/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 639 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 4552 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C, D, E, F, G, H) -> Com_1(f12(A, B, 0, B, E, F, G, H)) :|: A >= B + 1 f12(A, B, C, D, E, F, G, H) -> Com_1(f12(A, B, C, D, E + 1, J, I, H)) :|: A >= E && I >= J f12(A, B, C, D, E, F, G, H) -> Com_1(f12(A, B, J, E, E + 1, I, K, H)) :|: A >= E && I >= 1 + K f22(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E + 1, F, G, J)) :|: A >= E f29(A, B, C, D, E, F, G, H) -> Com_1(f29(A, B, C, D, E + 1, F, G, J)) :|: A >= E f35(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 f35(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D, E, F, G, H)) :|: C >= 1 f37(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && 0 >= I + 1 f37(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 f48(A, B, C, D, E, F, G, H) -> Com_1(f48(A, B, C, D, E + 1, F, G, H)) :|: A >= E f37(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D + 1, E, F, G, 0)) :|: A >= D f35(A, B, C, D, E, F, G, H) -> Com_1(f0(A, B + 1, 0, D, E, F, G, H)) :|: C >= 0 && C <= 0 f48(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D + 1, E, F, G, H)) :|: E >= 1 + A f43(A, B, C, D, E, F, G, H) -> Com_1(f48(A, B, C, D, E, F, G, H)) :|: E >= 1 + A f37(A, B, C, D, E, F, G, H) -> Com_1(f0(A, B + 1, C, D, E, F, G, H)) :|: D >= 1 + A f29(A, B, C, D, E, F, G, H) -> Com_1(f35(A, B, C, D, E, F, G, H)) :|: E >= 1 + A f22(A, B, C, D, E, F, G, H) -> Com_1(f29(A, B, C, D, E, F, G, H)) :|: E >= 1 + A f12(A, B, C, D, E, F, G, H) -> Com_1(f35(A, B, C, B, E, F, G, H)) :|: E >= 1 + A && B >= D && B <= D f12(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, F, G, H)) :|: B >= D + 1 && E >= 1 + A f12(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, F, G, H)) :|: D >= 1 + B && E >= 1 + A f0(A, B, C, D, E, F, G, H) -> Com_1(f58(A, B, C, D, E, F, G, H)) :|: B >= A start(A, B, C, D, E, F, G, H) -> Com_1(f0(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) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Fresh_7, Fresh_8, Ar_7)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1, Fresh_5, Fresh_6, Ar_7)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Fresh_3)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Fresh_2)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f37(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, Fresh_1)) [ Ar_0 >= Ar_3 /\ 0 >= I + 1 ] (Comp: ?, Cost: 1) f37(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, Fresh_0)) [ 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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6, 0)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f37(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f0(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f35(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f22(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) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(f58(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(f0(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(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\ Ar_1 = Ar_3 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f48(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) f37(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) f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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: f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 ] f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 ] f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\ Ar_1 = Ar_3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\ Ar_1 = Ar_3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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(f48) = 1 Pol(f37) = 1 Pol(f43) = 1 Pol(f29) = 1 Pol(f35) = 1 Pol(f0) = 1 Pol(f22) = 1 Pol(f12) = 1 Pol(f58) = 0 Pol(start) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\ Ar_1 = Ar_3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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(f48) = V_1 - V_5 + 1 Pol(f37) = V_1 - V_5 + 1 Pol(f43) = V_1 - V_5 + 1 Pol(f29) = V_1 - V_5 + 1 Pol(f35) = V_1 - V_5 + 1 Pol(f0) = V_1 - V_5 + 1 Pol(f22) = V_1 - V_5 + 1 Pol(f12) = V_1 - V_5 + 1 Pol(f58) = 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 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 ] f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] strictly and produces the following problem: 6: T: (Comp: ?, Cost: 1) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\ Ar_1 = Ar_3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\ Ar_1 = Ar_3 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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(f48) = V_1 - V_2 - 1 Pol(f37) = V_1 - V_2 - 1 Pol(f43) = V_1 - V_2 - 1 Pol(f29) = V_1 - V_2 - 1 Pol(f35) = V_1 - V_2 - 1 Pol(f0) = V_1 - V_2 Pol(f22) = V_1 - V_2 - 1 Pol(f12) = V_1 - V_2 - 1 Pol(f58) = V_1 - V_2 Pol(start) = V_1 - V_2 Pol(koat_start) = V_1 - V_2 orients all transitions weakly and the transition f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ] (Comp: ?, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] (Comp: ?, Cost: 1) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: 3*Ar_0 + Ar_1 + 2*Ar_4 + 2, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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(f48) = 1 Pol(f37) = 1 Pol(f43) = 1 Pol(f0) = 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(f0(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(f0(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(f0(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(f0(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(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))", 0-4) = Ar_4 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-1) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 192 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-1) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-3) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 48 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\\ Ar_1 = Ar_3 ]", 0-0) = Ar_0 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\\ Ar_1 = Ar_3 ]", 0-1) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\\ Ar_1 = Ar_3 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_1, Ar_4)) [ Ar_4 >= Ar_0 + 1 /\\ Ar_1 = Ar_3 ]", 0-3) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-0) = Ar_0 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-1) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-3) = 4*Ar_0 + 4*Ar_4 + 192 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 