3.66/1.98 WORST_CASE(?, O(1)) 3.66/1.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 3.66/1.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.66/1.99 3.66/1.99 3.66/1.99 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). 3.66/1.99 3.66/1.99 (0) CpxIntTrs 3.66/1.99 (1) Koat Proof [FINISHED, 223 ms] 3.66/1.99 (2) BOUNDS(1, 1) 3.66/1.99 3.66/1.99 3.66/1.99 ---------------------------------------- 3.66/1.99 3.66/1.99 (0) 3.66/1.99 Obligation: 3.66/1.99 Complexity Int TRS consisting of the following rules: 3.66/1.99 f0(A, B, C, D, E, F, G) -> Com_1(f8(-(1), -(1), 1, D, E, F, G)) :|: TRUE 3.66/1.99 f8(A, B, C, D, E, F, G) -> Com_1(f8(A, B, C + 1, D, E, F, G)) :|: 100 >= C 3.66/1.99 f18(A, B, C, D, E, F, G) -> Com_1(f22(A, B, C, D, 1, 1, G)) :|: 99 >= D 3.66/1.99 f22(A, B, C, D, E, F, G) -> Com_1(f33(A, B, C, D, E, F, G)) :|: F >= 100 3.66/1.99 f22(A, B, C, D, E, F, G) -> Com_1(f33(A, B, C, D, E, F, G)) :|: 99 >= F && F + D >= 101 3.66/1.99 f22(A, B, C, D, E, F, G) -> Com_1(f22(A, B, C, D, E, F + 1, G)) :|: 99 >= F && 100 >= D + F 3.66/1.99 f22(A, B, C, D, E, F, G) -> Com_1(f22(A, B, C, D, 0, F + 1, H)) :|: 99 >= F && 100 >= D + F 3.66/1.99 f33(A, B, C, D, E, F, G) -> Com_1(f18(A, B, C, D + 1, 0, F, G)) :|: E >= 0 && E <= 0 3.66/1.99 f18(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D, E, F, G)) :|: D >= 100 3.66/1.99 f33(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D, E, F, G)) :|: 0 >= E + 1 3.66/1.99 f33(A, B, C, D, E, F, G) -> Com_1(f40(A, B, C, D, E, F, G)) :|: E >= 1 3.66/1.99 f8(A, B, C, D, E, F, G) -> Com_1(f18(A, B, C, 1, 0, F, G)) :|: C >= 101 3.66/1.99 3.66/1.99 The start-symbols are:[f0_7] 3.66/1.99 3.66/1.99 3.66/1.99 ---------------------------------------- 3.66/1.99 3.66/1.99 (1) Koat Proof (FINISHED) 3.66/1.99 YES(?, 20800) 3.66/1.99 3.66/1.99 3.66/1.99 3.66/1.99 Initial complexity problem: 3.66/1.99 3.66/1.99 1: T: 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f8(-1, -1, 1, ar_3, ar_4, ar_5, ar_6)) 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f8(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6)) [ 100 >= ar_2 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, 1, 1, ar_6)) [ 99 >= ar_3 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, 0, ar_5 + 1, h)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f18(ar_0, ar_1, ar_2, ar_3 + 1, 0, ar_5, ar_6)) [ ar_4 = 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_4 + 1 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_4 >= 1 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f18(ar_0, ar_1, ar_2, 1, 0, ar_5, ar_6)) [ ar_2 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 3.66/1.99 3.66/1.99 start location: koat_start 3.66/1.99 3.66/1.99 leaf cost: 0 3.66/1.99 3.66/1.99 3.66/1.99 3.66/1.99 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_2, ar_3, ar_4, ar_5]. 3.66/1.99 3.66/1.99 We thus obtain the following problem: 3.66/1.99 3.66/1.99 2: T: 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/1.99 3.66/1.99 start location: koat_start 3.66/1.99 3.66/1.99 leaf cost: 0 3.66/1.99 3.66/1.99 3.66/1.99 3.66/1.99 Repeatedly propagating knowledge in problem 2 produces the following problem: 3.66/1.99 3.66/1.99 3: T: 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/1.99 3.66/1.99 start location: koat_start 3.66/1.99 3.66/1.99 leaf cost: 0 3.66/1.99 3.66/1.99 3.66/1.99 3.66/1.99 A polynomial rank function with 3.66/1.99 3.66/1.99 Pol(koat_start) = 2 3.66/1.99 3.66/1.99 Pol(f0) = 2 3.66/1.99 3.66/1.99 Pol(f8) = 2 3.66/1.99 3.66/1.99 Pol(f18) = 1 3.66/1.99 3.66/1.99 Pol(f33) = 1 3.66/1.99 3.66/1.99 Pol(f40) = 0 3.66/1.99 3.66/1.99 Pol(f22) = 1 3.66/1.99 3.66/1.99 orients all transitions weakly and the transitions 3.66/1.99 3.66/1.99 f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/1.99 3.66/1.99 f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/1.99 3.66/1.99 f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/1.99 3.66/1.99 f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/1.99 3.66/1.99 strictly and produces the following problem: 3.66/1.99 3.66/1.99 4: T: 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/1.99 3.66/1.99 start location: koat_start 3.66/1.99 3.66/1.99 leaf cost: 0 3.66/1.99 3.66/1.99 3.66/1.99 3.66/1.99 A polynomial rank function with 3.66/1.99 3.66/1.99 Pol(koat_start) = 99 3.66/1.99 3.66/1.99 Pol(f0) = 99 3.66/1.99 3.66/1.99 Pol(f8) = 99 3.66/1.99 3.66/1.99 Pol(f18) = -V_2 + 100 3.66/1.99 3.66/1.99 Pol(f33) = -V_2 + 99 3.66/1.99 