/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).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, 269 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 4022 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, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= 2 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= B + 1 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, C, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 + S && A >= D f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f13(A, B, S, D + 1, C, S, S, H, I, J, K, L, M, N, O, P, Q, R)) :|: S >= C && A >= D f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, 0, 0, J, K, L, M, N, O, P, Q, R)) :|: A >= D f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, S, T, J + T, K, L, M, N, O, P, Q, R)) :|: 0 >= S + 1 && A >= D f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D + 1, E, F, G, S, T, J + T, K, L, M, N, O, P, Q, R)) :|: S >= 1 && A >= D f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= K f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f55(A, B, C, D + 1, E, F, G, H, I, S, K, L, M, N, O, P, Q, R)) :|: A >= D f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f61(A, B, C, D + 1, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: A >= D f61(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K + 1, L, M, N, O, P, Q, R)) :|: D >= 1 + A f55(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f61(A, B, C, D, E, F, G, H, I, J, K, S, M, N, O, P, Q, R)) :|: D >= 1 + A f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: K >= 1 + A f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K, L, S, T, T, P, Q, R)) :|: D >= 1 + A f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f53(A, B, C, D, E, F, G, H, I, J, K, L, M, N, -(S), T, S, R)) :|: 0 >= U + 1 && D >= 1 + A f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f34(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: D >= 1 + A f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f10(A, B + 1, 0, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, 0)) :|: D >= 1 + A && C >= 0 && C <= 0 f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: 0 >= C + 1 && D >= 1 + A f13(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f29(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: C >= 1 && D >= 1 + A f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A && 0 >= S + 1 f10(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R) -> Com_1(f73(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R)) :|: B >= A The start-symbols are:[f0_18] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 37*Ar_0 + 3*Ar_10 + 32*Ar_3 + 2*Ar_1 + 38) 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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= 2 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_2, Fresh_11, Fresh_11, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_2, Fresh_10, Fresh_10, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, 0, 0, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Fresh_8, Fresh_9, Ar_9 + Fresh_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ 0 >= Fresh_8 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Fresh_6, Fresh_7, Ar_9 + Fresh_7, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Fresh_6 >= 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Fresh_5, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10 + 1, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_3 >= 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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Fresh_4, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_10 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Fresh_2, Fresh_3, Fresh_3, Ar_15, Ar_16, Ar_17)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, -Fresh_0, Fresh_1, Fresh_0, Ar_17)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, 0)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ Ar_1 >= Ar_0 ] (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, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16, Ar_17)) [ 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_1, Ar_2, Ar_3, Ar_10]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Fresh_6 >= 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ 0 >= Fresh_8 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 2: f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Fresh_6 >= 1 /\ Ar_0 >= Ar_3 ] f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ 0 >= Fresh_8 + 1 /\ Ar_0 >= Ar_3 ] f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f61) = 1 Pol(f53) = 1 Pol(f55) = 1 Pol(f10) = 1 Pol(f34) = 1 Pol(f29) = 1 Pol(f13) = 1 Pol(f73) = 0 Pol(f0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transitions f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f61) = V_1 - V_4 + 1 Pol(f53) = V_1 - V_4 + 1 Pol(f55) = V_1 - V_4 + 1 Pol(f10) = V_1 - V_4 + 1 Pol(f34) = V_1 - V_4 + 1 Pol(f29) = V_1 - V_4 + 1 Pol(f13) = V_1 - V_4 + 1 Pol(f73) = V_1 - V_4 Pol(f0) = V_1 - V_4 + 1 Pol(koat_start) = V_1 - V_4 + 1 orients all transitions weakly and the transitions f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] strictly and produces the following problem: 6: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f61) = 1 Pol(f53) = 1 Pol(f55) = 1 Pol(f10) = 0 Pol(f13) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ]", 0-4) = Ar_10 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ]", 