48 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-0) = Ar_0 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-1) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-3) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 48 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ]", 0-0) = Ar_0 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ]", 0-1) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ]", 0-2) = 0 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ]", 0-3) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 48 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-0) = Ar_0 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-1) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-2) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-3) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 1 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 48 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ]", 0-0) = Ar_0 S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ]", 0-1) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ]", 0-2) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ]", 0-3) = ? S("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_2 + 1 ]", 0-4) = 4*Ar_0 + 4*Ar_4 + 48 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\\ Ar_4 >= Ar_0 + 1 ]", 0-1) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\\ Ar_4 >= Ar_0 + 1 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_1 + 1 /\\ Ar_4 >= Ar_0 + 1 ]", 0-3) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\\ Ar_4 >= Ar_0 + 1 ]", 0-1) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\\ Ar_4 >= Ar_0 + 1 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_3 + 1 /\\ Ar_4 >= Ar_0 + 1 ]", 0-3) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-1) = ? S("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-2) = ? S("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-3) = ? S("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ]", 0-1) = ? S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ]", 0-2) = ? S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ]", 0-3) = ? S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ]", 0-0) = Ar_0 S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ]", 0-1) = ? S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ]", 0-2) = ? S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ]", 0-3) = ? S("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-1) = ? S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-2) = ? S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-3) = ? S("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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(f48(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(f48(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(f48(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(f48(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(f48(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("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-0) = Ar_0 S("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-1) = ? S("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-2) = ? S("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]", 0-3) = ? S("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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 f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] f37(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 ] f37(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 ] f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4)) [ Ar_0 >= Ar_3 ] f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4)) [ Ar_3 >= Ar_0 + 1 ] weakly and the transition f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) f37(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) f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(Ar_0, Ar_1 + 1, 0, Ar_3, Ar_4)) [ Ar_2 = 0 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: 3*Ar_0 + Ar_1 + 2*Ar_4 + 2, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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 f12: X_1 - X_2 - 1 >= 0 For symbol f22: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f29: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f35: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 For symbol f37: -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 f48: -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 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(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: Ar_0 + Ar_1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: 7*Ar_0 + 6*Ar_4 + Ar_1 + 6, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f37(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) f37(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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(f48(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: Ar_0 + Ar_1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: 7*Ar_0 + 6*Ar_4 + Ar_1 + 6, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f37(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) f37(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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(f48(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48) = 3*V_1 - 3*V_4 + 1 Pol(f37) = 3*V_1 - 3*V_4 + 3 Pol(f43) = 3*V_1 - 3*V_4 + 2 and size complexities S("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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(f48(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(f48(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(f48(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(f48(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("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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("f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-0) = Ar_0 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-1) = 23*Ar_0 + 23*Ar_1 + 23*Ar_4 + 10051 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-3) = 23*Ar_0 + 23*Ar_1 + 23*Ar_4 + 5316979 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_8 >= Fresh_7 ]", 0-4) = 3*Ar_0 + 3*Ar_4 + 18 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-0) = Ar_0 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-1) = 23*Ar_0 + 23*Ar_1 + 23*Ar_4 + 10051 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-2) = ? S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-3) = 3*Ar_0 + 3*Ar_4 + 54 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 >= Ar_4 /\\ Fresh_5 >= Fresh_6 + 1 ]", 0-4) = 3*Ar_0 + 