3.66/1.99 Pol(f40) = -V_2 3.66/1.99 3.66/1.99 Pol(f22) = -V_2 + 99 3.66/1.99 3.66/1.99 orients all transitions weakly and the transition 3.66/1.99 3.66/1.99 f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/1.99 3.66/1.99 strictly and produces the following problem: 3.66/1.99 3.66/1.99 5: T: 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/1.99 3.66/1.99 (Comp: 2, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/1.99 3.66/1.99 (Comp: 99, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/1.99 3.66/1.99 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/1.99 3.66/1.99 (Comp: 1, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/1.99 3.66/1.99 start location: koat_start 3.66/1.99 3.66/1.99 leaf cost: 0 3.66/1.99 3.66/1.99 3.66/1.99 3.66/1.99 A polynomial rank function with 3.66/1.99 3.66/1.99 Pol(f8) = 0 3.66/1.99 3.66/1.99 Pol(f33) = 1 3.66/1.99 3.66/1.99 Pol(f18) = 0 3.66/1.99 3.66/1.99 Pol(f22) = 2 3.66/1.99 3.66/1.99 and size complexities 3.66/1.99 3.66/1.99 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-0) = 1 3.66/1.99 3.66/1.99 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-1) = ar_3 3.66/1.99 3.66/1.99 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-2) = ar_4 3.66/1.99 3.66/1.99 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-3) = ar_5 3.66/1.99 3.66/1.99 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-1) = ar_3 3.66/1.99 3.66/1.99 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-2) = ar_4 3.66/1.99 3.66/1.99 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-3) = ar_5 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-2) = 1 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-3) = 1 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-2) = 1 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-2) = 1 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-2) = 1 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-2) = 0 3.66/1.99 3.66/1.99 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-2) = 0 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-2) = 0 3.66/1.99 3.66/1.99 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-2) = 1 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-1) = ? 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-2) = 1 3.66/1.99 3.66/1.99 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-3) = 100 3.66/1.99 3.66/1.99 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-0) = 101 3.66/1.99 3.66/1.99 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-1) = 1 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-2) = 0 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-3) = ar_5 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_2 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_3 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_4 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_5 3.66/2.00 3.66/2.00 orients the transitions 3.66/2.00 3.66/2.00 f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/2.00 3.66/2.00 f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 weakly and the transitions 3.66/2.00 3.66/2.00 f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/2.00 3.66/2.00 strictly and produces the following problem: 3.66/2.00 3.66/2.00 6: T: 3.66/2.00 3.66/2.00 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/2.00 3.66/2.00 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/2.00 3.66/2.00 (Comp: 99, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/2.00 3.66/2.00 (Comp: ?, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/2.00 3.66/2.00 (Comp: 1, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/2.00 3.66/2.00 start location: koat_start 3.66/2.00 3.66/2.00 leaf cost: 0 3.66/2.00 3.66/2.00 3.66/2.00 3.66/2.00 A polynomial rank function with 3.66/2.00 3.66/2.00 Pol(koat_start) = 100 3.66/2.00 3.66/2.00 Pol(f0) = 100 3.66/2.00 3.66/2.00 Pol(f8) = -V_1 + 101 3.66/2.00 3.66/2.00 Pol(f18) = -V_1 3.66/2.00 3.66/2.00 Pol(f33) = -V_1 3.66/2.00 3.66/2.00 Pol(f40) = -V_1 3.66/2.00 3.66/2.00 Pol(f22) = -V_1 3.66/2.00 3.66/2.00 orients all transitions weakly and the transition 3.66/2.00 3.66/2.00 f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/2.00 3.66/2.00 strictly and produces the following problem: 3.66/2.00 3.66/2.00 7: T: 3.66/2.00 3.66/2.00 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/2.00 3.66/2.00 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 (Comp: ?, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/2.00 