3.74/1.98 WORST_CASE(?, O(1)) 3.74/1.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 3.74/1.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.74/1.99 3.74/1.99 3.74/1.99 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 3.74/1.99 3.74/1.99 (0) CpxIntTrs 3.74/1.99 (1) Koat Proof [FINISHED, 208 ms] 3.74/1.99 (2) BOUNDS(1, 1) 3.74/1.99 3.74/1.99 3.74/1.99 ---------------------------------------- 3.74/1.99 3.74/1.99 (0) 3.74/1.99 Obligation: 3.74/1.99 Complexity Int TRS consisting of the following rules: 3.74/1.99 f0(A, B, C, D, E, F, G) -> Com_1(f61(5, 17, 0, 0, E, F, G)) :|: TRUE 3.74/1.99 f61(A, B, C, D, E, F, G) -> Com_1(f61(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 3.74/1.99 f61(A, B, C, D, E, F, G) -> Com_1(f61(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 3.74/1.99 f61(A, B, C, D, E, F, G) -> Com_1(f61(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 3.74/1.99 f69(A, B, C, D, E, F, G) -> Com_1(f72(A, B, C, D, 0, F, G)) :|: A >= D + 1 3.74/1.99 f72(A, B, C, D, E, F, G) -> Com_1(f72(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 3.74/1.99 f83(A, B, C, D, E, F, G) -> Com_1(f89(A, B, C, D, E, H, I)) :|: B >= D + 1 3.74/1.99 f83(A, B, C, D, E, F, G) -> Com_1(f83(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 3.74/1.99 f93(A, B, C, D, E, F, G) -> Com_1(f93(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 3.74/1.99 f93(A, B, C, D, E, F, G) -> Com_1(f89(A, B, C, D, E, F, G)) :|: D >= A 3.74/1.99 f83(A, B, C, D, E, F, G) -> Com_1(f93(A, B, C, 0, E, F, G)) :|: D >= B 3.74/1.99 f72(A, B, C, D, E, F, G) -> Com_1(f69(A, B, C, D + 1, E, F, G)) :|: E >= B 3.74/1.99 f69(A, B, C, D, E, F, G) -> Com_1(f83(A, B, C, 0, E, F, G)) :|: D >= A 3.74/1.99 f61(A, B, C, D, E, F, G) -> Com_1(f69(A, B, C, 0, E, F, G)) :|: D >= A 3.74/1.99 3.74/1.99 The start-symbols are:[f0_7] 3.74/1.99 3.74/1.99 3.74/1.99 ---------------------------------------- 3.74/1.99 3.74/1.99 (1) Koat Proof (FINISHED) 3.74/1.99 YES(?, 2618) 3.74/1.99 3.74/1.99 3.74/1.99 3.74/1.99 Initial complexity problem: 3.74/1.99 3.74/1.99 1: T: 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f61(5, 17, 0, 0, ar_4, ar_5, ar_6)) 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f61(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 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f61(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 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f69(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, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (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, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 3.74/1.99 3.74/1.99 (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 ] 3.74/1.99 3.74/1.99 start location: koat_start 3.74/1.99 3.74/1.99 leaf cost: 0 3.74/1.99 3.74/1.99 3.74/1.99 3.74/1.99 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 3.74/1.99 3.74/1.99 We thus obtain the following problem: 3.74/1.99 3.74/1.99 2: T: 3.74/1.99 3.74/1.99 (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 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/1.99 3.74/1.99 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/1.99 3.74/1.99 start location: koat_start 3.74/1.99 3.74/1.99 leaf cost: 0 3.74/1.99 3.74/1.99 3.74/1.99 3.74/1.99 Testing for reachability in the complexity graph removes the following transition from problem 2: 3.74/1.99 3.74/1.99 f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 We thus obtain the following problem: 3.74/2.00 3.74/2.00 3: T: 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/2.00 3.74/2.00 (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 ] 3.74/2.00 3.74/2.00 start location: koat_start 3.74/2.00 3.74/2.00 leaf cost: 0 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 Repeatedly propagating knowledge in problem 3 produces the following problem: 3.74/2.00 3.74/2.00 4: T: 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/2.00 3.74/2.00 (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 ] 3.74/2.00 3.74/2.00 start location: koat_start 3.74/2.00 3.74/2.00 leaf cost: 0 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 A polynomial rank function with 3.74/2.00 3.74/2.00 Pol(f93) = 1 3.74/2.00 3.74/2.00 Pol(f89) = 0 3.74/2.00 3.74/2.00 Pol(f72) = 3 3.74/2.00 3.74/2.00 Pol(f69) = 3 3.74/2.00 3.74/2.00 Pol(f83) = 2 3.74/2.00 3.74/2.00 Pol(f61) = 4 3.74/2.00 3.74/2.00 Pol(f0) = 4 3.74/2.00 3.74/2.00 Pol(koat_start) = 4 3.74/2.00 3.74/2.00 orients all transitions weakly and the transitions 3.74/2.00 3.74/2.00 f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 strictly and produces the following problem: 3.74/2.00 3.74/2.00 5: T: 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/2.00 3.74/2.00 (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 ] 3.74/2.00 3.74/2.00 start location: koat_start 3.74/2.00 3.74/2.00 leaf cost: 0 