3*Ar_4 + 18 S("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-0) = Ar_0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-2) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, 0, Ar_1, Ar_4)) [ Ar_0 >= Ar_1 + 1 ]", 0-4) = 3*Ar_0 + 3*Ar_4 + 18 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-0) = Ar_0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-2) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ]", 0-3) = ? S("f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(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(f0(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(f0(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(f0(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(f0(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(f0(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 f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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 ] f37(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 ] f37(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 ] f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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 f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f48(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 ] f37(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 ] f37(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 ] f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 ] (Comp: Ar_0 + Ar_1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Fresh_4, Ar_4, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 >= Ar_4 /\ Fresh_5 >= Fresh_6 + 1 ] (Comp: Ar_0 + Ar_4 + 1, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1)) [ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 >= Ar_4 /\ Fresh_8 >= Fresh_7 ] (Comp: 7*Ar_0 + 6*Ar_4 + Ar_1 + 6, Cost: 1) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f35(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f22(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) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f29(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f0(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) f37(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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) f37(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) f37(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) f29(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f35(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(f48(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) f48(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(f37(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: 0.619 sec (SMT: 0.427 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 21: f0 -> f58 : [ B>=A ], cost: 1 1: f12 -> f12 : E'=1+E, F'=free, G'=free_1, [ A>=E && free_1>=free ], cost: 1 2: f12 -> f12 : C'=free_2, D'=E, E'=1+E, F'=free_4, G'=free_3, [ A>=E && free_4>=1+free_3 ], cost: 1 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 17: f22 -> f29 : [ E>=1+A ], cost: 1 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 16: f29 -> f35 : [ E>=1+A ], cost: 1 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f37 -> f43 : H'=free_7, [ A>=D && 0>=1+free_8 ], cost: 1 8: f37 -> f43 : H'=free_9, [ A>=D && free_10>=1 ], cost: 1 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 14: f43 -> f48 : [ E>=1+A ], cost: 1 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 22: start -> f0 : [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 22: start -> f0 : [], cost: 1 Removed unreachable and leaf rules: Start location: start 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 1: f12 -> f12 : E'=1+E, F'=free, G'=free_1, [ A>=E && free_1>=free ], cost: 1 2: f12 -> f12 : C'=free_2, D'=E, E'=1+E, F'=free_4, G'=free_3, [ A>=E && free_4>=1+free_3 ], cost: 1 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 17: f22 -> f29 : [ E>=1+A ], cost: 1 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 16: f29 -> f35 : [ E>=1+A ], cost: 1 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f37 -> f43 : H'=free_7, [ A>=D && 0>=1+free_8 ], cost: 1 8: f37 -> f43 : H'=free_9, [ A>=D && free_10>=1 ], cost: 1 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 14: f43 -> f48 : [ E>=1+A ], cost: 1 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 22: start -> f0 : [], cost: 1 Simplified all rules, resulting in: Start location: start 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 1: f12 -> f12 : E'=1+E, F'=free, G'=free_1, [ A>=E && free_1>=free ], cost: 1 2: f12 -> f12 : C'=free_2, D'=E, E'=1+E, F'=free_4, G'=free_3, [ A>=E && free_4>=1+free_3 ], cost: 1 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 17: f22 -> f29 : [ E>=1+A ], cost: 1 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 16: f29 -> f35 : [ E>=1+A ], cost: 1 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f37 -> f43 : H'=free_7, [ A>=D ], cost: 1 8: f37 -> f43 : H'=free_9, [ A>=D ], cost: 1 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 14: f43 -> f48 : [ E>=1+A ], cost: 1 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 22: start -> f0 : [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 1: f12 -> f12 : E'=1+E, F'=free, G'=free_1, [ A>=E && free_1>=free ], cost: 1 2: f12 -> f12 : C'=free_2, D'=E, E'=1+E, F'=free_4, G'=free_3, [ A>=E && free_4>=1+free_3 ], 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: f22 -> f22 : 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: f29 -> f29 : 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: f37 -> f37 : 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: f48 -> f48 : 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: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 23: f12 -> f12 : E'=1+A, F'=free, G'=free_1, [ A>=E && free_1>=free ], cost: 1+A-E 24: f12 -> f12 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=E && free_4>=1+free_3 ], cost: 1+A-E 17: f22 -> f29 : [ E>=1+A ], cost: 1 25: f22 -> f22 : E'=1+A, H'=free_5, [ A>=E ], cost: 1+A-E 16: f29 -> f35 : [ E>=1+A ], cost: 1 26: f29 -> f29 : E'=1+A, H'=free_6, [ A>=E ], cost: 1+A-E 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 7: f37 -> f43 : H'=free_7, [ A>=D ], cost: 1 8: f37 -> f43 : H'=free_9, [ A>=D ], cost: 1 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 27: f37 -> f37 : D'=1+A, H'=0, [ A>=D ], cost: 1-D+A 14: f43 -> f48 : [ E>=1+A ], cost: 1 28: f43 -> f43 : E'=1+A, [ A>=E ], cost: 1+A-E 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 29: f48 -> f48 : E'=1+A, [ A>=E ], cost: 1+A-E 22: start -> f0 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 