/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 518 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 1425 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 The start-symbols are:[f0_10] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 15*Ar_4 + 65) Initial complexity problem: 1: T: (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, Fresh_0, Fresh_1, 0, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9)) (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] start location: koat_start leaf cost: 0 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]. We thus obtain the following problem: 2: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 8 Pol(f0) = 8 Pol(f17) = 8 Pol(f27) = 7 Pol(f37) = 6 Pol(f45) = 5 Pol(f55) = 4 Pol(f65) = 3 Pol(f75) = 2 Pol(f83) = 1 Pol(f93) = 0 orients all transitions weakly and the transitions 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] strictly and produces the following problem: 4: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = V_3 Pol(f27) = V_3 Pol(f37) = V_3 Pol(f45) = V_3 Pol(f55) = V_3 Pol(f65) = V_3 Pol(f75) = V_3 Pol(f83) = -V_1 + V_3 Pol(f93) = -V_1 + V_3 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 5: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = V_3 Pol(f27) = V_3 Pol(f37) = V_3 Pol(f45) = V_3 Pol(f55) = V_3 Pol(f65) = V_3 Pol(f75) = V_3 - V_8 Pol(f83) = V_3 - V_8 Pol(f93) = V_3 - V_8 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 6: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = V_3 Pol(f27) = V_3 Pol(f37) = V_3 Pol(f45) = V_3 Pol(f55) = V_3 Pol(f65) = V_3 - V_7 Pol(f75) = V_3 - V_7 Pol(f83) = V_3 - V_7 Pol(f93) = V_3 - V_7 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 7: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = V_3 Pol(f27) = V_3 Pol(f37) = V_3 Pol(f45) = V_3 Pol(f55) = V_3 - V_6 Pol(f65) = V_3 - V_6 Pol(f75) = V_3 - V_6 Pol(f83) = V_3 - V_6 Pol(f93) = V_3 - V_6 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 8: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = V_3 Pol(f27) = V_3 Pol(f37) = V_3 - V_5 Pol(f45) = V_3 - V_5 Pol(f55) = V_3 - V_5 Pol(f65) = V_3 - V_5 Pol(f75) = V_3 - V_5 Pol(f83) = V_3 - V_5 Pol(f93) = V_3 - V_5 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 9: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = V_3 Pol(f27) = V_3 - V_4 Pol(f37) = V_3 - V_4 Pol(f45) = V_3 - V_4 Pol(f55) = V_3 - V_4 Pol(f65) = V_3 - V_4 Pol(f75) = V_3 - V_4 Pol(f83) = V_3 - V_4 Pol(f93) = V_3 - V_4 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 10: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = V_3 Pol(f0) = V_3 Pol(f17) = -V_2 + V_3 Pol(f27) = -V_2 + V_3 Pol(f37) = -V_2 + V_3 Pol(f45) = -V_2 + V_3 Pol(f55) = -V_2 + V_3 Pol(f65) = -V_2 + V_3 Pol(f75) = -V_2 + V_3 Pol(f83) = -V_2 + V_3 Pol(f93) = -V_2 + V_3 orients all transitions weakly and the transition 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 ] strictly and produces the following problem: 11: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f45) = -V_1 + V_3 and size complexities 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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) = ? 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 orients the transitions 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 ] weakly and the transition 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 ] strictly and produces the following problem: 12: T: (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) start location: koat_start leaf cost: 0 Complexity upper bound 15*Ar_4 + 65 Time: 0.547 sec (SMT: 0.258 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f0 0: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=0, [], cost: 1 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 