3.67/1.96 WORST_CASE(?, O(1)) 4.50/1.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.50/1.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.50/1.97 4.50/1.97 4.50/1.97 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 4.50/1.97 4.50/1.97 (0) CpxIntTrs 4.50/1.97 (1) Koat Proof [FINISHED, 210 ms] 4.50/1.97 (2) BOUNDS(1, 1) 4.50/1.97 4.50/1.97 4.50/1.97 ---------------------------------------- 4.50/1.97 4.50/1.97 (0) 4.50/1.97 Obligation: 4.50/1.97 Complexity Int TRS consisting of the following rules: 4.50/1.97 f0(A, B, C, D, E, F, G) -> Com_1(f31(5, 7, 0, 0, E, F, G)) :|: TRUE 4.50/1.97 f31(A, B, C, D, E, F, G) -> Com_1(f31(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D 4.50/1.97 f31(A, B, C, D, E, F, G) -> Com_1(f31(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1 4.50/1.97 f31(A, B, C, D, E, F, G) -> Com_1(f31(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C 4.50/1.97 f39(A, B, C, D, E, F, G) -> Com_1(f42(A, B, C, D, 0, F, G)) :|: A >= D + 1 4.50/1.97 f42(A, B, C, D, E, F, G) -> Com_1(f42(A, B, C, D, E + 1, H, I)) :|: B >= E + 1 4.50/1.97 f53(A, B, C, D, E, F, G) -> Com_1(f59(A, B, C, D, E, H, I)) :|: B >= D + 1 4.50/1.97 f53(A, B, C, D, E, F, G) -> Com_1(f53(A, B, C, D + 1, E, H, I)) :|: B >= D + 1 4.50/1.97 f63(A, B, C, D, E, F, G) -> Com_1(f63(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 4.50/1.97 f63(A, B, C, D, E, F, G) -> Com_1(f59(A, B, C, D, E, F, G)) :|: D >= A 4.50/1.97 f53(A, B, C, D, E, F, G) -> Com_1(f63(A, B, C, 0, E, F, G)) :|: D >= B 4.50/1.97 f42(A, B, C, D, E, F, G) -> Com_1(f39(A, B, C, D + 1, E, F, G)) :|: E >= B 4.50/1.97 f39(A, B, C, D, E, F, G) -> Com_1(f53(A, B, C, 0, E, F, G)) :|: D >= A 4.50/1.97 f31(A, B, C, D, E, F, G) -> Com_1(f39(A, B, C, 0, E, F, G)) :|: D >= A 4.50/1.97 4.50/1.97 The start-symbols are:[f0_7] 4.50/1.97 4.50/1.97 4.50/1.97 ---------------------------------------- 4.50/1.97 4.50/1.97 (1) Koat Proof (FINISHED) 4.50/1.97 YES(?, 958) 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 Initial complexity problem: 4.50/1.97 4.50/1.97 1: T: 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f31(5, 7, 0, 0, ar_4, ar_5, ar_6)) 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 4.50/1.97 4.50/1.97 We thus obtain the following problem: 4.50/1.97 4.50/1.97 2: T: 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 Testing for reachability in the complexity graph removes the following transition from problem 2: 4.50/1.97 4.50/1.97 f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 We thus obtain the following problem: 4.50/1.97 4.50/1.97 3: T: 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 Repeatedly propagating knowledge in problem 3 produces the following problem: 4.50/1.97 4.50/1.97 4: T: 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 A polynomial rank function with 4.50/1.97 4.50/1.97 Pol(f63) = 1 4.50/1.97 4.50/1.97 Pol(f59) = 0 4.50/1.97 4.50/1.97 Pol(f42) = 3 4.50/1.97 4.50/1.97 Pol(f39) = 3 4.50/1.97 4.50/1.97 Pol(f53) = 2 4.50/1.97 4.50/1.97 Pol(f31) = 4 4.50/1.97 4.50/1.97 Pol(f0) = 4 4.50/1.97 4.50/1.97 Pol(koat_start) = 4 4.50/1.97 4.50/1.97 orients all transitions weakly and the transitions 4.50/1.97 4.50/1.97 f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 f53(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_1 ] 4.50/1.97 4.50/1.97 f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 strictly and produces the following problem: 4.50/1.97 4.50/1.97 5: T: 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 A polynomial rank function with 4.50/1.97 4.50/1.97 Pol(f63) = V_1 - V_4 4.50/1.97 4.50/1.97 Pol(f53) = V_2 - V_4 4.50/1.97 4.50/1.97 Pol(f42) = V_1 - V_4 4.50/1.97 4.50/1.97 Pol(f39) = V_1 - V_4 + 1 4.50/1.97 4.50/1.97 Pol(f31) = V_1 - V_4 4.50/1.97 4.50/1.97 and size complexities 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-0) = 5 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-1) = 7 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-2) = 0 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-3) = 0 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 orients the transitions 4.50/1.97 4.50/1.97 f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 weakly and the transitions 4.50/1.97 4.50/1.97 f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 strictly and produces the following problem: 4.50/1.97 4.50/1.97 6: T: 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 A polynomial rank function with 4.50/1.97 4.50/1.97 Pol(f42) = 1 4.50/1.97 4.50/1.97 Pol(f39) = 0 4.50/1.97 4.50/1.97 and size complexities 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-0) = 5 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-1) = 7 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-2) = 0 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-3) = 0 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 79 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 orients the transitions 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 weakly and the transition 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 strictly and produces the following problem: 4.50/1.97 4.50/1.97 7: T: 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: ?, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 A polynomial rank function with 4.50/1.97 4.50/1.97 Pol(f42) = V_2 - V_5 4.50/1.97 4.50/1.97 and size complexities 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 4.50/1.97 4.50/1.97 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-0) = 5 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-1) = 7 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-2) = 0 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-3) = 0 4.50/1.97 4.50/1.97 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4))", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 79 4.50/1.97 4.50/1.97 S("f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-3) = 0 4.50/1.97 4.50/1.97 S("f53(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_1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ? 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-0) = 5 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-1) = 7 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-2) = 0 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-3) = 78 4.50/1.97 4.50/1.97 S("f63(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_0 >= ar_3 + 1 ]", 0-4) = ? 4.50/1.97 4.50/1.97 orients the transitions 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 weakly and the transition 4.50/1.97 4.50/1.97 f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 strictly and produces the following problem: 4.50/1.97 4.50/1.97 8: T: 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f63(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_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f63(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 546, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f42(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f59(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f53(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f53(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_1 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f42(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f39(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 78, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ] 4.50/1.97 4.50/1.97 (Comp: 4, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f39(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f31(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ] 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(5, 7, 0, 0, ar_4)) 4.50/1.97 4.50/1.97 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 4.50/1.97 4.50/1.97 start location: koat_start 4.50/1.97 4.50/1.97 leaf cost: 0 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 Complexity upper bound 958 4.50/1.97 4.50/1.97 4.50/1.97 4.50/1.97 Time: 0.241 sec (SMT: 0.199 sec) 4.50/1.97 4.50/1.97 4.50/1.97 ---------------------------------------- 4.50/1.97 4.50/1.97 (2) 4.50/1.97 BOUNDS(1, 1) 4.54/1.99 EOF