3.46/2.08 WORST_CASE(?, O(1)) 4.31/2.08 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.31/2.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.31/2.08 4.31/2.08 4.31/2.08 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 4.31/2.08 4.31/2.08 (0) CpxIntTrs 4.31/2.08 (1) Koat Proof [FINISHED, 193 ms] 4.31/2.08 (2) BOUNDS(1, 1) 4.31/2.08 4.31/2.08 4.31/2.08 ---------------------------------------- 4.31/2.08 4.31/2.08 (0) 4.31/2.08 Obligation: 4.31/2.08 Complexity Int TRS consisting of the following rules: 4.31/2.08 f0(A, B, C, D, E, F, G) -> Com_1(f40(5, 10, 0, 0, E, F, G)) :|: TRUE 4.31/2.08 f40(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 4.31/2.08 f40(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 4.31/2.08 f40(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 4.31/2.08 f48(A, B, C, D, E, F, G) -> Com_1(f51(A, B, C, D, 0, F, G)) :|: A >= D + 1 4.31/2.08 f51(A, B, C, D, E, F, G) -> Com_1(f51(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 4.31/2.08 f62(A, B, C, D, E, F, G) -> Com_1(f68(A, B, C, D, E, H, I)) :|: B >= D + 1 4.31/2.08 f62(A, B, C, D, E, F, G) -> Com_1(f62(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 4.31/2.08 f72(A, B, C, D, E, F, G) -> Com_1(f72(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 4.31/2.08 f72(A, B, C, D, E, F, G) -> Com_1(f68(A, B, C, D, E, F, G)) :|: D >= A 4.31/2.08 f62(A, B, C, D, E, F, G) -> Com_1(f72(A, B, C, 0, E, F, G)) :|: D >= B 4.31/2.08 f51(A, B, C, D, E, F, G) -> Com_1(f48(A, B, C, D + 1, E, F, G)) :|: E >= B 4.31/2.08 f48(A, B, C, D, E, F, G) -> Com_1(f62(A, B, C, 0, E, F, G)) :|: D >= A 4.31/2.08 f40(A, B, C, D, E, F, G) -> Com_1(f48(A, B, C, 0, E, F, G)) :|: D >= A 4.31/2.08 4.31/2.08 The start-symbols are:[f0_7] 4.31/2.08 4.31/2.08 4.31/2.08 ---------------------------------------- 4.31/2.08 4.31/2.08 (1) Koat Proof (FINISHED) 4.31/2.08 YES(?, 1372) 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 Initial complexity problem: 4.31/2.08 4.31/2.08 1: T: 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f40(5, 10, 0, 0, ar_4, ar_5, ar_6)) 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(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 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(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 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (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 ] 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 4.31/2.08 4.31/2.08 We thus obtain the following problem: 4.31/2.08 4.31/2.08 2: T: 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 Testing for reachability in the complexity graph removes the following transition from problem 2: 4.31/2.08 4.31/2.08 f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 We thus obtain the following problem: 4.31/2.08 4.31/2.08 3: T: 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 Repeatedly propagating knowledge in problem 3 produces the following problem: 4.31/2.08 4.31/2.08 4: T: 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 A polynomial rank function with 4.31/2.08 4.31/2.08 Pol(f72) = 1 4.31/2.08 4.31/2.08 Pol(f68) = 0 4.31/2.08 4.31/2.08 Pol(f51) = 3 4.31/2.08 4.31/2.08 Pol(f48) = 3 4.31/2.08 4.31/2.08 Pol(f62) = 2 4.31/2.08 4.31/2.08 Pol(f40) = 4 4.31/2.08 4.31/2.08 Pol(f0) = 4 4.31/2.08 4.31/2.08 Pol(koat_start) = 4 4.31/2.08 4.31/2.08 orients all transitions weakly and the transitions 4.31/2.08 4.31/2.08 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 strictly and produces the following problem: 4.31/2.08 4.31/2.08 5: T: 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 A polynomial rank function with 4.31/2.08 4.31/2.08 Pol(f72) = V_1 - V_4 4.31/2.08 4.31/2.08 Pol(f62) = V_2 - V_4 4.31/2.08 4.31/2.08 Pol(f51) = V_1 - V_4 4.31/2.08 4.31/2.08 Pol(f48) = V_1 - V_4 + 1 4.31/2.08 4.31/2.08 Pol(f40) = V_1 - V_4 4.31/2.08 4.31/2.08 and size complexities 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-0) = 5 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-1) = 10 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-2) = 0 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-3) = 0 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 orients the transitions 4.31/2.08 4.31/2.08 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 weakly and the transitions 4.31/2.08 4.31/2.08 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 