/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).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, 76 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_wcet2_start(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb0_in(v_.0, v_i, v_j.0)) :|: TRUE eval_wcet2_bb0_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb1_in(v_i, v_i, v_j.0)) :|: TRUE eval_wcet2_bb1_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb2_in(v_.0, v_i, 0)) :|: v_.0 < 5 eval_wcet2_bb1_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb5_in(v_.0, v_i, v_j.0)) :|: v_.0 >= 5 eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb3_in(v_.0, v_i, v_j.0)) :|: v_.0 > 2 && v_j.0 <= 9 eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb4_in(v_.0, v_i, v_j.0)) :|: v_.0 <= 2 eval_wcet2_bb2_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb4_in(v_.0, v_i, v_j.0)) :|: v_j.0 > 9 eval_wcet2_bb3_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb2_in(v_.0, v_i, v_j.0 + 1)) :|: TRUE eval_wcet2_bb4_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_bb1_in(v_.0 + 1, v_i, v_j.0)) :|: TRUE eval_wcet2_bb5_in(v_.0, v_i, v_j.0) -> Com_1(eval_wcet2_stop(v_.0, v_i, v_j.0)) :|: TRUE The start-symbols are:[eval_wcet2_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 56*ar_1 + 258) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 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) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2start) = 2 Pol(evalwcet2bb0in) = 2 Pol(evalwcet2bb1in) = 2 Pol(evalwcet2bb2in) = 2 Pol(evalwcet2bb5in) = 1 Pol(evalwcet2bb3in) = 2 Pol(evalwcet2bb4in) = 2 Pol(evalwcet2stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: ?, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2start) = -2*V_2 + 9 Pol(evalwcet2bb0in) = -2*V_2 + 9 Pol(evalwcet2bb1in) = -2*V_1 + 9 Pol(evalwcet2bb2in) = -2*V_1 + 8 Pol(evalwcet2bb5in) = -2*V_1 Pol(evalwcet2bb3in) = -2*V_1 + 8 Pol(evalwcet2bb4in) = -2*V_1 + 7 Pol(evalwcet2stop) = -2*V_1 Pol(koat_start) = -2*V_2 + 9 orients all transitions weakly and the transitions evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2bb4in) = 1 Pol(evalwcet2bb1in) = 0 Pol(evalwcet2bb3in) = 2 Pol(evalwcet2bb2in) = 2 and size complexities S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-0) = ? S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-2) = ? S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = ? S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ? S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ? S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1 S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-0) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-1) = ar_1 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-2) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-0) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-1) = ar_1 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-2) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ? S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-0) = ? S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-1) = ar_1 S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-2) = ? S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-0) = ? S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-1) = ar_1 S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-2) = 0 S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1 S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2 S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 orients the transitions evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] weakly and the transitions evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: ?, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: 6*ar_1 + 27, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: 6*ar_1 + 27, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalwcet2bb3in) = -V_3 + 9 Pol(evalwcet2bb2in) = -V_3 + 10 and size complexities S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-0) = 7*ar_1 + 64827 S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2))", 0-2) = ? S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = 7*ar_1 + 1323 S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ? S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 7*ar_1 + 1323 S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1 S("evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-0) = 7*ar_1 + 1323 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-1) = ar_1 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ]", 0-2) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-0) = 7*ar_1 + 1323 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-1) = ar_1 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ]", 0-2) = ? S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-0) = 7*ar_1 + 1323 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-1) = ar_1 S("evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\\ 9 >= ar_2 ]", 0-2) = ? S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-0) = 7*ar_1 + 9261 S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-1) = ar_1 S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ]", 0-2) = ? S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-0) = 7*ar_1 + 1323 S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-1) = ar_1 S("evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ]", 0-2) = 0 S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-0) = ar_1 S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2))", 0-2) = ar_2 S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 orients the transitions evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] weakly and the transition evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: 20*ar_1 + 90, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: 6*ar_1 + 27, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: ?, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: 6*ar_1 + 27, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 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) evalwcet2start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evalwcet2bb0in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_1, ar_1, ar_2)) (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, 0)) [ 4 >= ar_0 ] (Comp: 2, Cost: 1) evalwcet2bb1in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= 5 ] (Comp: 20*ar_1 + 90, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb3in(ar_0, ar_1, ar_2)) [ ar_0 >= 3 /\ 9 >= ar_2 ] (Comp: 2*ar_1 + 9, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ 2 >= ar_0 ] (Comp: 6*ar_1 + 27, Cost: 1) evalwcet2bb2in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= 10 ] (Comp: 20*ar_1 + 90, Cost: 1) evalwcet2bb3in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: 6*ar_1 + 27, Cost: 1) evalwcet2bb4in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evalwcet2bb5in(ar_0, ar_1, ar_2) -> Com_1(evalwcet2stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evalwcet2start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 56*ar_1 + 258 Time: 0.096 sec (SMT: 0.081 sec) ---------------------------------------- (2) BOUNDS(1, n^1)