/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 285 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speed_popl10_sequential_single_start(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb0_in(v_1, v_n, v_x.0, v_x.1)) :|: TRUE eval_speed_popl10_sequential_single_bb0_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb1_in(v_1, v_n, 0, v_x.1)) :|: TRUE eval_speed_popl10_sequential_single_bb1_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb2_in(v_1, v_n, v_x.0, v_x.1)) :|: v_x.0 < v_n eval_speed_popl10_sequential_single_bb1_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb4_in(v_1, v_n, v_x.0, v_x.0)) :|: v_x.0 >= v_n eval_speed_popl10_sequential_single_bb2_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_0(v_1, v_n, v_x.0, v_x.1)) :|: TRUE eval_speed_popl10_sequential_single_0(v_1, v_n, v_x.0, v_x.1) -> Com_2(eval_nondet_start(v_1, v_n, v_x.0, v_x.1), eval_speed_popl10_sequential_single_1(nondef.0, v_n, v_x.0, v_x.1)) :|: TRUE eval_speed_popl10_sequential_single_1(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb4_in(v_1, v_n, v_x.0, v_x.0)) :|: v_1 > 0 eval_speed_popl10_sequential_single_1(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb3_in(v_1, v_n, v_x.0, v_x.1)) :|: v_1 <= 0 eval_speed_popl10_sequential_single_bb3_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb1_in(v_1, v_n, v_x.0 + 1, v_x.1)) :|: TRUE eval_speed_popl10_sequential_single_bb4_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb5_in(v_1, v_n, v_x.0, v_x.1)) :|: v_x.1 < v_n eval_speed_popl10_sequential_single_bb4_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb6_in(v_1, v_n, v_x.0, v_x.1)) :|: v_x.1 >= v_n eval_speed_popl10_sequential_single_bb5_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_bb4_in(v_1, v_n, v_x.0, v_x.1 + 1)) :|: TRUE eval_speed_popl10_sequential_single_bb6_in(v_1, v_n, v_x.0, v_x.1) -> Com_1(eval_speed_popl10_sequential_single_stop(v_1, v_n, v_x.0, v_x.1)) :|: TRUE The start-symbols are:[eval_speed_popl10_sequential_single_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 63*Ar_1 + 14) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestop(Ar_0, 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(evalspeedpopl10sequentialsinglestart(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: 1, Cost: 1) evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestop(Ar_0, 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(evalspeedpopl10sequentialsinglestart(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(evalspeedpopl10sequentialsinglestart) = 3 Pol(evalspeedpopl10sequentialsinglebb0in) = 3 Pol(evalspeedpopl10sequentialsinglebb1in) = 3 Pol(evalspeedpopl10sequentialsinglebb2in) = 3 Pol(evalspeedpopl10sequentialsinglebb4in) = 2 Pol(evalspeedpopl10sequentialsingle0) = 3 Pol(evalspeedpopl10sequentialsingle00) = 0 Pol(evalnondetstart) = 0 Pol(evalspeedpopl10sequentialsingle01) = 3 Pol(evalspeedpopl10sequentialsingle1) = 3 Pol(evalspeedpopl10sequentialsinglebb3in) = 3 Pol(evalspeedpopl10sequentialsinglebb5in) = 2 Pol(evalspeedpopl10sequentialsinglebb6in) = 1 Pol(evalspeedpopl10sequentialsinglestop) = 0 Pol(koat_start) = 3 orients all transitions weakly and the transitions evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_3 >= 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_0 + 1 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) (Comp: 3, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 >= Ar_3 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 >= Ar_2 + 1 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestop(Ar_0, 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(evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalspeedpopl10sequentialsingle0: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsingle00: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsingle01: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsingle1: X_4 - X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsinglebb1in: X_1 >= 0 For symbol