7.27/3.17 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.27/3.17 7.27/3.17 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 7.27/3.17 7.27/3.17 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 7.27/3.17 7.27/3.17 6: f65 -> f65 : Q'=1+Q, [ E>=1+Q ], cost: 1 7.27/3.17 7.27/3.17 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7.27/3.17 7.27/3.17 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 7.27/3.17 7.27/3.17 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 7.27/3.17 7.27/3.17 8: f83 -> f83 : A'=1+A, [ E>=1+A ], cost: 1 7.27/3.17 7.27/3.17 9: f83 -> f93 : [ A>=E ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Removed unreachable and leaf rules: 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.27/3.17 7.27/3.17 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 7.27/3.17 7.27/3.17 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 7.27/3.17 7.27/3.17 2: f27 -> f27 : F'=1+F, [ E>=1+F ], cost: 1 7.27/3.17 7.27/3.17 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 7.27/3.17 7.27/3.17 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 7.27/3.17 7.27/3.17 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.27/3.17 7.27/3.17 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 7.27/3.17 7.27/3.17 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.27/3.17 7.27/3.17 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 7.27/3.17 7.27/3.17 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 7.27/3.17 7.27/3.17 6: f65 -> f65 : Q'=1+Q, [ E>=1+Q ], cost: 1 7.27/3.17 7.27/3.17 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7.27/3.17 7.27/3.17 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 7.27/3.17 7.27/3.17 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 7.27/3.17 7.27/3.17 8: f83 -> f83 : A'=1+A, [ E>=1+A ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 ### Simplification by acceleration and chaining ### 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 1. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 1 with metering function -D+E, yielding the new rule 17. 7.27/3.17 7.27/3.17 Removing the simple loops: 1. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 2. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 2: f27 -> f27 : F'=1+F, [ E>=1+F ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 2 with metering function -F+E, yielding the new rule 18. 7.27/3.17 7.27/3.17 Removing the simple loops: 2. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 3. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 3 with metering function -G+E, yielding the new rule 19. 7.27/3.17 7.27/3.17 Removing the simple loops: 3. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 4. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 4 with metering function -A+E, yielding the new rule 20. 7.27/3.17 7.27/3.17 Removing the simple loops: 4. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 5. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 5 with metering function -H+E, yielding the new rule 21. 7.27/3.17 7.27/3.17 Removing the simple loops: 5. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 6. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 6: f65 -> f65 : Q'=1+Q, [ E>=1+Q ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 6 with metering function -Q+E, yielding the new rule 22. 7.27/3.17 7.27/3.17 Removing the simple loops: 6. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 7. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 7 with metering function -J+E, yielding the new rule 23. 7.27/3.17 7.27/3.17 Removing the simple loops: 7. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerating simple loops of location 8. 7.27/3.17 7.27/3.17 Accelerating the following rules: 7.27/3.17 7.27/3.17 8: f83 -> f83 : A'=1+A, [ E>=1+A ], cost: 1 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated rule 8 with metering function -A+E, yielding the new rule 24. 7.27/3.17 7.27/3.17 Removing the simple loops: 8. 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Accelerated all simple loops using metering functions (where possible): 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.27/3.17 7.27/3.17 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 7.27/3.17 7.27/3.17 17: f17 -> f17 : D'=E, [ E>=1+D ], cost: -D+E 7.27/3.17 7.27/3.17 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 7.27/3.17 7.27/3.17 18: f27 -> f27 : F'=E, [ E>=1+F ], cost: -F+E 7.27/3.17 7.27/3.17 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.27/3.17 7.27/3.17 19: f37 -> f37 : G'=E, [ E>=1+G ], cost: -G+E 7.27/3.17 7.27/3.17 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.27/3.17 7.27/3.17 20: f45 -> f45 : A'=E, [ E>=1+A ], cost: -A+E 7.27/3.17 7.27/3.17 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 7.27/3.17 7.27/3.17 21: f55 -> f55 : H'=E, [ E>=1+H ], cost: -H+E 7.27/3.17 7.27/3.17 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7.27/3.17 7.27/3.17 22: f65 -> f65 : Q'=E, [ E>=1+Q ], cost: -Q+E 7.27/3.17 7.27/3.17 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 7.27/3.17 7.27/3.17 23: f75 -> f75 : J'=E, [ E>=1+J ], cost: -J+E 7.27/3.17 7.27/3.17 24: f83 -> f83 : A'=E, [ E>=1+A ], cost: -A+E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Chained accelerated rules (with incoming rules): 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.27/3.17 7.27/3.17 25: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=E, [ E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 7.27/3.17 7.27/3.17 26: f17 -> f27 : F'=E, [ D>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 7.27/3.17 7.27/3.17 27: f27 -> f37 : G'=E, [ F>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.27/3.17 