0-0) = Ar_0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ]", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ]", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ]", 0-3) = Ar_3 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ]", 0-4) = Ar_10 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 192 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\\ 0 >= S + 1 ]", 0-0) = Ar_0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\\ 0 >= S + 1 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\\ 0 >= S + 1 ]", 0-2) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\\ 0 >= S + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 192 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\\ 0 >= S + 1 ]", 0-4) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = 0 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\\ Ar_2 = 0 ]", 0-0) = Ar_0 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\\ Ar_2 = 0 ]", 0-1) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\\ Ar_2 = 0 ]", 0-2) = 0 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\\ Ar_2 = 0 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\\ Ar_2 = 0 ]", 0-4) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\\ Ar_0 >= Ar_3 ]", 0-0) = Ar_0 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\\ Ar_0 >= Ar_3 ]", 0-1) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\\ Ar_0 >= Ar_3 ]", 0-2) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\\ Ar_0 >= Ar_3 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\\ Ar_0 >= Ar_3 ]", 0-4) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\\ Ar_0 >= Ar_3 ]", 0-0) = Ar_0 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\\ Ar_0 >= Ar_3 ]", 0-1) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\\ Ar_0 >= Ar_3 ]", 0-2) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\\ Ar_0 >= Ar_3 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\\ Ar_0 >= Ar_3 ]", 0-4) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\\ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ]", 0-1) = ? S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ]", 0-2) = ? S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ]", 0-4) = ? S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ]", 0-0) = Ar_0 S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ]", 0-1) = ? S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ]", 0-2) = ? S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ]", 0-4) = ? S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ]", 0-0) = Ar_0 S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ]", 0-1) = ? S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ]", 0-2) = ? S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ]", 0-4) = ? S("f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_3 + 48 S("f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ]", 0-4) = ? orients the transitions f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] weakly and the transition f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] strictly and produces the following problem: 8: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: 9*Ar_0 + 9*Ar_3 + 9, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f61) = V_1 - V_5 Pol(f53) = V_1 - V_5 + 1 Pol(f55) = V_1 - V_5 Pol(f10) = V_1 - V_5 + 1 Pol(f34) = V_1 - V_5 + 1 Pol(f29) = V_1 - V_5 + 1 Pol(f13) = V_1 - V_5 + 1 Pol(f73) = V_1 - V_5 Pol(f0) = V_1 - V_5 + 1 Pol(koat_start) = V_1 - V_5 + 1 orients all transitions weakly and the transition f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] strictly and produces the following problem: 9: T: (Comp: ?, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_10 + 1, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: 9*Ar_0 + 9*Ar_3 + 9, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 9 produces the following problem: 10: T: (Comp: 2*Ar_0 + Ar_10 + Ar_3 + 2, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: 2*Ar_0 + Ar_10 + Ar_3 + 2, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_10 + 1, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: 9*Ar_0 + 9*Ar_3 + 9, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f61) = V_1 - V_2 - 1 Pol(f53) = V_1 - V_2 - 1 Pol(f55) = V_1 - V_2 - 1 Pol(f10) = V_1 - V_2 Pol(f34) = V_1 - V_2 - 1 Pol(f29) = V_1 - V_2 - 1 Pol(f13) = V_1 - V_2 - 1 Pol(f73) = V_1 - V_2 Pol(f0) = V_1 - V_2 Pol(koat_start) = V_1 - V_2 orients all transitions weakly and the transition f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] strictly and produces the following problem: 11: T: (Comp: 2*Ar_0 + Ar_10 + Ar_3 + 2, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: 2*Ar_0 + Ar_10 + Ar_3 + 2, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_10 + 1, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: 9*Ar_0 + 9*Ar_3 + 9, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: Ar_0 + Ar_1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 11 produces the following problem: 12: T: (Comp: 2*Ar_0 + Ar_10 + Ar_3 + 2, Cost: 1) f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10 + 1)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_0 >= Ar_3 ] (Comp: 2*Ar_0 + Ar_10 + Ar_3 + 2, Cost: 1) f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f61(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_10 + 1, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f55(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= Ar_10 ] (Comp: 9*Ar_0 + 9*Ar_3 + 9, Cost: 1) f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_10)) [ Ar_10 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f53(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= U + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 4*Ar_0 + 4*Ar_3 + 4, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f34(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 >= Ar_2 + 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: 2*Ar_0 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_2 >= 1 /\ Ar_3 >= Ar_0 + 1 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_10)) [ Ar_2 >= Fresh_11 + 1 /\ Ar_0 >= Ar_3 ] (Comp: Ar_0 + Ar_3 + 1, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, Fresh_10, Ar_3 + 1, Ar_10)) [ Fresh_10 >= Ar_2 /\ Ar_0 >= Ar_3 ] (Comp: 3*Ar_0 + Ar_1 + 2*Ar_3 + 2, Cost: 1) f13(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_10)) [ Ar_3 >= Ar_0 + 1 /\ Ar_2 = 0 ] (Comp: Ar_0 + Ar_1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f13(Ar_0, Ar_1, 0, Ar_3, Ar_10)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 /\ 0 >= S + 1 ] (Comp: 1, Cost: 1) f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f73(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_1 >= Ar_0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ Ar_0 >= 2 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_10)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 37*Ar_0 + 3*Ar_10 + 32*Ar_3 + 2*Ar_1 + 38 Time: 0.310 sec (SMT: 0.212 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 20: f10 -> f73 : [ B>=A && 0>=1+free_13 ], cost: 1 21: f10 -> f73 : [ B>=A ], cost: 1 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16: f29 -> f34 : [ D>=1+A ], cost: 1 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=J+free_3, [ 0>=1+free_2 && A>=D ], cost: 1 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ 0>=1+free_12 && D>=1+A ], cost: 1 8: f53 -> f55 : [ A>=K ], cost: 1 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: f0 -> f10 : [ A>=2 ], cost: 1 Removed unreachable and leaf rules: Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16: f29 -> f34 : [ D>=1+A ], cost: 1 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=J+free_3, [ 0>=1+free_2 && A>=D ], cost: 1 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ 0>=1+free_12 && D>=1+A ], cost: 1 8: f53 -> f55 : [ A>=K ], cost: 1 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 Simplified all rules, resulting in: Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 16: f29 -> f34 : [ D>=1+A ], cost: 1 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=J+free_3, [ 0>=1+free_2 && A>=D ], cost: 1 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 8: f53 -> f55 : [ A>=K ], cost: 1 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 2: f13 -> f13 : D'=1+D, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1 3: f13 -> f13 : C'=free_1, D'=1+D, E'=C, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1 Accelerated rule 2 with metering function 1-D+A, yielding the new rule 22. Accelerated rule 3 with metering function 1-D+A, yielding the new rule 23. Removing the simple loops: 2 3. Accelerating simple loops of location 3. Accelerating the following rules: 4: f29 -> f29 : D'=1+D, [ A>=D ], cost: 1 Accelerated rule 4 with metering function 1-D+A, yielding the new rule 24. Removing the simple loops: 4. Accelerating simple loops of location 4. Accelerating the following rules: 5: f34 -> f34 : D'=1+D, H'=0, Q'=0, [ A>=D ], cost: 1 6: f34 -> f34 : D'=1+D, H'=free_2, Q'=free_3, J'=J+free_3, [ 0>=1+free_2 && A>=D ], cost: 1 7: f34 -> f34 : D'=1+D, H'=free_4, Q'=free_5, J'=J+free_5, [ free_4>=1 && A>=D ], cost: 1 Accelerated rule 5 with metering function 1-D+A, yielding the new rule 25. Accelerated rule 6 with metering function 1-D+A, yielding the new rule 26. Accelerated rule 7 with metering function 1-D+A, yielding the new rule 27. Removing the simple loops: 5 6 7. Accelerating simple loops of location 6. Accelerating the following rules: 9: f55 -> f55 : D'=1+D, J'=free_6, [ A>=D ], cost: 1 Accelerated rule 9 with metering function 1-D+A, yielding the new rule 28. Removing the simple loops: 9. Accelerating simple loops of location 7. Accelerating the following rules: 10: f61 -> f61 : D'=1+D, [ A>=D ], cost: 1 Accelerated rule 10 with metering function 1-D+A, yielding the new rule 29. Removing the simple loops: 10. Accelerated all simple loops using metering functions (where possible): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 22: f13 -> f13 : D'=1+A, E'=C, F'=free, G'=free, [ C>=1+free && A>=D ], cost: 1-D+A 23: f13 -> f13 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ free_1>=C && A>=D ], cost: 1-D+A 16: f29 -> f34 : [ D>=1+A ], cost: 1 24: f29 -> f29 : D'=1+A, [ A>=D ], cost: 1-D+A 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 25: f34 -> f34 : D'=1+A, H'=0, Q'=0, [ A>=D ], cost: 1-D+A 26: f34 -> f34 : D'=1+A, H'=free_2, Q'=free_3, J'=-(-1+D-A)*free_3+J, [ 0>=1+free_2 && A>=D ], cost: 1-D+A 27: f34 -> f34 : D'=1+A, H'=free_4, Q'=free_5, J'=J-(-1+D-A)*free_5, [ free_4>=1 && A>=D ], cost: 1-D+A 8: f53 -> f55 : [ A>=K ], cost: 1 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 28: f55 -> f55 : D'=1+A, J'=free_6, [ A>=D ], cost: 1-D+A 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 29: f61 -> f61 : D'=1+A, [ A>=D ], cost: 1-D+A