evalspeedpopl10sequentialsinglebb2in: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsinglebb3in: -X_5 >= 0 /\ X_4 - X_5 >= 0 /\ -X_4 - X_5 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 >= 0 /\ -X_4 + X_5 >= 0 /\ -X_4 >= 0 /\ X_2 - X_4 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsinglebb4in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsinglebb5in: X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0 For symbol evalspeedpopl10sequentialsinglebb6in: X_3 >= 0 /\ -X_2 + X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_3 - Ar_4 >= 0 /\ -Ar_3 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ -Ar_3 >= 0 /\ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: ?, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 7*V_2 Pol(evalspeedpopl10sequentialsinglestart) = 7*V_2 Pol(evalspeedpopl10sequentialsinglebb6in) = -5*V_1 + 7*V_2 - 2*V_3 - 5 Pol(evalspeedpopl10sequentialsinglestop) = -5*V_1 + 7*V_2 - 2*V_3 - 5 Pol(evalspeedpopl10sequentialsinglebb5in) = -5*V_1 + 7*V_2 - 2*V_3 - 6 Pol(evalspeedpopl10sequentialsinglebb4in) = -5*V_1 + 7*V_2 - 2*V_3 - 5 Pol(evalspeedpopl10sequentialsinglebb3in) = -7*V_1 + 7*V_2 - 6 Pol(evalspeedpopl10sequentialsinglebb1in) = -7*V_1 + 7*V_2 Pol(evalspeedpopl10sequentialsingle1) = -7*V_1 + 7*V_2 - 5 Pol(evalspeedpopl10sequentialsingle0) = -7*V_1 + 7*V_2 - 2 Pol(evalspeedpopl10sequentialsingle00) = 1 Pol(evalspeedpopl10sequentialsingle01) = -7*V_1 + 7*V_2 - 4 Pol(evalnondetstart) = 0 Pol(evalspeedpopl10sequentialsinglebb2in) = -7*V_1 + 7*V_2 - 1 Pol(evalspeedpopl10sequentialsinglebb0in) = 7*V_2 orients all transitions weakly and the transitions evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_3 - Ar_4 >= 0 /\ -Ar_3 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ -Ar_3 >= 0 /\ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglestop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_1 - Ar_2 - 1 >= 0 /\ Ar_2 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb6in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= Ar_1 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb5in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= 0 /\ Ar_0 + Ar_2 >= 0 /\ -Ar_0 + Ar_2 >= 0 /\ Ar_0 >= 0 /\ Ar_1 >= Ar_2 + 1 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_4 >= 0 /\ Ar_3 - Ar_4 >= 0 /\ -Ar_3 - Ar_4 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ -Ar_3 >= 0 /\ Ar_1 - Ar_3 - 1 >= 0 /\ Ar_0 - Ar_3 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ 0 >= Ar_3 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_3 - Ar_4 >= 0 /\ -Ar_3 + Ar_4 >= 0 /\ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 /\ Ar_3 >= 1 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_2(evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0), evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Fresh_0)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsingle01(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle1(Ar_0, Ar_1, Ar_2, Ar_4, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsingle00(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalnondetstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsingle0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_1 - 1 >= 0 /\ Ar_0 + Ar_1 - 1 >= 0 /\ -Ar_0 + Ar_1 - 1 >= 0 /\ Ar_0 >= 0 ] (Comp: 3, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb4in(Ar_0, Ar_1, Ar_0, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_0 >= Ar_1 ] (Comp: 7*Ar_1, Cost: 1) evalspeedpopl10sequentialsinglebb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= 0 /\ Ar_1 >= Ar_0 + 1 ] (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb1in(0, Ar_1, Ar_2, Ar_3, Ar_4)) (Comp: 1, Cost: 1) evalspeedpopl10sequentialsinglestart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalspeedpopl10sequentialsinglebb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) start location: koat_start leaf cost: 0 Complexity upper bound 63*Ar_1 + 14 Time: 0.327 sec (SMT: 0.244 sec) ---------------------------------------- (2) BOUNDS(1, n^1)