/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 129 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f14(A, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q)) :|: 9 >= A f33(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f36(A, B, C, 0, E, F, G, H, I, J, K, L, M, N, O, P, Q)) :|: 9 >= C f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f36(A, B, C, D + 1, E + S, F + 1, G, H, I, J, K, L, M, N, O, P, Q)) :|: 9 >= D && 0 >= R + 1 f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f36(A, B, C, D + 1, E, F, G + S, H + 1, I, J, K, L, M, N, O, P, Q)) :|: 9 >= D f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f33(A, B, C + 1, D, E, F, G, H, I, J, K, L, M, N, O, P, Q)) :|: D >= 10 f33(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f58(A, B, C, D, E, F, G, H, E, F, G, H, 1500, S, O, P, Q)) :|: C >= 10 f14(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f14(A, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, S, S, Q)) :|: 9 >= B f14(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f11(A + 1, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q)) :|: B >= 10 f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f33(A, B, 0, D, 0, 0, 0, 0, I, J, K, L, M, N, O, P, 1000)) :|: A >= 10 f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q) -> Com_1(f11(0, B, C, D, E, F, G, H, I, J, K, L, M, N, 0, P, Q)) :|: TRUE The start-symbols are:[f0_17] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 645) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ 9 >= Ar_0 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4 + Fresh_3, Ar_5 + 1, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6 + Fresh_2, Ar_7 + 1, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7, 1500, Fresh_1, Ar_14, Ar_15, Ar_16)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Fresh_0, Fresh_0, Ar_16)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3, 0, 0, 0, 0, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, 1000)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, 0, Ar_15, Ar_16)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8, Ar_9, Ar_10, Ar_11, Ar_12, Ar_13, Ar_14, Ar_15, Ar_16)) [ 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]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(f0) = 2 Pol(f11) = 2 Pol(f33) = 1 Pol(f14) = 2 Pol(f58) = 0 Pol(f36) = 1 orients all transitions weakly and the transitions f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: 2, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 10 Pol(f0) = 10 Pol(f11) = 10 Pol(f33) = -V_3 + 10 Pol(f14) = 10 Pol(f58) = -V_3 Pol(f36) = -V_3 + 9 orients all transitions weakly and the transition f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: 2, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: 10, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f36) = 1 Pol(f33) = 0 Pol(f14) = 0 Pol(f11) = 0 and size complexities S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-0) = ? S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-1) = 0 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-2) = Ar_2 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-3) = Ar_3 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-0) = ? S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-1) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-2) = ? S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-3) = 0 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-0) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-2) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-3) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-0) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-2) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-3) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-0) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-2) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-3) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-0) = ? S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-1) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-2) = ? S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-3) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-0) = ? S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-1) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-2) = Ar_2 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-3) = Ar_3 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-0) = ? S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-1) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-2) = Ar_2 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-3) = Ar_3 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-0) = ? S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-1) = 10 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-2) = 0 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-3) = Ar_3 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-0) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] weakly and the transition f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: 2, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: 10, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: 10, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: ?, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 10 Pol(f0) = 10 Pol(f11) = -V_1 + 10 Pol(f33) = -V_1 Pol(f14) = -V_1 + 9 Pol(f58) = -V_1 Pol(f36) = -V_1 orients all transitions weakly and the transition f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: 2, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: 10, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: 10, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: 10, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f36) = 0 Pol(f14) = 1 Pol(f11) = 0 and size complexities S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-0) = ? S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-1) = 0 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-2) = Ar_2 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-3) = Ar_3 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-0) = ? S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-1) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-2) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-3) = 0 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-0) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-2) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-3) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-0) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-2) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-3) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-0) = ? S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-2) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-3) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-0) = ? S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-1) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-2) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-3) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-0) = ? S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-1) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-2) = Ar_2 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-3) = Ar_3 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-0) = ? S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-1) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-2) = Ar_2 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-3) = Ar_3 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-0) = ? S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-1) = 10 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-2) = 0 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-3) = Ar_3 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-0) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] weakly and the transition f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: 10, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: ?, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: 2, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: 10, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: ?, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: 10, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: 10, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f36) = -V_4 + 10 Pol(f14) = -V_2 + 10 and size complexities S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-0) = 10 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-1) = 0 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-2) = Ar_2 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ]", 0-3) = Ar_3 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-0) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-1) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-2) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ]", 0-3) = 0 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-0) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-2) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\\ 0 >= R + 1 ]", 0-3) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-0) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-2) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ]", 0-3) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-0) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-1) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-2) = 10 S("f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ]", 0-3) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-0) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-1) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-2) = 10 S("f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ]", 0-3) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-0) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-1) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-2) = Ar_2 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ]", 0-3) = Ar_3 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-0) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-1) = 10 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-2) = Ar_2 S("f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ]", 0-3) = Ar_3 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-0) = 10 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-1) = 10 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-2) = 0 S("f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ]", 0-3) = Ar_3 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-0) = 0 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3 orients the transitions f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] weakly and the transitions f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(0, Ar_1, Ar_2, Ar_3)) (Comp: 2, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, 0, Ar_3)) [ Ar_0 >= 10 ] (Comp: 10, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f11(Ar_0 + 1, Ar_1, Ar_2, Ar_3)) [ Ar_1 >= 10 ] (Comp: 200, Cost: 1) f14(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, Ar_1 + 1, Ar_2, Ar_3)) [ 9 >= Ar_1 ] (Comp: 2, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f58(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 10 ] (Comp: 10, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f33(Ar_0, Ar_1, Ar_2 + 1, Ar_3)) [ Ar_3 >= 10 ] (Comp: 200, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 ] (Comp: 200, Cost: 1) f36(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, Ar_3 + 1)) [ 9 >= Ar_3 /\ 0 >= R + 1 ] (Comp: 10, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f36(Ar_0, Ar_1, Ar_2, 0)) [ 9 >= Ar_2 ] (Comp: 10, Cost: 1) f11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(f14(Ar_0, 0, Ar_2, Ar_3)) [ 9 >= Ar_0 ] start location: koat_start leaf cost: 0 Complexity upper bound 645 Time: 0.161 sec (SMT: 0.127 sec) ---------------------------------------- (2) BOUNDS(1, 1)