/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 87 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_t19_start(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb0_in(v_.0, v_.1, v_i, v_k)) :|: TRUE eval_t19_bb0_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb1_in(v_i, v_.1, v_i, v_k)) :|: TRUE eval_t19_bb1_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb2_in(v_.0, v_.1, v_i, v_k)) :|: v_.0 > 100 eval_t19_bb1_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb3_in(v_.0, v_.1, v_i, v_k)) :|: v_.0 <= 100 eval_t19_bb2_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb1_in(v_.0 - 1, v_.1, v_i, v_k)) :|: TRUE eval_t19_bb3_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb4_in(v_.0, v_.0 + v_k + 50, v_i, v_k)) :|: TRUE eval_t19_bb4_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb5_in(v_.0, v_.1, v_i, v_k)) :|: v_.1 >= 0 eval_t19_bb4_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb6_in(v_.0, v_.1, v_i, v_k)) :|: v_.1 < 0 eval_t19_bb5_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_bb4_in(v_.0, v_.1 - 1, v_i, v_k)) :|: TRUE eval_t19_bb6_in(v_.0, v_.1, v_i, v_k) -> Com_1(eval_t19_stop(v_.0, v_.1, v_i, v_k)) :|: TRUE The start-symbols are:[eval_t19_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_1 + 2*ar_3 + 422) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: ?, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 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) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: ?, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: ?, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt19start) = 4 Pol(evalt19bb0in) = 4 Pol(evalt19bb1in) = 4 Pol(evalt19bb2in) = 4 Pol(evalt19bb3in) = 3 Pol(evalt19bb4in) = 2 Pol(evalt19bb5in) = 2 Pol(evalt19bb6in) = 1 Pol(evalt19stop) = 0 Pol(koat_start) = 4 orients all transitions weakly and the transitions evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: 4, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: 4, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: 4, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: 4, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt19start) = V_2 + 51 Pol(evalt19bb0in) = V_2 + 51 Pol(evalt19bb1in) = V_1 + 51 Pol(evalt19bb2in) = V_1 + 50 Pol(evalt19bb3in) = V_1 + 51 Pol(evalt19bb4in) = V_3 - V_4 + 1 Pol(evalt19bb5in) = V_3 - V_4 Pol(evalt19bb6in) = V_3 - V_4 Pol(evalt19stop) = V_3 - V_4 Pol(koat_start) = V_2 + 51 orients all transitions weakly and the transition evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ar_1 + 51, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: 4, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ?, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: 4, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: 4, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: 4, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 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) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ar_1 + 51, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: 4, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ar_1 + 51, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: 4, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ?, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: 4, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: 4, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalt19start) = V_4 + 151 Pol(evalt19bb0in) = V_4 + 151 Pol(evalt19bb1in) = V_4 + 151 Pol(evalt19bb2in) = V_4 + 151 Pol(evalt19bb3in) = V_1 + V_4 + 51 Pol(evalt19bb4in) = V_3 + 1 Pol(evalt19bb5in) = V_3 Pol(evalt19bb6in) = V_3 Pol(evalt19stop) = V_3 Pol(koat_start) = V_4 + 151 orients all transitions weakly and the transition evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ar_1 + 51, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: 4, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ar_1 + 51, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: 4, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ar_3 + 151, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: 4, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: 4, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 6 produces the following problem: 7: T: (Comp: 1, Cost: 1) evalt19start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalt19bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_1, ar_1, ar_2, ar_3)) (Comp: ar_1 + 51, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 101 ] (Comp: 4, Cost: 1) evalt19bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb3in(ar_0, ar_1, ar_2, ar_3)) [ 100 >= ar_0 ] (Comp: ar_1 + 51, Cost: 1) evalt19bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb1in(ar_0 - 1, ar_1, ar_2, ar_3)) (Comp: 4, Cost: 1) evalt19bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_0 + ar_3 + 50, ar_3)) (Comp: ar_3 + 151, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 ] (Comp: 4, Cost: 1) evalt19bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb6in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 1 ] (Comp: ar_3 + 151, Cost: 1) evalt19bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19bb4in(ar_0, ar_1, ar_2 - 1, ar_3)) (Comp: 4, Cost: 1) evalt19bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalt19start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 2*ar_1 + 2*ar_3 + 422 Time: 0.126 sec (SMT: 0.110 sec) ---------------------------------------- (2) BOUNDS(1, n^1)