/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).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, 229 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(f12(2, H, I, 0, E, F, G)) :|: TRUE f12(A, B, C, D, E, F, G) -> Com_1(f15(A, B, C, D, 0, F, G)) :|: A >= D + 1 f15(A, B, C, D, E, F, G) -> Com_1(f15(A, B, C, D, E + 1, F, G)) :|: A >= E + 1 f23(A, B, C, D, E, F, G) -> Com_1(f26(A, B, C, D, 0, F, G)) :|: A >= D + 1 f26(A, B, C, D, E, F, G) -> Com_1(f30(A, B, C, D, E, 0, G)) :|: A >= E + 1 f30(A, B, C, D, E, F, G) -> Com_1(f30(A, B, C, D, E, F + 1, G)) :|: A >= F + 1 f30(A, B, C, D, E, F, G) -> Com_1(f26(A, B, C, D, E + 1, F, G)) :|: F >= A f26(A, B, C, D, E, F, G) -> Com_1(f23(A, B, C, D + 1, E, F, G)) :|: E >= A f23(A, B, C, D, E, F, G) -> Com_1(f52(A, B, C, D, E, F, 0)) :|: D >= A f23(A, B, C, D, E, F, G) -> Com_1(f52(A, B, C, D, E, F, 1)) :|: D >= A && 49 >= H f23(A, B, C, D, E, F, G) -> Com_1(f52(A, B, C, D, E, F, 1)) :|: D >= A f23(A, B, C, D, E, F, G) -> Com_1(f52(A, B, C, D, E, F, 1)) :|: D >= A && 42 >= H f23(A, B, C, D, E, F, G) -> Com_1(f52(A, B, C, D, E, F, 1)) :|: D >= A && 21 >= H f23(A, B, C, D, E, F, G) -> Com_1(f52(A, B, C, D, E, F, 1)) :|: D >= A && 18 >= H f15(A, B, C, D, E, F, G) -> Com_1(f12(A, B, C, D + 1, E, F, G)) :|: E >= A f12(A, B, C, D, E, F, G) -> Com_1(f23(A, B, C, 0, E, F, G)) :|: D >= A The start-symbols are:[f0_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 147) 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(f12(2, Fresh_0, Fresh_1, 0, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f15(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f26(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, 0, Ar_6)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6)) [ Ar_0 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f23(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f52(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, 0)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f52(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, 1)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f52(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, 1)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f52(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, 1)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f52(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, 1)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f52(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, 1)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f12(Ar_0, Ar_1, Ar_2, Ar_3 + 1, Ar_4, Ar_5, Ar_6)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(f23(Ar_0, Ar_1, Ar_2, 0, Ar_4, Ar_5, Ar_6)) [ Ar_3 >= Ar_0 ] (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_0, Ar_3, Ar_4, Ar_5]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, 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_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 2 Pol(f0) = 2 Pol(f12) = 2 Pol(f23) = 1 Pol(f15) = 2 Pol(f52) = 0 Pol(f26) = 1 Pol(f30) = 1 orients all transitions weakly and the transitions f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 3 Pol(f0) = 3 Pol(f12) = V_1 + 1 Pol(f23) = V_1 - V_2 + 1 Pol(f15) = V_1 + 1 Pol(f52) = V_1 - V_2 Pol(f26) = V_1 - V_2 Pol(f30) = V_1 - V_2 orients all transitions weakly and the transition f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 3, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f30) = 1 Pol(f26) = 1 Pol(f23) = 0 Pol(f15) = 0 Pol(f12) = 0 and size complexities S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-0) = 2 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-1) = 0 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-2) = Ar_4 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = Ar_5 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = Ar_5 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = 0 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-1) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-2) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-3) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-1) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-2) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-1) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-3) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = Ar_5 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_3 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] weakly and the transition f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 3, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: ?, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 3, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: ?, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f30) = V_1 - V_3 - 1 Pol(f26) = V_1 - V_3 Pol(f15) = V_1 - V_2 Pol(f12) = V_1 - V_2 + 1 and size complexities S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-0) = 2 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-1) = 0 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-2) = Ar_4 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = Ar_5 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = Ar_5 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = 3 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = 0 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-1) = 3 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-2) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-3) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-1) = 3 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-2) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = 3 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-3) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = Ar_5 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_3 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] weakly and the transitions f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] strictly and produces the following problem: 7: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 3, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: 9, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 3, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 9, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f30) = 1 Pol(f26) = 0 Pol(f15) = 1 Pol(f12) = 0 and size complexities S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-0) = 2 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-1) = 0 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-2) = Ar_4 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = Ar_5 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = Ar_5 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = 3 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = 0 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-1) = 3 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-2) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-3) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-1) = 3 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-2) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = 3 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-3) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = Ar_5 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_3 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] weakly and the transitions f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 18, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 3, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 18, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: ?, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: 9, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 3, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: ?, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 9, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f30) = V_1 - V_4 Pol(f15) = V_1 - V_3 and size complexities S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-0) = 2 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-1) = 0 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-2) = Ar_4 S("f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5))", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = 18 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = Ar_5 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = 18 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = Ar_5 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-2) = 0 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-1) = 3 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-2) = 18 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ]", 0-3) = 0 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-1) = 3 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-2) = 18 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ]", 0-3) = ? S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-0) = 2 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-1) = 3 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-2) = 18 S("f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ]", 0-3) = ? S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = 3 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = 18 S("f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 49 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 42 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 21 >= H ]", 0-3) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-0) = 2 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-1) = 3 S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-2) = ? S("f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\\ 18 >= H ]", 0-3) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-0) = 2 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-1) = 18 S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-2) = ? S("f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ]", 0-3) = Ar_5 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-0) = 2 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-1) = 0 S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-2) = ? S("f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ]", 0-3) = Ar_5 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-1) = Ar_3 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-2) = Ar_4 S("koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ]", 0-3) = Ar_5 orients the transitions f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] weakly and the transitions f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] strictly and produces the following problem: 9: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f0(Ar_0, Ar_3, Ar_4, Ar_5)) [ 0 <= 0 ] (Comp: 2, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, 0, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 18, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 18 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 21 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 42 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 /\ 49 >= H ] (Comp: 2, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f52(Ar_0, Ar_3, Ar_4, Ar_5)) [ Ar_3 >= Ar_0 ] (Comp: 3, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f23(Ar_0, Ar_3 + 1, Ar_4, Ar_5)) [ Ar_4 >= Ar_0 ] (Comp: 18, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_5 >= Ar_0 ] (Comp: 36, Cost: 1) f30(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, Ar_5 + 1)) [ Ar_0 >= Ar_5 + 1 ] (Comp: 9, Cost: 1) f26(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f30(Ar_0, Ar_3, Ar_4, 0)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 3, Cost: 1) f23(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f26(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 36, Cost: 1) f15(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, Ar_4 + 1, Ar_5)) [ Ar_0 >= Ar_4 + 1 ] (Comp: 9, Cost: 1) f12(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f15(Ar_0, Ar_3, 0, Ar_5)) [ Ar_0 >= Ar_3 + 1 ] (Comp: 1, Cost: 1) f0(Ar_0, Ar_3, Ar_4, Ar_5) -> Com_1(f12(2, 0, Ar_4, Ar_5)) start location: koat_start leaf cost: 0 Complexity upper bound 147 Time: 0.205 sec (SMT: 0.138 sec) ---------------------------------------- (2) BOUNDS(1, 1)