/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 78 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C) -> Com_1(f10(1, B, C)) :|: TRUE f10(A, B, C) -> Com_1(f13(A, 1, C)) :|: 5 >= A f13(A, B, C) -> Com_1(f13(A, B + 1, C)) :|: 5 >= B f21(A, B, C) -> Com_1(f24(A, 1, C)) :|: 5 >= A f24(A, B, C) -> Com_1(f27(A, B, 1)) :|: 5 >= B f27(A, B, C) -> Com_1(f27(A, B, C + 1)) :|: 5 >= C f27(A, B, C) -> Com_1(f24(A, B + 1, C)) :|: C >= 6 f24(A, B, C) -> Com_1(f21(A + 1, B, C)) :|: B >= 6 f21(A, B, C) -> Com_1(f39(A, B, C)) :|: A >= 6 f13(A, B, C) -> Com_1(f10(A + 1, B, C)) :|: B >= 6 f10(A, B, C) -> Com_1(f21(1, B, C)) :|: A >= 6 The start-symbols are:[f0_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 1443) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: ?, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: ?, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 2 Pol(f10) = 2 Pol(f13) = 2 Pol(f21) = 1 Pol(f24) = 1 Pol(f27) = 1 Pol(f39) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f0) = 5 Pol(f10) = 5 Pol(f13) = 5 Pol(f21) = -V_1 + 6 Pol(f24) = -V_1 + 5 Pol(f27) = -V_1 + 5 Pol(f39) = -V_1 + 6 Pol(koat_start) = 5 orients all transitions weakly and the transition f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: 5, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f27) = 1 Pol(f24) = 1 Pol(f21) = 0 Pol(f13) = 0 Pol(f10) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = 6 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = Ar_2 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = ? S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = Ar_2 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = ? S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = ? S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-0) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-1) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-0) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-1) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-0) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-1) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-2) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = ? S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 + 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-0) = ? S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-0) = 1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] weakly and the transition f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: ?, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: 5, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: 5, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f27) = -V_2 + 5 Pol(f24) = -V_2 + 6 Pol(f13) = -V_1 + 5 Pol(f10) = -V_1 + 6 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = 6 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = Ar_2 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = ? S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = Ar_2 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 6 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = ? S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-0) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-1) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-0) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-1) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-0) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-1) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-2) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = 6 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 + 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-0) = ? S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-0) = 1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] weakly and the transitions f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: 42, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: 5, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: 42, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: 5, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f27) = 1 Pol(f24) = 0 Pol(f13) = 1 Pol(f10) = 0 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = 6 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = Ar_2 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = ? S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = Ar_2 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 6 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = ? S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-0) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-1) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-0) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-1) = ? S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-0) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-1) = ? S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-2) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = 6 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 + 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-0) = ? S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = ? S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-0) = 1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] weakly and the transitions f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: 42, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: ?, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: 5, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: 42, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: ?, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: 84, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: 5, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 84, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f27) = -V_3 + 6 Pol(f13) = -V_2 + 6 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = 6 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = Ar_2 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = 85 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = Ar_2 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-0) = 6 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-1) = 85 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-0) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-1) = 85 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-0) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-1) = 85 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ]", 0-2) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-0) = 6 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-1) = 85 S("f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ]", 0-2) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-0) = 6 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-1) = 85 S("f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ]", 0-2) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = 6 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 + 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-0) = 85 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-1) = 6 S("f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ]", 0-2) = Ar_2 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-0) = 85 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-1) = 1 S("f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ]", 0-2) = Ar_2 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-0) = 1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-1) = Ar_1 S("f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2))", 0-2) = Ar_2 orients the transitions f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] weakly and the transitions f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) f0(Ar_0, Ar_1, Ar_2) -> Com_1(f10(1, Ar_1, Ar_2)) (Comp: 42, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: 588, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f13(Ar_0, Ar_1 + 1, Ar_2)) [ 5 >= Ar_1 ] (Comp: 5, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, 1, Ar_2)) [ 5 >= Ar_0 ] (Comp: 42, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, 1)) [ 5 >= Ar_1 ] (Comp: 588, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f27(Ar_0, Ar_1, Ar_2 + 1)) [ 5 >= Ar_2 ] (Comp: 84, Cost: 1) f27(Ar_0, Ar_1, Ar_2) -> Com_1(f24(Ar_0, Ar_1 + 1, Ar_2)) [ Ar_2 >= 6 ] (Comp: 5, Cost: 1) f24(Ar_0, Ar_1, Ar_2) -> Com_1(f21(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f21(Ar_0, Ar_1, Ar_2) -> Com_1(f39(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 84, Cost: 1) f13(Ar_0, Ar_1, Ar_2) -> Com_1(f10(Ar_0 + 1, Ar_1, Ar_2)) [ Ar_1 >= 6 ] (Comp: 2, Cost: 1) f10(Ar_0, Ar_1, Ar_2) -> Com_1(f21(1, Ar_1, Ar_2)) [ Ar_0 >= 6 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(f0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 1443 Time: 0.200 sec (SMT: 0.166 sec) ---------------------------------------- (2) BOUNDS(1, 1)