Chained accelerated rules (with incoming rules): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 30: f10 -> f13 : C'=0, D'=1+A, E'=0, F'=free, G'=free, [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 31: f10 -> f13 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16: f29 -> f34 : [ D>=1+A ], cost: 1 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 8: f53 -> f55 : [ A>=K ], cost: 1 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 32: f53 -> f55 : D'=1+A, J'=free_6, [ A>=K && A>=D ], cost: 2-D+A 12: f55 -> f61 : L'=free_7, [ D>=1+A ], cost: 1 11: f61 -> f53 : K'=1+K, [ D>=1+A ], cost: 1 Eliminated locations (on linear paths): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 1: f10 -> f13 : C'=0, [ A>=1+B ], cost: 1 30: f10 -> f13 : C'=0, D'=1+A, E'=0, F'=free, G'=free, [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 31: f10 -> f13 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 17: f13 -> f10 : B'=1+B, C'=0, R'=0, [ D>=1+A && C==0 ], cost: 1 18: f13 -> f29 : [ 0>=1+C && D>=1+A ], cost: 1 19: f13 -> f29 : [ C>=1 && D>=1+A ], cost: 1 16: f29 -> f34 : [ D>=1+A ], cost: 1 14: f34 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 1 15: f34 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 1 8: f53 -> f55 : [ A>=K ], cost: 1 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 32: f53 -> f55 : D'=1+A, J'=free_6, [ A>=K && A>=D ], cost: 2-D+A 33: f55 -> f53 : K'=1+K, L'=free_7, [ D>=1+A ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 34: f10 -> f10 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 35: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 36: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, R'=0, [ A>=1+B && A>=D && free_1==0 ], cost: 3-D+A 37: f10 -> f29 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 40: f29 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 41: f29 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 2 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 42: f53 -> f53 : K'=1+K, L'=free_7, [ A>=K && D>=1+A ], cost: 3 43: f53 -> f53 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A Accelerating simple loops of location 1. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 34: f10 -> f10 : B'=1+B, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2 35: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 36: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=1+B && A>=D ], cost: 3-D+A Accelerated rule 34 with metering function A-B, yielding the new rule 44. Found no metering function for rule 35. Found no metering function for rule 36. Removing the simple loops: 34. Accelerating simple loops of location 5. Accelerating the following rules: 42: f53 -> f53 : K'=1+K, L'=free_7, [ A>=K && D>=1+A ], cost: 3 43: f53 -> f53 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A Accelerated rule 42 with metering function 1+A-K, yielding the new rule 45. Found no metering function for rule 43. Removing the simple loops: 42. Accelerated all simple loops using metering functions (where possible): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 35: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 36: f10 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=1+B && A>=D ], cost: 3-D+A 37: f10 -> f29 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 44: f10 -> f10 : B'=A, C'=0, R'=0, [ A>=1+B && D>=1+A ], cost: 2*A-2*B 40: f29 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 41: f29 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 2 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 43: f53 -> f53 : D'=1+A, J'=free_6, K'=1+K, L'=free_7, [ A>=K && A>=D ], cost: 4-D+A 45: f53 -> f53 : K'=1+A, L'=free_7, [ A>=K && D>=1+A ], cost: 3+3*A-3*K Chained accelerated rules (with incoming rules): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 37: f10 -> f29 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, [ A>=1+B && A>=D && free_1>=1 ], cost: 3-D+A 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 40: f29 -> f53 : M'=free_8, N'=free_9, O'=free_9, [ D>=1+A ], cost: 2 41: f29 -> f53 : O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A ], cost: 2 52: f29 -> f53 : K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ D>=1+A && A>=K ], cost: 5+3*A-3*K 53: f29 -> f53 : K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ D>=1+A && A>=K ], cost: 5+3*A-3*K 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 47: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ K>=1+A && A>=2+B && 0>=1+free && A>=D ], cost: 4-D+A 49: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ K>=1+A && A>=2+B && A>=D ], cost: 4-D+A 51: f53 -> f10 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B Eliminated locations (on tree-shaped paths): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 54: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 55: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 56: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 57: f10 -> f53 : C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 13: f53 -> f10 : B'=1+B, [ K>=1+A ], cost: 1 47: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ K>=1+A && A>=2+B && 0>=1+free && A>=D ], cost: 4-D+A 49: f53 -> f10 : B'=2+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ K>=1+A && A>=2+B && A>=D ], cost: 4-D+A 51: f53 -> f10 : B'=A, C'=0, R'=0, [ K>=1+A && A>=2+B && D>=1+A ], cost: -1+2*A-2*B Eliminated