7.27/3.17 28: f37 -> f45 : A'=E, [ G>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.27/3.17 7.27/3.17 29: f45 -> f55 : H'=E, [ A>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 7.27/3.17 7.27/3.17 30: f55 -> f65 : Q'=E, [ H>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7.27/3.17 7.27/3.17 31: f65 -> f75 : J'=E, [ Q>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 7.27/3.17 7.27/3.17 32: f75 -> f83 : A'=E, [ J>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Removed unreachable locations (and leaf rules with constant cost): 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 0: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=0, [], cost: 1 7.27/3.17 7.27/3.17 25: f0 -> f17 : A'=0, B'=free_1, C'=free, D'=E, [ E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 7.27/3.17 7.27/3.17 26: f17 -> f27 : F'=E, [ D>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 7.27/3.17 7.27/3.17 27: f27 -> f37 : G'=E, [ F>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 7.27/3.17 7.27/3.17 28: f37 -> f45 : A'=E, [ G>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 7.27/3.17 7.27/3.17 29: f45 -> f55 : H'=E, [ A>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 7.27/3.17 7.27/3.17 30: f55 -> f65 : Q'=E, [ H>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7.27/3.17 7.27/3.17 31: f65 -> f75 : J'=E, [ Q>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 32: f75 -> f83 : A'=E, [ J>=E && E>=1 ], cost: 1+E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Eliminated locations (on tree-shaped paths): 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 33: f0 -> f27 : A'=0, B'=free_1, C'=free, D'=0, F'=0, [ 0>=E ], cost: 2 7.27/3.17 7.27/3.17 34: f0 -> f27 : A'=0, B'=free_1, C'=free, D'=E, F'=0, [ E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 35: f0 -> f27 : A'=0, B'=free_1, C'=free, D'=E, F'=E, [ E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 36: f27 -> f45 : A'=0, G'=0, [ F>=E && 0>=E ], cost: 2 7.27/3.17 7.27/3.17 37: f27 -> f45 : A'=0, G'=E, [ F>=E && E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 38: f27 -> f45 : A'=E, G'=E, [ F>=E && E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 39: f45 -> f65 : H'=0, Q'=0, [ A>=E && 0>=E ], cost: 2 7.27/3.17 7.27/3.17 40: f45 -> f65 : H'=E, Q'=0, [ A>=E && E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 41: f45 -> f65 : H'=E, Q'=E, [ A>=E && E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 42: f65 -> f83 : A'=E, J'=E, [ Q>=E && E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Eliminated locations (on tree-shaped paths): 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 43: f0 -> f45 : A'=0, B'=free_1, C'=free, D'=0, F'=0, G'=0, [ 0>=E ], cost: 4 7.27/3.17 7.27/3.17 44: f0 -> f45 : A'=0, B'=free_1, C'=free, D'=E, F'=E, G'=E, [ E>=1 ], cost: 4+3*E 7.27/3.17 7.27/3.17 45: f0 -> f45 : A'=E, B'=free_1, C'=free, D'=E, F'=E, G'=E, [ E>=1 ], cost: 4+4*E 7.27/3.17 7.27/3.17 46: f0 -> [18] : [ E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 48: f45 -> f83 : A'=E, H'=E, Q'=E, J'=E, [ A>=E && E>=1 ], cost: 4+4*E 7.27/3.17 7.27/3.17 49: f45 -> [19] : [ A>=E && E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Eliminated locations (on tree-shaped paths): 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 46: f0 -> [18] : [ E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 50: f0 -> f83 : A'=E, B'=free_1, C'=free, D'=E, F'=E, G'=E, H'=E, Q'=E, J'=E, [ E>=1 ], cost: 8+8*E 7.27/3.17 7.27/3.17 51: f0 -> [19] : A'=E, B'=free_1, C'=free, D'=E, F'=E, G'=E, [ E>=1 ], cost: 6+5*E 7.27/3.17 7.27/3.17 52: f0 -> [20] : [ E>=1 ], cost: 4+3*E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 ### Computing asymptotic complexity ### 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Fully simplified ITS problem 7.27/3.17 7.27/3.17 Start location: f0 7.27/3.17 7.27/3.17 46: f0 -> [18] : [ E>=1 ], cost: 2+E 7.27/3.17 7.27/3.17 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 7.27/3.17 7.27/3.17 50: f0 -> f83 : A'=E, B'=free_1, C'=free, D'=E, F'=E, G'=E, H'=E, Q'=E, J'=E, [ E>=1 ], cost: 8+8*E 7.27/3.17 7.27/3.17 51: f0 -> [19] : A'=E, B'=free_1, C'=free, D'=E, F'=E, G'=E, [ E>=1 ], cost: 6+5*E 7.27/3.17 7.27/3.17 52: f0 -> [20] : [ E>=1 ], cost: 4+3*E 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Computing asymptotic complexity for rule 46 7.27/3.17 7.27/3.17 Solved the limit problem by the following transformations: 7.27/3.17 7.27/3.17 Created initial limit problem: 7.27/3.17 7.27/3.17 2+E (+), E (+/+!) [not solved] 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 removing all constraints (solved by SMT) 7.27/3.17 7.27/3.17 resulting limit problem: [solved] 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 applying transformation rule (C) using substitution {E==n} 7.27/3.17 7.27/3.17 resulting limit problem: 7.27/3.17 7.27/3.17 [solved] 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Solution: 7.27/3.17 7.27/3.17 E / n 7.27/3.17 7.27/3.17 Resulting cost 2+n has complexity: Poly(n^1) 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Found new complexity Poly(n^1). 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 Obtained the following overall complexity (w.r.t. the length of the input n): 7.27/3.17 7.27/3.17 Complexity: Poly(n^1) 7.27/3.17 7.27/3.17 Cpx degree: 1 7.27/3.17 7.27/3.17 Solved cost: 2+n 7.27/3.17 7.27/3.17 Rule cost: 2+E 7.27/3.17 7.27/3.17 Rule guard: [ E>=1 ] 7.27/3.17 7.27/3.17 7.27/3.17 7.27/3.17 WORST_CASE(Omega(n^1),?) 7.27/3.17 7.27/3.17 7.27/3.17 ---------------------------------------- 7.27/3.17 7.27/3.17 (4) 7.27/3.17 BOUNDS(n^1, INF) 7.28/3.20 EOF