3.76/1.94 WORST_CASE(?, O(1)) 3.76/1.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 3.76/1.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.76/1.95 3.76/1.95 3.76/1.95 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 3.76/1.95 3.76/1.95 (0) CpxIntTrs 3.76/1.95 (1) Koat Proof [FINISHED, 209 ms] 3.76/1.95 (2) BOUNDS(1, 1) 3.76/1.95 3.76/1.95 3.76/1.95 ---------------------------------------- 3.76/1.95 3.76/1.95 (0) 3.76/1.95 Obligation: 3.76/1.95 Complexity Int TRS consisting of the following rules: 3.76/1.95 f0(A, B, C, D, E, F, G) -> Com_1(f55(5, 15, 0, 0, E, F, G)) :|: TRUE 3.76/1.95 f55(A, B, C, D, E, F, G) -> Com_1(f55(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 3.76/1.95 f55(A, B, C, D, E, F, G) -> Com_1(f55(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 3.76/1.95 f55(A, B, C, D, E, F, G) -> Com_1(f55(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 3.76/1.95 f63(A, B, C, D, E, F, G) -> Com_1(f66(A, B, C, D, 0, F, G)) :|: A >= D + 1 3.76/1.95 f66(A, B, C, D, E, F, G) -> Com_1(f66(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 3.76/1.95 f77(A, B, C, D, E, F, G) -> Com_1(f83(A, B, C, D, E, H, I)) :|: B >= D + 1 3.76/1.95 f77(A, B, C, D, E, F, G) -> Com_1(f77(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 3.76/1.95 f87(A, B, C, D, E, F, G) -> Com_1(f87(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 3.76/1.95 f87(A, B, C, D, E, F, G) -> Com_1(f83(A, B, C, D, E, F, G)) :|: D >= A 3.76/1.95 f77(A, B, C, D, E, F, G) -> Com_1(f87(A, B, C, 0, E, F, G)) :|: D >= B 3.76/1.95 f66(A, B, C, D, E, F, G) -> Com_1(f63(A, B, C, D + 1, E, F, G)) :|: E >= B 3.76/1.95 f63(A, B, C, D, E, F, G) -> Com_1(f77(A, B, C, 0, E, F, G)) :|: D >= A 3.76/1.95 f55(A, B, C, D, E, F, G) -> Com_1(f63(A, B, C, 0, E, F, G)) :|: D >= A 3.76/1.95 3.76/1.95 The start-symbols are:[f0_7] 3.76/1.95 3.76/1.95 3.76/1.95 ---------------------------------------- 3.76/1.95 3.76/1.95 (1) Koat Proof (FINISHED) 3.76/1.95 YES(?, 2222) 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 Initial complexity problem: 3.76/1.95 3.76/1.95 1: T: 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f55(5, 15, 0, 0, ar_4, ar_5, ar_6)) 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f55(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 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f55(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 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(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, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(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, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(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, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 3.76/1.95 3.76/1.95 We thus obtain the following problem: 3.76/1.95 3.76/1.95 2: T: 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 Testing for reachability in the complexity graph removes the following transition from problem 2: 3.76/1.95 3.76/1.95 f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 We thus obtain the following problem: 3.76/1.95 3.76/1.95 3: T: 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 Repeatedly propagating knowledge in problem 3 produces the following problem: 3.76/1.95 3.76/1.95 4: T: 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 A polynomial rank function with 3.76/1.95 3.76/1.95 Pol(f87) = 1 3.76/1.95 3.76/1.95 Pol(f83) = 0 3.76/1.95 3.76/1.95 Pol(f66) = 3 3.76/1.95 3.76/1.95 Pol(f63) = 3 3.76/1.95 3.76/1.95 Pol(f77) = 2 3.76/1.95 3.76/1.95 Pol(f55) = 4 3.76/1.95 3.76/1.95 Pol(f0) = 4 3.76/1.95 3.76/1.95 Pol(koat_start) = 4 3.76/1.95 3.76/1.95 orients all transitions weakly and the transitions 3.76/1.95 3.76/1.95 f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 strictly and produces the following problem: 3.76/1.95 3.76/1.95 5: T: 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 A polynomial rank function with 3.76/1.95 3.76/1.95 Pol(f87) = V_1 - V_4 3.76/1.95 3.76/1.95 Pol(f77) = V_2 - V_4 3.76/1.95 3.76/1.95 Pol(f66) = V_1 - V_4 3.76/1.95 3.76/1.95 Pol(f63) = V_1 - V_4 + 1 3.76/1.95 3.76/1.95 Pol(f55) = V_1 - V_4 3.76/1.95 3.76/1.95 and size complexities 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-0) = 5 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-1) = 15 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-2) = 0 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-3) = 0 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(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 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 orients the transitions 3.76/1.95 3.76/1.95 f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 weakly and the transitions 3.76/1.95 3.76/1.95 f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 