locations (on tree-shaped paths): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 60: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 61: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 63: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 64: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 65: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, R'=0, [ A>=D && free_1>=1 && A>=K && A>=2+B ], cost: 7-D+6*A-3*K-2*B 66: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 68: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K Applied pruning (of leafs and parallel rules): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 60: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 64: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K Accelerating simple loops of location 1. Accelerating the following rules: 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 60: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 64: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K Found no metering function for rule 58. Found no metering function for rule 59. Found no metering function for rule 60. Found no metering function for rule 62. Found no metering function for rule 64. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 58: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 59: f10 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 4-D+3*A-2*B 60: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 6-D+A 62: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 64: f10 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K Chained accelerated rules (with incoming rules): Start location: f0 0: f0 -> f10 : [ A>=2 ], cost: 1 46: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=free, G'=free, R'=0, [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 48: f0 -> f10 : B'=1+B, C'=0, D'=1+A, E'=0, F'=0, G'=0, R'=0, [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 50: f0 -> f10 : B'=A, C'=0, R'=0, [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 70: f0 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 71: f0 -> f10 : B'=A, C'=0, D'=1+A, E'=free_1, F'=free_1, G'=free_1, M'=free_8, N'=free_9, O'=free_9, R'=0, [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 72: f0 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 73: f0 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, M'=free_8, N'=free_9, O'=free_9, [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 74: f0 -> f10 : B'=1+B, C'=free_1, D'=1+A, E'=free_1, F'=free_1, G'=free_1, K'=1+A, L'=free_7, O'=-free_10, P'=free_11, Q_1'=free_10, [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 38: f10 -> [14] : [ A>=1+B && 0>=1+free && A>=D ], cost: 2-D+A 39: f10 -> [14] : [ A>=1+B && free_1>=0 && A>=D ], cost: 2-D+A 67: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 ], cost: 5-D+A 69: f10 -> [17] : [ A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 8-D+4*A-3*K Eliminated locations (on tree-shaped paths): Start location: f0 75: f0 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 76: f0 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 77: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 78: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 79: f0 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 80: f0 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 81: f0 -> [19] : [ A>=2 && A>=1+B && D>=1+A ], cost: 1+2*A-2*B 82: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 83: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 84: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 85: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K 86: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K Applied pruning (of leafs and parallel rules): Start location: f0 75: f0 -> [14] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 3-D+A 76: f0 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 77: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 78: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 9-D+4*A-3*K 79: f0 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 80: f0 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 83: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 84: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 86: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: f0 76: f0 -> [14] : [ A>=2 && A>=1+B && free_1>=0 && A>=D ], cost: 3-D+A 77: f0 -> [17] : [ A>=2 && A>=1+B && A>=D && free_1>=1 ], cost: 6-D+A 79: f0 -> [19] : [ A>=2 && A>=1+B && 0>=1+free && A>=D ], cost: 4-D+A 80: f0 -> [19] : [ A>=2 && A>=1+B && A>=D ], cost: 4-D+A 83: f0 -> [19] : [ A>=2 && A>=D && free_1>=1 && K>=1+A && A>=2+B ], cost: 5-D+3*A-2*B 84: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && K>=1+A ], cost: 7-D+A 86: f0 -> [19] : [ A>=2 && A>=1+B && A>=D && free_1>=1 && A>=K ], cost: 10-D+4*A-3*K Computing asymptotic complexity for rule 76 Solved the limit problem by the following transformations: Created initial limit problem: -1+A (+/+!), A-B (+/+!), 1+free_1 (+/+!), 3-D+A (+), 1-D+A (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free_1==n,D==0,A==n,B==-1+n} resulting limit problem: [solved] Solution: free_1 / n D / 0 A / n B / -1+n Resulting cost 3+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: 3+n Rule cost: 3-D+A Rule guard: [ A>=2 && A>=1+B && free_1>=0 && A>=D ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)