3.66/2.00 (Comp: 99, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/2.00 3.66/2.00 (Comp: 100, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/2.00 3.66/2.00 (Comp: 1, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/2.00 3.66/2.00 start location: koat_start 3.66/2.00 3.66/2.00 leaf cost: 0 3.66/2.00 3.66/2.00 3.66/2.00 3.66/2.00 A polynomial rank function with 3.66/2.00 3.66/2.00 Pol(f22) = -V_4 + 100 3.66/2.00 3.66/2.00 and size complexities 3.66/2.00 3.66/2.00 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-0) = 1 3.66/2.00 3.66/2.00 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-1) = ar_3 3.66/2.00 3.66/2.00 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-2) = ar_4 3.66/2.00 3.66/2.00 S("f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5))", 0-3) = ar_5 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-1) = ar_3 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-2) = ar_4 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ]", 0-3) = ar_5 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-2) = 1 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ]", 0-3) = 1 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-2) = 1 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-2) = 1 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\\ ar_5 + ar_3 >= 101 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-2) = 1 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-2) = 0 3.66/2.00 3.66/2.00 S("f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\\ 100 >= ar_3 + ar_5 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-2) = 0 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-2) = 0 3.66/2.00 3.66/2.00 S("f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-2) = 1 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-1) = 199 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-2) = 1 3.66/2.00 3.66/2.00 S("f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ]", 0-3) = 100 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-0) = 101 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-1) = 1 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-2) = 0 3.66/2.00 3.66/2.00 S("f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ]", 0-3) = ar_5 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_2 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_3 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_4 3.66/2.00 3.66/2.00 S("koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_5 3.66/2.00 3.66/2.00 orients the transitions 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 weakly and the transitions 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 strictly and produces the following problem: 3.66/2.00 3.66/2.00 8: T: 3.66/2.00 3.66/2.00 (Comp: 1, Cost: 0) koat_start(ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, 1, 0, ar_5)) [ ar_2 >= 101 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 1 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.66/2.00 3.66/2.00 (Comp: 2, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f40(ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= 100 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f33(ar_2, ar_3, ar_4, ar_5) -> Com_1(f18(ar_2, ar_3 + 1, 0, ar_5)) [ ar_4 = 0 ] 3.66/2.00 3.66/2.00 (Comp: 9999, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 0, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 (Comp: 9999, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, ar_4, ar_5 + 1)) [ 99 >= ar_5 /\ 100 >= ar_3 + ar_5 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ 99 >= ar_5 /\ ar_5 + ar_3 >= 101 ] 3.66/2.00 3.66/2.00 (Comp: 198, Cost: 1) f22(ar_2, ar_3, ar_4, ar_5) -> Com_1(f33(ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= 100 ] 3.66/2.00 3.66/2.00 (Comp: 99, Cost: 1) f18(ar_2, ar_3, ar_4, ar_5) -> Com_1(f22(ar_2, ar_3, 1, 1)) [ 99 >= ar_3 ] 3.66/2.00 3.66/2.00 (Comp: 100, Cost: 1) f8(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(ar_2 + 1, ar_3, ar_4, ar_5)) [ 100 >= ar_2 ] 3.66/2.00 3.66/2.00 (Comp: 1, Cost: 1) f0(ar_2, ar_3, ar_4, ar_5) -> Com_1(f8(1, ar_3, ar_4, ar_5)) 3.66/2.00 3.66/2.00 start location: koat_start 3.66/2.00 3.66/2.00 leaf cost: 0 3.66/2.00 3.66/2.00 3.66/2.00 3.66/2.00 Complexity upper bound 20800 3.66/2.00 3.66/2.00 3.66/2.00 3.66/2.00 Time: 0.244 sec (SMT: 0.199 sec) 3.66/2.00 3.66/2.00 3.66/2.00 ---------------------------------------- 3.66/2.00 3.66/2.00 (2) 3.66/2.00 BOUNDS(1, 1) 3.66/2.01 EOF