/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).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, 134 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f0(A, B, C, D, E, F, G) -> Com_1(f8(-(1), -(1), 1, D, E, F, G)) :|: TRUE f8(A, B, C, D, E, F, G) -> Com_1(f8(A, B, C + 1, D, E, F, G)) :|: 100 >= C f18(A, B, C, D, E, F, G) -> Com_1(f22(A, B, C, D, 1, 1, G)) :|: 99 >= D f22(A, B, C, D, E, F, G) -> Com_1(f33(A, B, C, D, E, F, G)) :|: F >= 100 f22(A, B, C, D, E, F, G) -> Com_1(f33(A, B, C, D, E, F, G)) :|: 99 >= F && F + D >= 101 f22(A, B, C, D, E, F, G) -> Com_1(f22(A, B, C, D, E, F + 1, G)) :|: 99 >= F && 100 >= D + F f22(A, B, C, D, E, F, G) -> Com_1(f22(A, B, C, D, 0, F + 1, H)) :|: 99 >= F && 100 >= D + F f33(A, B, C, D, E, F, G) -> Com_1(f18(A, B, C, D + 1, 0, F, G)) :|: E >= 0 && E <= 0 f18(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D, E, F, G)) :|: D >= 100 f33(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D, E, F, G)) :|: 0 >= E + 1 f33(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D, E, F, G)) :|: E >= 1 f8(A, B, C, D, E, F, G) -> Com_1(f18(A, B, C, 1, 0, F, G)) :|: C >= 101 The start-symbols are:[f0_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 20800) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f8(-1, -1, 1, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f8(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4, Ar_5, Ar_6)) [ 100 >= Ar_2 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, 1, 1, Ar_6)) [ 99 >= Ar_3 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 >= 100 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f22(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5 + 1, Fresh_0)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f18(Ar_0, Ar_1, Ar_2, Ar_3 + 1, 0, Ar_5, Ar_6)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f18(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f40(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_3 >= 100 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f40(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f33(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f40(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) f8(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f18(Ar_0, Ar_1, Ar_2, 1, 0, Ar_5, Ar_6)) [ Ar_2 >= 101 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_2, Ar_3, Ar_4, Ar_5]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: ?, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: ?, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) 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_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: ?, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(f0) = 2 Pol(f8) = 2 Pol(f18) = 1 Pol(f33) = 1 Pol(f40) = 0 Pol(f22) = 1 orients all transitions weakly and the transitions f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: ?, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 99 Pol(f0) = 99 Pol(f8) = 99 Pol(f18) = -V_2 + 100 Pol(f33) = -V_2 + 99 Pol(f40) = -V_2 Pol(f22) = -V_2 + 99 orients all transitions weakly and the transition f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: ?, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: 99, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f8) = 0 Pol(f33) = 1 Pol(f18) = 0 Pol(f22) = 2 and size complexities S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-0) = 1 S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_3 S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_4 S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_5 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-0) = 101 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-1) = Ar_3 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-2) = Ar_4 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-3) = Ar_5 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-0) = 101 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-1) = ? S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-2) = 1 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-3) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-1) = ? S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-2) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-3) = 100 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-1) = ? S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-2) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-3) = 100 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-1) = ? S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-2) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-3) = 100 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-1) = ? S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-2) = 0 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-3) = 100 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-0) = 101 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-1) = ? S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-2) = 0 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-3) = 100 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-0) = 101 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-1) = ? S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-2) = 0 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-3) = 100 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-0) = 101 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-1) = ? S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-2) = 1 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-3) = 100 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-0) = 101 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-1) = ? S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-2) = 1 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-3) = 100 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-0) = 101 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-1) = 1 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-2) = 0 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-3) = Ar_5 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_2 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_3 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] weakly and the transitions f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: 198, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: 198, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: 198, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: 99, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: ?, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 100 Pol(f0) = 100 Pol(f8) = -V_1 + 101 Pol(f18) = -V_1 Pol(f33) = -V_1 Pol(f40) = -V_1 Pol(f22) = -V_1 orients all transitions weakly and the transition f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: 198, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: ?, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: 198, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: 198, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: 99, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: 100, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f22) = -V_4 + 100 and size complexities S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-0) = 1 S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-1) = Ar_3 S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-2) = Ar_4 S("f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5))", 0-3) = Ar_5 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-0) = 101 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-1) = Ar_3 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-2) = Ar_4 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ]", 0-3) = Ar_5 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-0) = 101 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-1) = 199 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-2) = 1 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ]", 0-3) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-1) = 199 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-2) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ]", 0-3) = 100 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-1) = 199 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-2) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\\ Ar_5 + Ar_3 >= 101 ]", 0-3) = 100 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-1) = 199 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-2) = 1 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-3) = 100 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-0) = 101 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-1) = 199 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-2) = 0 S("f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\\ 100 >= Ar_3 + Ar_5 ]", 0-3) = 100 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-0) = 101 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-1) = 199 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-2) = 0 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ]", 0-3) = 100 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-0) = 101 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-1) = 199 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-2) = 0 S("f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ]", 0-3) = 100 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-0) = 101 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-1) = 199 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-2) = 1 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ]", 0-3) = 100 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-0) = 101 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-1) = 199 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-2) = 1 S("f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ]", 0-3) = 100 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-0) = 101 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-1) = 1 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-2) = 0 S("f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ]", 0-3) = Ar_5 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_2 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_3 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] weakly and the transitions f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, 1, 0, Ar_5)) [ Ar_2 >= 101 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_4 >= 1 ] (Comp: 2, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ 0 >= Ar_4 + 1 ] (Comp: 2, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f40(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= 100 ] (Comp: 198, Cost: 1) f33(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f18(Ar_2, Ar_3 + 1, 0, Ar_5)) [ Ar_4 = 0 ] (Comp: 9999, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 0, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: 9999, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, Ar_4, Ar_5 + 1)) [ 99 >= Ar_5 /\ 100 >= Ar_3 + Ar_5 ] (Comp: 198, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ 99 >= Ar_5 /\ Ar_5 + Ar_3 >= 101 ] (Comp: 198, Cost: 1) f22(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f33(Ar_2, Ar_3, Ar_4, Ar_5)) [ Ar_5 >= 100 ] (Comp: 99, Cost: 1) f18(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f22(Ar_2, Ar_3, 1, 1)) [ 99 >= Ar_3 ] (Comp: 100, Cost: 1) f8(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(Ar_2 + 1, Ar_3, Ar_4, Ar_5)) [ 100 >= Ar_2 ] (Comp: 1, Cost: 1) f0(Ar_2, Ar_3, Ar_4, Ar_5) -> Com_1(f8(1, Ar_3, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 Complexity upper bound 20800 Time: 0.183 sec (SMT: 0.150 sec) ---------------------------------------- (2) BOUNDS(1, 1)