/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^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 727 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 5561 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f2(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, 0, B, E, F, G, H)) :|: A >= B + 1 f8(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, C, D, E + 1, J, I, H)) :|: A >= E && I >= J f8(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, J, E, E + 1, I, K, H)) :|: A >= E && I >= 1 + K f19(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E + 1, F, G, J)) :|: A >= E f27(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E + 1, F, G, J)) :|: A >= E f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: C >= 1 f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && 0 >= I + 1 f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && I >= 1 f43(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E + 1, F, G, H)) :|: A >= E f49(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E + 1, F, G, H)) :|: A >= E f36(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, 0)) :|: A >= D f34(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, 0, D, E, F, G, H)) :|: C >= 0 && C <= 0 f49(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, H)) :|: E >= 1 + A f43(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E, F, G, H)) :|: E >= 1 + A f36(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, C, D, E, F, G, H)) :|: D >= 1 + A f27(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, E, F, G, H)) :|: E >= 1 + A f19(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E, F, G, H)) :|: E >= 1 + A f8(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, B, E, F, G, H)) :|: E >= 1 + A && B >= D && B <= D f8(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E, F, G, H)) :|: B >= D + 1 && E >= 1 + A f8(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E, F, G, H)) :|: D >= 1 + B && E >= 1 + A f2(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, C, D, E, F, G, H)) :|: B >= A start(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B, C, D, E, F, G, H)) :|: TRUE The start-symbols are:[start_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 312460831275774*ar_0 + 44637261614347*ar_1 + 267823569665387*ar_4 + 5040*ar_0^2 + 9150*ar_0*ar_4 + 5550*ar_0*ar_1 + 4830*ar_1*ar_4 + 690*ar_1^2 + 4140*ar_4^2 + 267823569661249) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, j, i, ar_7)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1, i, k, ar_7)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 = 0 ] (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 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_4]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 2: f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] We thus obtain the following problem: 3: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 3 produces the following problem: 4: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f49) = 1 Pol(f36) = 1 Pol(f43) = 1 Pol(f27) = 1 Pol(f34) = 1 Pol(f2) = 1 Pol(f19) = 1 Pol(f8) = 1 Pol(f1) = 0 Pol(start) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] strictly and produces the following problem: 5: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f49) = V_1 - V_5 + 1 Pol(f36) = V_1 - V_5 + 1 Pol(f43) = V_1 - V_5 + 1 Pol(f27) = V_1 - V_5 + 1 Pol(f34) = V_1 - V_5 + 1 Pol(f2) = V_1 - V_5 + 1 Pol(f19) = V_1 - V_5 + 1 Pol(f8) = V_1 - V_5 + 1 Pol(f1) = V_1 - V_5 Pol(start) = V_1 - V_5 + 1 Pol(koat_start) = V_1 - V_5 + 1 orients all transitions weakly and the transitions f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] strictly and produces the following problem: 6: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ?, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f49) = V_1 - V_2 - 1 Pol(f36) = V_1 - V_2 - 1 Pol(f43) = V_1 - V_2 - 1 Pol(f27) = V_1 - V_2 - 1 Pol(f34) = V_1 - V_2 - 1 Pol(f2) = V_1 - V_2 Pol(f19) = V_1 - V_2 - 1 Pol(f8) = V_1 - V_2 - 1 Pol(f1) = V_1 - V_2 Pol(start) = V_1 - V_2 Pol(koat_start) = V_1 - V_2 orients all transitions weakly and the transition f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] strictly and produces the following problem: 8: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ar_0 + ar_1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 8 produces the following problem: 9: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ar_0 + ar_1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f49) = 1 Pol(f36) = 1 Pol(f43) = 1 Pol(f2) = 0 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 4*ar_0 + 4*ar_4 + 192 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-1) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-3) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-1) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-3) = 4*ar_0 + 4*ar_4 + 192 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-1) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-3) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-0) = ar_0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-1) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-2) = 0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-3) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-0) = ar_0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-1) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-2) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-3) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-0) = ar_0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-1) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-2) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-3) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-1) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-1) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-1) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-0) = ar_0 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-1) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-2) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-3) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 orients the transitions f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] weakly and the transition f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] strictly and produces the following problem: 10: T: (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ar_0 + ar_1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 10 to obtain the following invariants: For symbol f19: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f27: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f34: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f36: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f43: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f49: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f8: X_1 - X_2 - 1 >= 0 This yielded the following problem: 11: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ar_0 + ar_1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] start location: koat_start leaf cost: 0 Testing for unsatisfiable constraints removes the following transition from problem 11: f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 ] We thus obtain the following problem: 12: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ar_0 + ar_1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] (Comp: ?, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f49) = 3*V_1 - 3*V_4 + 1 Pol(f36) = 3*V_1 - 3*V_4 + 3 Pol(f43) = 3*V_1 - 3*V_4 + 2 and size complexities S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 64691683493 S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = ? S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 2812681891 S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 122290517 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 122290517 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-0) = ar_0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-2) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ? S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-0) = ar_0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-2) = 0 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 5316979 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-3) = 3*ar_0 + 3*ar_4 + 54 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-0) = ar_0 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-2) = ? S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173 S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173 S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ? S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 3*ar_0 + 3*ar_4 + 54 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 orients the transitions f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] weakly and the transitions f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] strictly and produces the following problem: 13: T: (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] (Comp: ar_0 + ar_1, Cost: 1) f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ] (Comp: ar_0 + ar_4 + 1, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ] (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ] (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] start location: koat_start leaf cost: 0 Complexity upper bound 312460831275774*ar_0 + 44637261614347*ar_1 + 267823569665387*ar_4 + 5040*ar_0^2 + 9150*ar_0*ar_4 + 5550*ar_0*ar_1 + 4830*ar_1*ar_4 + 690*ar_1^2 + 4140*ar_4^2 + 267823569661249 Time: 0.754 sec (SMT: 0.543 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1 21: f2 -> f1 : [ B>=A ], cost: 1 1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1 20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1 3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 17: f19 -> f27 : [ E>=1+A ], cost: 1 4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 16: f27 -> f34 : [ E>=1+A ], cost: 1 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f36 -> f43 : H'=free_8, [ A>=D && 0>=1+free_7 ], cost: 1 8: f36 -> f43 : H'=free_10, [ A>=D && free_9>=1 ], cost: 1 11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 14: f43 -> f49 : [ E>=1+A ], cost: 1 10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 22: start -> f2 : [], cost: 1 Removed unreachable and leaf rules: Start location: start 0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1 1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1 20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1 3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 17: f19 -> f27 : [ E>=1+A ], cost: 1 4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 16: f27 -> f34 : [ E>=1+A ], cost: 1 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f36 -> f43 : H'=free_8, [ A>=D && 0>=1+free_7 ], cost: 1 8: f36 -> f43 : H'=free_10, [ A>=D && free_9>=1 ], cost: 1 11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 14: f43 -> f49 : [ E>=1+A ], cost: 1 10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 22: start -> f2 : [], cost: 1 Simplified all rules, resulting in: Start location: start 0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1 1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1 20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1 3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 17: f19 -> f27 : [ E>=1+A ], cost: 1 4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 16: f27 -> f34 : [ E>=1+A ], cost: 1 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f36 -> f43 : H'=free_8, [ A>=D ], cost: 1 8: f36 -> f43 : H'=free_10, [ A>=D ], cost: 1 11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 14: f43 -> f49 : [ E>=1+A ], cost: 1 10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 22: start -> f2 : [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 Accelerated rule 1 with metering function 1+A-E, yielding the new rule 23. Accelerated rule 2 with metering function 1+A-E, yielding the new rule 24. Removing the simple loops: 1 2. Accelerating simple loops of location 2. Accelerating the following rules: 3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 Accelerated rule 3 with metering function 1+A-E, yielding the new rule 25. Removing the simple loops: 3. Accelerating simple loops of location 3. Accelerating the following rules: 4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 Accelerated rule 4 with metering function 1+A-E, yielding the new rule 26. Removing the simple loops: 4. Accelerating simple loops of location 5. Accelerating the following rules: 11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1 Accelerated rule 11 with metering function 1-D+A, yielding the new rule 27. Removing the simple loops: 11. Accelerating simple loops of location 6. Accelerating the following rules: 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 Accelerated rule 9 with metering function 1+A-E, yielding the new rule 28. Removing the simple loops: 9. Accelerating simple loops of location 7. Accelerating the following rules: 10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1 Accelerated rule 10 with metering function 1+A-E, yielding the new rule 29. Removing the simple loops: 10. Accelerated all simple loops using metering functions (where possible): Start location: start 0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1 18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1 20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1 23: f8 -> f8 : E'=1+A, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1+A-E 24: f8 -> f8 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1+A-E 17: f19 -> f27 : [ E>=1+A ], cost: 1 25: f19 -> f19 : E'=1+A, H'=free_5, [ A>=E ], cost: 1+A-E 16: f27 -> f34 : [ E>=1+A ], cost: 1 26: f27 -> f27 : E'=1+A, H'=free_6, [ A>=E ], cost: 1+A-E 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f36 -> f43 : H'=free_8, [ A>=D ], cost: 1 8: f36 -> f43 : H'=free_10, [ A>=D ], cost: 1 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 27: f36 -> f36 : D'=1+A, H'=0, [ A>=D ], cost: 1-D+A 14: f43 -> f49 : [ E>=1+A ], cost: 1 28: f43 -> f43 : E'=1+A, [ A>=E ], cost: 1+A-E 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 29: f49 -> f49 : E'=1+A, [ A>=E ], cost: 1+A-E 22: start -> f2 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1 30: f2 -> f8 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 31: f2 -> f8 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1 20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1 17: f19 -> f27 : [ E>=1+A ], cost: 1 16: f27 -> f34 : [ E>=1+A ], cost: 1 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 7: f36 -> f43 : H'=free_8, [ A>=D ], cost: 1 8: f36 -> f43 : H'=free_10, [ A>=D ], cost: 1 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 35: f36 -> f43 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 2+A-E 36: f36 -> f43 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 2+A-E 14: f43 -> f49 : [ E>=1+A ], cost: 1 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f2 : [], cost: 1 Eliminated locations (on linear paths): Start location: start 0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1 30: f2 -> f8 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 31: f2 -> f8 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1 20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1 37: f19 -> f34 : [ E>=1+A ], cost: 2 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 7: f36 -> f43 : H'=free_8, [ A>=D ], cost: 1 8: f36 -> f43 : H'=free_10, [ A>=D ], cost: 1 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 35: f36 -> f43 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 2+A-E 36: f36 -> f43 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 2+A-E 14: f43 -> f49 : [ E>=1+A ], cost: 1 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f2 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start 38: f2 -> f34 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2 39: f2 -> f34 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 40: f2 -> f19 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 37: f19 -> f34 : [ E>=1+A ], cost: 2 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 43: f36 -> f49 : H'=free_8, [ A>=D && E>=1+A ], cost: 2 44: f36 -> f49 : H'=free_10, [ A>=D && E>=1+A ], cost: 2 45: f36 -> f49 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 3+A-E 46: f36 -> f49 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 3+A-E 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f2 : [], cost: 1 Eliminated locations (on linear paths): Start location: start 38: f2 -> f34 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2 39: f2 -> f34 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 47: f2 -> f34 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 5+A-E 5: f34 -> f36 : [ 0>=1+C ], cost: 1 6: f34 -> f36 : [ C>=1 ], cost: 1 12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 43: f36 -> f49 : H'=free_8, [ A>=D && E>=1+A ], cost: 2 44: f36 -> f49 : H'=free_10, [ A>=D && E>=1+A ], cost: 2 45: f36 -> f49 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 3+A-E 46: f36 -> f49 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 3+A-E 13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1 34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f2 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 48: f2 -> f2 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3==0 ], cost: 6+A-E 53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 56: f36 -> f36 : D'=1+D, H'=free_8, [ A>=D && E>=1+A ], cost: 3 57: f36 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 58: f36 -> f36 : D'=1+D, H'=free_10, [ A>=D && E>=1+A ], cost: 3 59: f36 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f36 -> f36 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 61: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 22: start -> f2 : [], cost: 1 Applied pruning (of leafs and parallel rules): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 48: f2 -> f2 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3==0 ], cost: 6+A-E 53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 56: f36 -> f36 : D'=1+D, H'=free_8, [ A>=D && E>=1+A ], cost: 3 59: f36 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f36 -> f36 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 22: start -> f2 : [], cost: 1 Accelerating simple loops of location 0. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 48: f2 -> f2 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 6+A-E Accelerated rule 48 with metering function A-B, yielding the new rule 64. Found no metering function for rule 49. Found no metering function for rule 52. Removing the simple loops: 48. Accelerating simple loops of location 5. Accelerating the following rules: 56: f36 -> f36 : D'=1+D, H'=free_8, [ A>=D && E>=1+A ], cost: 3 59: f36 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f36 -> f36 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E Accelerated rule 56 with metering function 1-D+A, yielding the new rule 65. 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 63. Removing the simple loops: 56. Accelerated all simple loops using metering functions (where possible): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 6+A-E 53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 64: f2 -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 3*A-3*B 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 59: f36 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f36 -> f36 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 65: f36 -> f36 : D'=1+A, H'=free_8, [ A>=D && E>=1+A ], cost: 3-3*D+3*A 22: start -> f2 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 72: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 73: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1 66: f36 -> f2 : B'=2+B, C'=0, D'=1+B, E'=1+A, F'=free_1, G'=free, [ D>=1+A && A>=2+B && A>=E && free>=free_1 ], cost: 5+A-E 68: f36 -> f2 : B'=2+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ D>=1+A && A>=2+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 70: f36 -> f2 : B'=A, C'=0, D'=-1+A, [ D>=1+A && A>=2+B && E>=1+A ], cost: -2+3*A-3*B 22: start -> f2 : [], cost: 1 67: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 69: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 71: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B Eliminated locations (on tree-shaped