3.99/1.90 WORST_CASE(?, O(1)) 4.23/1.91 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.23/1.91 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.23/1.91 4.23/1.91 4.23/1.91 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 4.23/1.91 4.23/1.91 (0) CpxIntTrs 4.23/1.91 (1) Koat Proof [FINISHED, 230 ms] 4.23/1.91 (2) BOUNDS(1, 1) 4.23/1.91 4.23/1.91 4.23/1.91 ---------------------------------------- 4.23/1.91 4.23/1.91 (0) 4.23/1.91 Obligation: 4.23/1.91 Complexity Int TRS consisting of the following rules: 4.23/1.91 f0(A, B, C, D, E, F, G) -> Com_1(f34(5, 8, 0, 0, E, F, G)) :|: TRUE 4.23/1.91 f34(A, B, C, D, E, F, G) -> Com_1(f34(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 4.23/1.91 f34(A, B, C, D, E, F, G) -> Com_1(f34(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 4.23/1.91 f34(A, B, C, D, E, F, G) -> Com_1(f34(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 4.23/1.91 f42(A, B, C, D, E, F, G) -> Com_1(f45(A, B, C, D, 0, F, G)) :|: A >= D + 1 4.23/1.91 f45(A, B, C, D, E, F, G) -> Com_1(f45(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 4.23/1.91 f56(A, B, C, D, E, F, G) -> Com_1(f62(A, B, C, D, E, H, I)) :|: B >= D + 1 4.23/1.91 f56(A, B, C, D, E, F, G) -> Com_1(f56(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 4.23/1.91 f66(A, B, C, D, E, F, G) -> Com_1(f66(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 4.23/1.91 f66(A, B, C, D, E, F, G) -> Com_1(f62(A, B, C, D, E, F, G)) :|: D >= A 4.23/1.91 f56(A, B, C, D, E, F, G) -> Com_1(f66(A, B, C, 0, E, F, G)) :|: D >= B 4.23/1.91 f45(A, B, C, D, E, F, G) -> Com_1(f42(A, B, C, D + 1, E, F, G)) :|: E >= B 4.23/1.91 f42(A, B, C, D, E, F, G) -> Com_1(f56(A, B, C, 0, E, F, G)) :|: D >= A 4.23/1.91 f34(A, B, C, D, E, F, G) -> Com_1(f42(A, B, C, 0, E, F, G)) :|: D >= A 4.23/1.91 4.23/1.91 The start-symbols are:[f0_7] 4.23/1.91 4.23/1.91 4.23/1.91 ---------------------------------------- 4.23/1.91 4.23/1.91 (1) Koat Proof (FINISHED) 4.23/1.91 YES(?, 1088) 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 Initial complexity problem: 4.23/1.91 4.23/1.91 1: T: 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f34(5, 8, 0, 0, ar_4, ar_5, ar_6)) 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f34(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 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f34(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 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(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, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(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, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 4.23/1.91 4.23/1.91 We thus obtain the following problem: 4.23/1.91 4.23/1.91 2: T: 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 Testing for reachability in the complexity graph removes the following transition from problem 2: 4.23/1.91 4.23/1.91 f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 We thus obtain the following problem: 4.23/1.91 4.23/1.91 3: T: 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 Repeatedly propagating knowledge in problem 3 produces the following problem: 4.23/1.91 4.23/1.91 4: T: 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 A polynomial rank function with 4.23/1.91 4.23/1.91 Pol(f66) = 1 4.23/1.91 4.23/1.91 Pol(f62) = 0 4.23/1.91 4.23/1.91 Pol(f45) = 3 4.23/1.91 4.23/1.91 Pol(f42) = 3 4.23/1.91 4.23/1.91 Pol(f56) = 2 4.23/1.91 4.23/1.91 Pol(f34) = 4 4.23/1.91 4.23/1.91 Pol(f0) = 4 4.23/1.91 4.23/1.91 Pol(koat_start) = 4 4.23/1.91 4.23/1.91 orients all transitions weakly and the transitions 4.23/1.91 4.23/1.91 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 strictly and produces the following problem: 4.23/1.91 4.23/1.91 5: T: 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 A polynomial rank function with 4.23/1.91 4.23/1.91 Pol(f66) = V_1 - V_4 4.23/1.91 4.23/1.91 Pol(f56) = V_2 - V_4 4.23/1.91 4.23/1.91 Pol(f45) = V_1 - V_4 4.23/1.91 4.23/1.91 Pol(f42) = V_1 - V_4 + 1 4.23/1.91 4.23/1.91 Pol(f34) = V_1 - V_4 4.23/1.91 4.23/1.91 and size complexities 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-0) = 5 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-1) = 8 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-2) = 0 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-3) = 0 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(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 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 orients the transitions 4.23/1.91 4.23/1.91 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 weakly and the transitions 4.23/1.91 4.23/1.91 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 strictly and produces the following problem: 4.23/1.91 4.23/1.91 6: T: 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 A polynomial rank function with 4.23/1.91 4.23/1.91 Pol(f45) = 1 4.23/1.91 4.23/1.91 Pol(f42) = 0 4.23/1.91 4.23/1.91 and size complexities 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-0) = 5 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-1) = 8 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-2) = 0 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-3) = 0 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 83 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(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 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 orients the transitions 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 weakly and the transition 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 strictly and produces the following problem: 4.23/1.91 4.23/1.91 7: T: 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: ?, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 A polynomial rank function with 4.23/1.91 4.23/1.91 Pol(f45) = V_2 - V_5 4.23/1.91 4.23/1.91 and size complexities 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 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 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-0) = 5 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-1) = 8 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-2) = 0 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-3) = 0 4.23/1.91 4.23/1.91 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4))", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 83 4.23/1.91 4.23/1.91 S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(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 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 8 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 82 4.23/1.91 4.23/1.91 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 4.23/1.91 4.23/1.91 orients the transitions 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 weakly and the transition 4.23/1.91 4.23/1.91 f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 strictly and produces the following problem: 4.23/1.91 4.23/1.91 8: T: 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 656, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f45(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f62(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f56(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f45(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f56(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 82, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.23/1.91 4.23/1.91 (Comp: 4, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.23/1.91 4.23/1.91 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(5, 8, 0, 0, ar_4)) 4.23/1.91 4.23/1.91 (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 ] 4.23/1.91 4.23/1.91 start location: koat_start 4.23/1.91 4.23/1.91 leaf cost: 0 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 Complexity upper bound 1088 4.23/1.91 4.23/1.91 4.23/1.91 4.23/1.91 Time: 0.219 sec (SMT: 0.177 sec) 4.23/1.91 4.23/1.91 4.23/1.91 ---------------------------------------- 4.23/1.91 4.23/1.91 (2) 4.23/1.91 BOUNDS(1, 1) 4.23/1.93 EOF