30: f0 -> f12 : C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 31: f0 -> f12 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 17: f22 -> f29 : [ E>=1+A ], cost: 1 16: f29 -> f35 : [ E>=1+A ], cost: 1 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 7: f37 -> f43 : H'=free_7, [ A>=D ], cost: 1 8: f37 -> f43 : H'=free_9, [ A>=D ], cost: 1 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 35: f37 -> f43 : E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 2+A-E 36: f37 -> f43 : E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 2+A-E 14: f43 -> f48 : [ E>=1+A ], cost: 1 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f0 : [], cost: 1 Eliminated locations (on linear paths): Start location: start 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 30: f0 -> f12 : C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 31: f0 -> f12 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 37: f22 -> f35 : [ E>=1+A ], cost: 2 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 7: f37 -> f43 : H'=free_7, [ A>=D ], cost: 1 8: f37 -> f43 : H'=free_9, [ A>=D ], cost: 1 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 35: f37 -> f43 : E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 2+A-E 36: f37 -> f43 : E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 2+A-E 14: f43 -> f48 : [ E>=1+A ], cost: 1 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f0 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start 38: f0 -> f35 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2 39: f0 -> f35 : C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 40: f0 -> f22 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 3+A-E 41: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 37: f22 -> f35 : [ E>=1+A ], cost: 2 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 43: f37 -> f48 : H'=free_7, [ A>=D && E>=1+A ], cost: 2 44: f37 -> f48 : H'=free_9, [ A>=D && E>=1+A ], cost: 2 45: f37 -> f48 : E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 3+A-E 46: f37 -> f48 : E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 3+A-E 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f0 : [], cost: 1 Eliminated locations (on linear paths): Start location: start 38: f0 -> f35 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2 39: f0 -> f35 : C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 41: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 47: f0 -> f35 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 5+A-E 5: f35 -> f37 : [ 0>=1+C ], cost: 1 6: f35 -> f37 : [ C>=1 ], cost: 1 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 43: f37 -> f48 : H'=free_7, [ A>=D && E>=1+A ], cost: 2 44: f37 -> f48 : H'=free_9, [ A>=D && E>=1+A ], cost: 2 45: f37 -> f48 : E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 3+A-E 46: f37 -> f48 : E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 3+A-E 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 22: start -> f0 : [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start 41: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 48: f0 -> f0 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 4+A-E 50: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 6+A-E 51: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 6+A-E 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2==0 ], cost: 6+A-E 53: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 7+A-E 54: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 7+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 56: f37 -> f37 : D'=1+D, H'=free_7, [ A>=D && E>=1+A ], cost: 3 57: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 58: f37 -> f37 : D'=1+D, H'=free_9, [ A>=D && E>=1+A ], cost: 3 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 4+A-E 61: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 4+A-E 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 22: start -> f0 : [], cost: 1 Applied pruning (of leafs and parallel rules): Start location: start 41: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 48: f0 -> f0 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 4+A-E 50: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 6+A-E 51: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 6+A-E 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2==0 ], cost: 6+A-E 53: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 7+A-E 54: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 7+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 56: f37 -> f37 : D'=1+D, H'=free_7, [ A>=D && E>=1+A ], cost: 3 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 4+A-E 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 4+A-E 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 22: start -> f0 : [], cost: 1 Accelerating simple loops of location 0. Simplified some of the simple loops (and removed duplicate rules). Accelerating the following rules: 48: f0 -> f0 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 4+A-E 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], 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: f37 -> f37 : D'=1+D, H'=free_7, [ A>=D && E>=1+A ], cost: 3 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 4+A-E 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 4+A-E 63: f37 -> f37 : 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: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 4+A-E 50: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 6+A-E 51: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 6+A-E 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 6+A-E 53: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 7+A-E 54: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 7+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 64: f0 -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 3*A-3*B 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_7, [ A>=D && A>=E ], cost: 4+A-E 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_9, [ A>=D && A>=E ], cost: 4+A-E 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 65: f37 -> f37 : D'=1+A, H'=free_7, [ A>=D && E>=1+A ], cost: 3-3*D+3*A 22: start -> f0 : [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start 41: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 50: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 6+A-E 51: f0 -> f37 : C'=free_2, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 6+A-E 53: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 7+A-E 54: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 7+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 72: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 