strictly and produces the following problem: 4.31/2.08 4.31/2.08 6: T: 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 A polynomial rank function with 4.31/2.08 4.31/2.08 Pol(f51) = 1 4.31/2.08 4.31/2.08 Pol(f48) = 0 4.31/2.08 4.31/2.08 and size complexities 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-0) = 5 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-1) = 10 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-2) = 0 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-3) = 0 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 91 4.31/2.08 4.31/2.08 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.08 4.31/2.08 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 4.31/2.08 4.31/2.08 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 90 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.08 4.31/2.08 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.08 4.31/2.08 orients the transitions 4.31/2.08 4.31/2.08 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 weakly and the transition 4.31/2.08 4.31/2.08 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 strictly and produces the following problem: 4.31/2.08 4.31/2.08 7: T: 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: ?, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: 90, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.08 4.31/2.08 (Comp: 4, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.08 4.31/2.08 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.08 4.31/2.08 start location: koat_start 4.31/2.08 4.31/2.08 leaf cost: 0 4.31/2.08 4.31/2.08 4.31/2.08 4.31/2.08 A polynomial rank function with 4.31/2.08 4.31/2.08 Pol(f51) = V_2 - V_5 4.31/2.08 4.31/2.08 and size complexities 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 4.31/2.08 4.31/2.08 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-0) = 5 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-1) = 10 4.31/2.08 4.31/2.08 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-2) = 0 4.31/2.09 4.31/2.09 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-3) = 0 4.31/2.09 4.31/2.09 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4))", 0-4) = ar_4 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 91 4.31/2.09 4.31/2.09 S("f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 10 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 90 4.31/2.09 4.31/2.09 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 4.31/2.09 4.31/2.09 orients the transitions 4.31/2.09 4.31/2.09 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.09 4.31/2.09 weakly and the transition 4.31/2.09 4.31/2.09 f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.09 4.31/2.09 strictly and produces the following problem: 4.31/2.09 4.31/2.09 8: T: 4.31/2.09 4.31/2.09 (Comp: 90, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.31/2.09 4.31/2.09 (Comp: 4, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.09 4.31/2.09 (Comp: 900, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.31/2.09 4.31/2.09 (Comp: 90, Cost: 1) f51(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.31/2.09 4.31/2.09 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f68(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.09 4.31/2.09 (Comp: 90, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.31/2.09 4.31/2.09 (Comp: 4, Cost: 1) f62(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.31/2.09 4.31/2.09 (Comp: 90, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f51(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.31/2.09 4.31/2.09 (Comp: 4, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.09 4.31/2.09 (Comp: 90, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.31/2.09 4.31/2.09 (Comp: 4, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.31/2.09 4.31/2.09 (Comp: 1, Cost: 1) f40(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.31/2.09 4.31/2.09 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f40(5, 10, 0, 0, ar_4)) 4.31/2.09 4.31/2.09 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.31/2.09 4.31/2.09 start location: koat_start 4.31/2.09 4.31/2.09 leaf cost: 0 4.31/2.09 4.31/2.09 4.31/2.09 4.31/2.09 Complexity upper bound 1372 4.31/2.09 4.31/2.09 4.31/2.09 4.31/2.09 Time: 0.237 sec (SMT: 0.195 sec) 4.31/2.09 4.31/2.09 4.31/2.09 ---------------------------------------- 4.31/2.09 4.31/2.09 (2) 4.31/2.09 BOUNDS(1, 1) 4.33/2.12 EOF