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 A polynomial rank function with 3.74/2.00 3.74/2.00 Pol(f93) = V_1 - V_4 3.74/2.00 3.74/2.00 Pol(f83) = V_2 - V_4 3.74/2.00 3.74/2.00 Pol(f72) = V_1 - V_4 3.74/2.00 3.74/2.00 Pol(f69) = V_1 - V_4 + 1 3.74/2.00 3.74/2.00 Pol(f61) = V_1 - V_4 3.74/2.00 3.74/2.00 and size complexities 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-0) = 5 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-1) = 17 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-2) = 0 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-3) = 0 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(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 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 orients the transitions 3.74/2.00 3.74/2.00 f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 weakly and the transitions 3.74/2.00 3.74/2.00 f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 strictly and produces the following problem: 3.74/2.00 3.74/2.00 6: T: 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 (Comp: ?, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/2.00 3.74/2.00 (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 ] 3.74/2.00 3.74/2.00 start location: koat_start 3.74/2.00 3.74/2.00 leaf cost: 0 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 A polynomial rank function with 3.74/2.00 3.74/2.00 Pol(f72) = 1 3.74/2.00 3.74/2.00 Pol(f69) = 0 3.74/2.00 3.74/2.00 and size complexities 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-0) = 5 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-1) = 17 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-2) = 0 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-3) = 0 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 119 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(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 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 orients the transitions 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 weakly and the transition 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 strictly and produces the following problem: 3.74/2.00 3.74/2.00 7: T: 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/2.00 3.74/2.00 (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 ] 3.74/2.00 3.74/2.00 start location: koat_start 3.74/2.00 3.74/2.00 leaf cost: 0 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 A polynomial rank function with 3.74/2.00 3.74/2.00 Pol(f72) = V_2 - V_5 3.74/2.00 3.74/2.00 and size complexities 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 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 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-0) = 5 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-1) = 17 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-2) = 0 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-3) = 0 3.74/2.00 3.74/2.00 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4))", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 119 3.74/2.00 3.74/2.00 S("f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(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 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 17 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 118 3.74/2.00 3.74/2.00 S("f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 3.74/2.00 3.74/2.00 orients the transitions 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 weakly and the transition 3.74/2.00 3.74/2.00 f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 strictly and produces the following problem: 3.74/2.00 3.74/2.00 8: T: 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f93(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 2006, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f72(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f89(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f83(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f93(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f72(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f69(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 118, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.74/2.00 3.74/2.00 (Comp: 4, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f69(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f61(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.74/2.00 3.74/2.00 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f61(5, 17, 0, 0, ar_4)) 3.74/2.00 3.74/2.00 (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 ] 3.74/2.00 3.74/2.00 start location: koat_start 3.74/2.00 3.74/2.00 leaf cost: 0 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 Complexity upper bound 2618 3.74/2.00 3.74/2.00 3.74/2.00 3.74/2.00 Time: 0.236 sec (SMT: 0.193 sec) 3.74/2.00 3.74/2.00 3.74/2.00 ---------------------------------------- 3.74/2.00 3.74/2.00 (2) 3.74/2.00 BOUNDS(1, 1) 4.33/2.03 EOF