paths): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 74: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 75: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B 76: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E 77: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && free_3>=1 && A>=2+B ], cost: 5+4*A-E-3*B 78: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 79: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 7+4*A-E-3*B 80: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 81: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && free_3>=1 && A>=2+B ], cost: 7+4*A-E-3*B 82: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 83: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 84: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 85: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 86: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 87: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 22: start -> f2 : [], cost: 1 67: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 69: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 71: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B Applied pruning (of leafs and parallel rules): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 74: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 75: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B 78: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 79: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 7+4*A-E-3*B 80: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 86: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 87: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 22: start -> f2 : [], cost: 1 67: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 69: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 71: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B Accelerating simple loops of location 0. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 74: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 75: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 5+4*A-E-3*B 78: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 79: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 7+4*A-E-3*B 80: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E Found no metering function for rule 74. Found no metering function for rule 75. Found no metering function for rule 78. Found no metering function for rule 79. Found no metering function for rule 80. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 74: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 75: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 5+4*A-E-3*B 78: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 79: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 7+4*A-E-3*B 80: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 86: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 87: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 22: start -> f2 : [], cost: 1 67: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 69: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 71: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B Chained accelerated rules (with incoming rules): Start location: start 41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 86: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 87: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 22: start -> f2 : [], cost: 1 67: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 69: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 71: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 88: start -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 89: start -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B 90: start -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 91: start -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 8+4*A-E-3*B 92: start -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E Eliminated locations (on tree-shaped paths): Start location: start 93: start -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 94: start -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E 95: start -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 96: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 97: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 98: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 99: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 100: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 101: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 102: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B 103: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 104: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 8+4*A-E-3*B 105: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E Applied pruning (of leafs and parallel rules): Start location: start 93: start -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 94: start -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E 95: start -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 96: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 97: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 98: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 99: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 100: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 103: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 105: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start 98: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 99: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 100: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 103: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 105: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E Computing asymptotic complexity for rule 98 Solved the limit problem by the following transformations: Created initial limit problem: 1+free-free_1 (+/+!), 5+A-E (+), 1+A-E (+/+!), A-B (+/+!) [not solved] applying transformation rule (C) using substitution {A==1+B} resulting limit problem: 1 (+/+!), 6-E+B (+), 1+free-free_1 (+/+!), 2-E+B (+/+!) [not solved] applying transformation rule (C) using substitution {A==E} resulting limit problem: 1 (+/+!), 6-E+B (+), 1+free-free_1 (+/+!), 2-E+B (+/+!) [not solved] applying transformation rule (C) using substitution {free==free_1} resulting limit problem: 1 (+/+!), 6-E+B (+), 2-E+B (+/+!) [not solved] applying transformation rule (B), deleting 1 (+/+!) resulting limit problem: 6-E+B (+), 2-E+B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {E==-n,B==0} resulting limit problem: [solved] Solution: free / 0 free_1 / 0 A / 1 E / -n B / 0 Resulting cost 6+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: 6+n Rule cost: 5+A-E Rule guard: [ A>=1+B && A>=E && free>=free_1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)