strictly and produces the following problem: 3.76/1.95 3.76/1.95 6: T: 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: ?, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 A polynomial rank function with 3.76/1.95 3.76/1.95 Pol(f66) = 1 3.76/1.95 3.76/1.95 Pol(f63) = 0 3.76/1.95 3.76/1.95 and size complexities 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-0) = 5 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-1) = 15 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-2) = 0 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-3) = 0 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 111 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(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 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 orients the transitions 3.76/1.95 3.76/1.95 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 weakly and the transition 3.76/1.95 3.76/1.95 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 strictly and produces the following problem: 3.76/1.95 3.76/1.95 7: T: 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (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, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: 110, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.95 3.76/1.95 (Comp: 4, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.95 3.76/1.95 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.95 3.76/1.95 (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 ] 3.76/1.95 3.76/1.95 start location: koat_start 3.76/1.95 3.76/1.95 leaf cost: 0 3.76/1.95 3.76/1.95 3.76/1.95 3.76/1.95 A polynomial rank function with 3.76/1.95 3.76/1.95 Pol(f66) = V_2 - V_5 3.76/1.95 3.76/1.95 and size complexities 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 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 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-0) = 5 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-1) = 15 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-2) = 0 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-3) = 0 3.76/1.95 3.76/1.95 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4))", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 111 3.76/1.95 3.76/1.95 S("f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(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 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 110 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 15 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 3.76/1.95 3.76/1.95 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 110 3.76/1.96 3.76/1.96 S("f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ? 3.76/1.96 3.76/1.96 orients the transitions 3.76/1.96 3.76/1.96 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.96 3.76/1.96 weakly and the transition 3.76/1.96 3.76/1.96 f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.96 3.76/1.96 strictly and produces the following problem: 3.76/1.96 3.76/1.96 8: T: 3.76/1.96 3.76/1.96 (Comp: 110, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ] 3.76/1.96 3.76/1.96 (Comp: 4, Cost: 1) f87(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.96 3.76/1.96 (Comp: 1650, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 3.76/1.96 3.76/1.96 (Comp: 110, Cost: 1) f66(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 3.76/1.96 3.76/1.96 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f83(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.96 3.76/1.96 (Comp: 110, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 3.76/1.96 3.76/1.96 (Comp: 4, Cost: 1) f77(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f87(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ] 3.76/1.96 3.76/1.96 (Comp: 110, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f66(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 3.76/1.96 3.76/1.96 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f77(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.96 3.76/1.96 (Comp: 110, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 3.76/1.96 3.76/1.96 (Comp: 4, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f63(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 3.76/1.96 3.76/1.96 (Comp: 1, Cost: 1) f55(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 3.76/1.96 3.76/1.96 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f55(5, 15, 0, 0, ar_4)) 3.76/1.96 3.76/1.96 (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 ] 3.76/1.96 3.76/1.96 start location: koat_start 3.76/1.96 3.76/1.96 leaf cost: 0 3.76/1.96 3.76/1.96 3.76/1.96 3.76/1.96 Complexity upper bound 2222 3.76/1.96 3.76/1.96 3.76/1.96 3.76/1.96 Time: 0.234 sec (SMT: 0.193 sec) 3.76/1.96 3.76/1.96 3.76/1.96 ---------------------------------------- 3.76/1.96 3.76/1.96 (2) 3.76/1.96 BOUNDS(1, 1) 3.76/1.97 EOF