2: f27 -> f27 : F'=1+F, [ E>=1+F ], cost: 1 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 6: f65 -> f65 : Q'=1+Q, [ E>=1+Q ], cost: 1 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 8: f83 -> f83 : A'=1+A, [ E>=1+A ], cost: 1 9: f83 -> f93 : [ A>=E ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=0, [], cost: 1 Removed unreachable and leaf rules: Start location: f0 0: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=0, [], cost: 1 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 2: f27 -> f27 : F'=1+F, [ E>=1+F ], cost: 1 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 6: f65 -> f65 : Q'=1+Q, [ E>=1+Q ], cost: 1 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 8: f83 -> f83 : A'=1+A, [ E>=1+A ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f17 -> f17 : D'=1+D, [ E>=1+D ], cost: 1 Accelerated rule 1 with metering function -D+E, yielding the new rule 17. Removing the simple loops: 1. Accelerating simple loops of location 2. Accelerating the following rules: 2: f27 -> f27 : F'=1+F, [ E>=1+F ], cost: 1 Accelerated rule 2 with metering function -F+E, yielding the new rule 18. Removing the simple loops: 2. Accelerating simple loops of location 3. Accelerating the following rules: 3: f37 -> f37 : G'=1+G, [ E>=1+G ], cost: 1 Accelerated rule 3 with metering function -G+E, yielding the new rule 19. Removing the simple loops: 3. Accelerating simple loops of location 4. Accelerating the following rules: 4: f45 -> f45 : A'=1+A, [ E>=1+A ], cost: 1 Accelerated rule 4 with metering function -A+E, yielding the new rule 20. Removing the simple loops: 4. Accelerating simple loops of location 5. Accelerating the following rules: 5: f55 -> f55 : H'=1+H, [ E>=1+H ], cost: 1 Accelerated rule 5 with metering function -H+E, yielding the new rule 21. Removing the simple loops: 5. Accelerating simple loops of location 6. Accelerating the following rules: 6: f65 -> f65 : Q'=1+Q, [ E>=1+Q ], cost: 1 Accelerated rule 6 with metering function E-Q, yielding the new rule 22. Removing the simple loops: 6. Accelerating simple loops of location 7. Accelerating the following rules: 7: f75 -> f75 : J'=1+J, [ E>=1+J ], cost: 1 Accelerated rule 7 with metering function -J+E, yielding the new rule 23. Removing the simple loops: 7. Accelerating simple loops of location 8. Accelerating the following rules: 8: f83 -> f83 : A'=1+A, [ E>=1+A ], cost: 1 Accelerated rule 8 with metering function -A+E, yielding the new rule 24. Removing the simple loops: 8. Accelerated all simple loops using metering functions (where possible): Start location: f0 0: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=0, [], cost: 1 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 17: f17 -> f17 : D'=E, [ E>=1+D ], cost: -D+E 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 18: f27 -> f27 : F'=E, [ E>=1+F ], cost: -F+E 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 19: f37 -> f37 : G'=E, [ E>=1+G ], cost: -G+E 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 20: f45 -> f45 : A'=E, [ E>=1+A ], cost: -A+E 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 21: f55 -> f55 : H'=E, [ E>=1+H ], cost: -H+E 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 22: f65 -> f65 : Q'=E, [ E>=1+Q ], cost: E-Q 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 23: f75 -> f75 : J'=E, [ E>=1+J ], cost: -J+E 24: f83 -> f83 : A'=E, [ E>=1+A ], cost: -A+E Chained accelerated rules (with incoming rules): Start location: f0 0: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=0, [], cost: 1 25: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=E, [ E>=1 ], cost: 1+E 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 26: f17 -> f27 : F'=E, [ D>=E && E>=1 ], cost: 1+E 