/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 84 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_terminate_start(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: TRUE eval_terminate_bb0_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_bb1_in(v_i, v_j, v_k, v_i, v_j, v_k)) :|: TRUE eval_terminate_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.0 <= 100 && v_.01 <= v_.02 eval_terminate_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.0 > 100 eval_terminate_bb1_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: v_.01 > v_.02 eval_terminate_bb2_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_bb1_in(v_.01, v_.0 + 1, v_.02 - 1, v_i, v_j, v_k)) :|: TRUE eval_terminate_bb3_in(v_.0, v_.01, v_.02, v_i, v_j, v_k) -> Com_1(eval_terminate_stop(v_.0, v_.01, v_.02, v_i, v_j, v_k)) :|: TRUE The start-symbols are:[eval_terminate_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_1 + 2*ar_3 + 2*ar_5 + 210) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: ?, Cost: 1) evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ] (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5)) (Comp: ?, Cost: 1) evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 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) evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ] (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5)) (Comp: ?, Cost: 1) evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalterminatestart) = 2 Pol(evalterminatebb0in) = 2 Pol(evalterminatebb1in) = 2 Pol(evalterminatebb2in) = 2 Pol(evalterminatebb3in) = 1 Pol(evalterminatestop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (Comp: ?, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ] (Comp: 2, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5)) (Comp: 2, Cost: 1) evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalterminatestart) = -V_2 - V_4 + V_6 + 101 Pol(evalterminatebb0in) = -V_2 - V_4 + V_6 + 101 Pol(evalterminatebb1in) = -V_1 - V_3 + V_5 + 101 Pol(evalterminatebb2in) = -V_1 - V_3 + V_5 + 99 Pol(evalterminatebb3in) = -V_1 - V_3 + V_5 Pol(evalterminatestop) = -V_1 - V_3 + V_5 Pol(koat_start) = -V_2 - V_4 + V_6 + 101 orients all transitions weakly and the transition evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ] (Comp: 2, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5)) (Comp: 2, Cost: 1) evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 4 produces the following problem: 5: T: (Comp: 1, Cost: 1) evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 1) evalterminatebb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_1, ar_1, ar_3, ar_3, ar_5, ar_5)) (Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 100 >= ar_0 /\ ar_4 >= ar_2 ] (Comp: 2, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 101 ] (Comp: 2, Cost: 1) evalterminatebb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_4 + 1 ] (Comp: ar_1 + ar_3 + ar_5 + 101, Cost: 1) evalterminatebb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatebb1in(ar_2, ar_1, ar_0 + 1, ar_3, ar_4 - 1, ar_5)) (Comp: 2, Cost: 1) evalterminatebb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalterminatestart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2*ar_1 + 2*ar_3 + 2*ar_5 + 210 Time: 0.087 sec (SMT: 0.073 sec) ---------------------------------------- (2) BOUNDS(1, n^1)