/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 10 ms] (2) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: f300(A, B, C, D, E) -> Com_1(f300(-(1) + A, B, C, D, E)) :|: A >= 101 && 9 >= B f300(A, B, C, D, E) -> Com_1(f2(A, B, 0, 0, 0)) :|: 100 >= A && 9 >= B f300(A, B, C, D, E) -> Com_1(f2(A, B, 0, 0, 0)) :|: B >= 10 f1(A, B, C, D, E) -> Com_1(f300(1000, B, C, D, E)) :|: TRUE The start-symbols are:[f1_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 1003) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ] (Comp: ?, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ] (Comp: ?, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ] (Comp: ?, Cost: 1) f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: ?, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ] (Comp: ?, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ] (Comp: 1, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ] (Comp: 1, Cost: 1) f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f300) = 1 Pol(f2) = 0 Pol(f1) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ] strictly and produces the following problem: 3: T: (Comp: ?, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ] (Comp: 1, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ] (Comp: 1, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ] (Comp: 1, Cost: 1) f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(f300) = V_1 Pol(f2) = V_1 Pol(f1) = 1000 Pol(koat_start) = 1000 orients all transitions weakly and the transition f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ] strictly and produces the following problem: 4: T: (Comp: 1000, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ] (Comp: 1, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ] (Comp: 1, Cost: 1) f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ] (Comp: 1, Cost: 1) f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 1003 Time: 0.064 sec (SMT: 0.057 sec) ---------------------------------------- (2) BOUNDS(1, 1)