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 27: f27 -> f37 : G'=E, [ F>=E && E>=1 ], cost: 1+E 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 28: f37 -> f45 : A'=E, [ G>=E && E>=1 ], cost: 1+E 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 29: f45 -> f55 : H'=E, [ A>=E && E>=1 ], cost: 1+E 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 30: f55 -> f65 : Q'=E, [ H>=E && E>=1 ], cost: 1+E 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 31: f65 -> f75 : J'=E, [ Q>=E && E>=1 ], cost: 1+E 10: f75 -> f83 : A'=0, [ J>=E ], cost: 1 32: f75 -> f83 : A'=E, [ J>=E && E>=1 ], cost: 1+E Removed unreachable locations (and leaf rules with constant cost): Start location: f0 0: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=0, [], cost: 1 25: f0 -> f17 : A'=0, B'=free, C'=free_1, D'=E, [ E>=1 ], cost: 1+E 16: f17 -> f27 : F'=0, [ D>=E ], cost: 1 26: f17 -> f27 : F'=E, [ D>=E && E>=1 ], cost: 1+E 15: f27 -> f37 : G'=0, [ F>=E ], cost: 1 27: f27 -> f37 : G'=E, [ F>=E && E>=1 ], cost: 1+E 14: f37 -> f45 : A'=0, [ G>=E ], cost: 1 28: f37 -> f45 : A'=E, [ G>=E && E>=1 ], cost: 1+E 13: f45 -> f55 : H'=0, [ A>=E ], cost: 1 29: f45 -> f55 : H'=E, [ A>=E && E>=1 ], cost: 1+E 12: f55 -> f65 : Q'=0, [ H>=E ], cost: 1 30: f55 -> f65 : Q'=E, [ H>=E && E>=1 ], cost: 1+E 11: f65 -> f75 : J'=0, [ Q>=E ], cost: 1 31: f65 -> f75 : J'=E, [ Q>=E && E>=1 ], cost: 1+E 32: f75 -> f83 : A'=E, [ J>=E && E>=1 ], cost: 1+E Eliminated locations (on tree-shaped paths): Start location: f0 33: f0 -> f27 : A'=0, B'=free, C'=free_1, D'=0, F'=0, [ 0>=E ], cost: 2 34: f0 -> f27 : A'=0, B'=free, C'=free_1, D'=E, F'=0, [ E>=1 ], cost: 2+E 35: f0 -> f27 : A'=0, B'=free, C'=free_1, D'=E, F'=E, [ E>=1 ], cost: 2+2*E 36: f27 -> f45 : A'=0, G'=0, [ F>=E && 0>=E ], cost: 2 37: f27 -> f45 : A'=0, G'=E, [ F>=E && E>=1 ], cost: 2+E 38: f27 -> f45 : A'=E, G'=E, [ F>=E && E>=1 ], cost: 2+2*E 39: f45 -> f65 : H'=0, Q'=0, [ A>=E && 0>=E ], cost: 2 40: f45 -> f65 : H'=E, Q'=0, [ A>=E && E>=1 ], cost: 2+E 41: f45 -> f65 : H'=E, Q'=E, [ A>=E && E>=1 ], cost: 2+2*E 42: f65 -> f83 : A'=E, J'=E, [ Q>=E && E>=1 ], cost: 2+2*E Eliminated locations (on tree-shaped paths): Start location: f0 43: f0 -> f45 : A'=0, B'=free, C'=free_1, D'=0, F'=0, G'=0, [ 0>=E ], cost: 4 44: f0 -> f45 : A'=0, B'=free, C'=free_1, D'=E, F'=E, G'=E, [ E>=1 ], cost: 4+3*E 45: f0 -> f45 : A'=E, B'=free, C'=free_1, D'=E, F'=E, G'=E, [ E>=1 ], cost: 4+4*E 46: f0 -> [18] : [ E>=1 ], cost: 2+E 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 48: f45 -> f83 : A'=E, H'=E, Q'=E, J'=E, [ A>=E && E>=1 ], cost: 4+4*E 49: f45 -> [19] : [ A>=E && E>=1 ], cost: 2+E Eliminated locations (on tree-shaped paths): Start location: f0 46: f0 -> [18] : [ E>=1 ], cost: 2+E 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 50: f0 -> f83 : A'=E, B'=free, C'=free_1, D'=E, F'=E, G'=E, H'=E, Q'=E, J'=E, [ E>=1 ], cost: 8+8*E 51: f0 -> [19] : A'=E, B'=free, C'=free_1, D'=E, F'=E, G'=E, [ E>=1 ], cost: 6+5*E 52: f0 -> [20] : [ E>=1 ], cost: 4+3*E ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f0 46: f0 -> [18] : [ E>=1 ], cost: 2+E 47: f0 -> [18] : [ E>=1 ], cost: 2+2*E 50: f0 -> f83 : A'=E, B'=free, C'=free_1, D'=E, F'=E, G'=E, H'=E, Q'=E, J'=E, [ E>=1 ], cost: 8+8*E 51: f0 -> [19] : A'=E, B'=free, C'=free_1, D'=E, F'=E, G'=E, [ E>=1 ], cost: 6+5*E 52: f0 -> [20] : [ E>=1 ], cost: 4+3*E Computing asymptotic complexity for rule 46 Solved the limit problem by the following transformations: Created initial limit problem: 2+E (+), E (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {E==n} resulting limit problem: [solved] Solution: E / n Resulting cost 2+n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 2+n Rule cost: 2+E Rule guard: [ E>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)