9+A-E 73: f0 -> f37 : C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 66: f37 -> f0 : B'=2+B, C'=0, D'=1+B, E'=1+A, F'=free, G'=free_1, [ D>=1+A && A>=2+B && A>=E && free_1>=free ], cost: 5+A-E 68: f37 -> f0 : B'=2+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ D>=1+A && A>=2+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 70: f37 -> f0 : B'=A, C'=0, D'=-1+A, [ D>=1+A && A>=2+B && E>=1+A ], cost: -2+3*A-3*B 22: start -> f0 : [], cost: 1 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 71: start -> f0 : 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: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 74: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 8+A-E 75: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && 0>=1+free_2 && A>=2+B ], cost: 5+4*A-E-3*B 76: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 8+A-E 77: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && free_2>=1 && A>=2+B ], cost: 5+4*A-E-3*B 78: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 10+A-E 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=E && free_4>=1+free_3 && 0>=1+free_2 && A>=2+B ], cost: 7+4*A-E-3*B 80: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 10+A-E 81: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=E && free_4>=1+free_3 && free_2>=1 && A>=2+B ], cost: 7+4*A-E-3*B 82: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 6+A-E 83: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 6+A-E 84: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 7+A-E 85: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 7+A-E 86: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 9+A-E 87: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 22: start -> f0 : [], cost: 1 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 71: start -> f0 : 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: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 75: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && 0>=1+free_2 && A>=2+B ], cost: 5+4*A-E-3*B 76: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 8+A-E 77: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && free_2>=1 && A>=2+B ], cost: 5+4*A-E-3*B 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=E && free_4>=1+free_3 && 0>=1+free_2 && A>=2+B ], cost: 7+4*A-E-3*B 80: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 10+A-E 86: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 9+A-E 87: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 22: start -> f0 : [], cost: 1 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 71: start -> f0 : 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: 76: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 8+A-E 77: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 7+4*A-E-3*B 80: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 10+A-E Found no metering function for rule 76. Found no metering function for rule 77. 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: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 76: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 8+A-E 77: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 7+4*A-E-3*B 80: f0 -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 10+A-E 86: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 9+A-E 87: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 22: start -> f0 : [], cost: 1 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 71: start -> f0 : 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: f0 -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 2+A-E 42: f0 -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 2+A-E 55: f0 -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 86: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 9+A-E 87: f0 -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 22: start -> f0 : [], cost: 1 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free, G'=free_1, [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_4, G'=free_3, [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 71: start -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 88: start -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 89: start -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=0, [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 6+4*A-E-3*B 90: start -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 8+4*A-E-3*B 91: start -> f0 : B'=1+B, C'=free_2, D'=1+A, E'=1+A, F'=free_4, G'=free_3, H'=free_7, [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 11+A-E Eliminated locations (on tree-shaped paths): Start location: start 92: start -> [16] : [ A>=1+B && A>=E && free_1>=free ], cost: 3+A-E 93: start -> [16] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 3+A-E 94: start -> [17] : [ A>=1+B && A>=E && free_1>=free ], cost: 4+A-E 95: start -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 10+A-E 96: start -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 10+A-E 97: start -> [22] : [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 98: start -> [22] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 99: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 100: start -> [22] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 9+A-E 101: start -> [22] : [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 6+4*A-E-3*B 102: start -> [22] : [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 8+4*A-E-3*B 103: start -> [22] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 11+A-E ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start 95: start -> [20] : [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ], cost: 10+A-E 97: start -> [22] : [ A>=1+B && A>=E && free_1>=free ], cost: 5+A-E 98: start -> [22] : [ A>=1+B && A>=E && free_4>=1+free_3 ], cost: 7+A-E 99: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 102: start -> [22] : [ A>=E && free_4>=1+free_3 && A>=2+B ], cost: 8+4*A-E-3*B 103: start -> [22] : [ A>=1+B && A>=E && free_4>=1+free_3 && free_2>=1 ], cost: 11+A-E Computing asymptotic complexity for rule 95 Solved the limit problem by the following transformations: Created initial limit problem: 1+A-E (+/+!), A-B (+/+!), 10+A-E (+), free_4-free_3 (+/+!), -free_2 (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {free_4==0,A==1,free_2==-n,E==-n,B==0,free_3==-1} resulting limit problem: [solved] Solution: free_4 / 0 A / 1 free_2 / -n E / -n B / 0 free_3 / -1 Resulting cost 11+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: 11+n Rule cost: 10+A-E Rule guard: [ A>=1+B && A>=E && free_4>=1+free_3 && 0>=1+free_2 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)