/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^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 84 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_jama_ex3_start(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb0_in(v_i.0, v_j.0, v_n)) :|: TRUE eval_jama_ex3_bb0_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb1_in(1, v_j.0, v_n)) :|: TRUE eval_jama_ex3_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb2_in(v_i.0, v_i.0, v_n)) :|: v_i.0 <= v_n eval_jama_ex3_bb1_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb5_in(v_i.0, v_j.0, v_n)) :|: v_i.0 > v_n eval_jama_ex3_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb3_in(v_i.0, v_j.0, v_n)) :|: v_j.0 <= v_n eval_jama_ex3_bb2_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb4_in(v_i.0, v_j.0, v_n)) :|: v_j.0 > v_n eval_jama_ex3_bb3_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb2_in(v_i.0, v_j.0 + 1, v_n)) :|: TRUE eval_jama_ex3_bb4_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_bb1_in(v_i.0 + 1, v_j.0, v_n)) :|: TRUE eval_jama_ex3_bb5_in(v_i.0, v_j.0, v_n) -> Com_1(eval_jama_ex3_stop(v_i.0, v_j.0, v_n)) :|: TRUE The start-symbols are:[eval_jama_ex3_start_3] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 27*ar_1 + 6*ar_1^2 + 6) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: ?, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(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) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex3start) = 2 Pol(evaljamaex3bb0in) = 2 Pol(evaljamaex3bb1in) = 2 Pol(evaljamaex3bb2in) = 2 Pol(evaljamaex3bb5in) = 1 Pol(evaljamaex3bb3in) = 2 Pol(evaljamaex3bb4in) = 2 Pol(evaljamaex3stop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ?, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: 2, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex3start) = V_2 Pol(evaljamaex3bb0in) = V_2 Pol(evaljamaex3bb1in) = -V_1 + V_2 + 1 Pol(evaljamaex3bb2in) = -V_1 + V_2 Pol(evaljamaex3bb5in) = -V_1 + V_2 Pol(evaljamaex3bb3in) = -V_1 + V_2 Pol(evaljamaex3bb4in) = -V_1 + V_2 Pol(evaljamaex3stop) = -V_1 + V_2 Pol(koat_start) = V_2 orients all transitions weakly and the transition evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 1) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ar_1, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: 2, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: ?, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex3bb4in) = 1 Pol(evaljamaex3bb1in) = 0 Pol(evaljamaex3bb3in) = 2 Pol(evaljamaex3bb2in) = 2 and size complexities S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 S("evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2))", 0-0) = ? S("evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2))", 0-2) = ? S("evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = ? S("evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ? S("evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = ? S("evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1 S("evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ? S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ? S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1 S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ? S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = ? S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1 S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ? S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ? S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1 S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ? S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-0) = ? S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-2) = ? S("evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2))", 0-0) = 1 S("evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2))", 0-2) = ar_2 S("evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 S("evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 orients the transitions evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] weakly and the transitions evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 1) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ar_1, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: 2, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: 2*ar_1, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: 2*ar_1, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evaljamaex3bb3in) = V_2 - V_3 Pol(evaljamaex3bb2in) = V_2 - V_3 + 1 and size complexities S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2 S("evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2))", 0-0) = 2*ar_1 + 20 S("evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2))", 0-2) = ? S("evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2))", 0-0) = 2*ar_1 + 4 S("evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2))", 0-2) = ? S("evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1))", 0-0) = 2*ar_1 + 4 S("evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1))", 0-1) = ar_1 S("evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1))", 0-2) = ? S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 4 S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1 S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ? S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-0) = 2*ar_1 + 4 S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-1) = ar_1 S("evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ]", 0-2) = ? S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-0) = 2*ar_1 + 10 S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ar_1 S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ? S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-0) = 2*ar_1 + 4 S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-1) = ar_1 S("evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ]", 0-2) = 2*ar_1 + 10 S("evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2))", 0-0) = 1 S("evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2))", 0-2) = ar_2 S("evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2))", 0-0) = ar_0 S("evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2))", 0-1) = ar_1 S("evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2))", 0-2) = ar_2 orients the transitions evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] weakly and the transition evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 1) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ar_1, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: 2, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: 3*ar_1^2 + 11*ar_1, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: 2*ar_1, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: 2*ar_1, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(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) evaljamaex3start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb0in(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 1) evaljamaex3bb0in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(1, ar_1, ar_2)) (Comp: ar_1, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_0)) [ ar_1 >= ar_0 ] (Comp: 2, Cost: 1) evaljamaex3bb1in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb5in(ar_0, ar_1, ar_2)) [ ar_0 >= ar_1 + 1 ] (Comp: 3*ar_1^2 + 11*ar_1, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb3in(ar_0, ar_1, ar_2)) [ ar_1 >= ar_2 ] (Comp: 2*ar_1, Cost: 1) evaljamaex3bb2in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb4in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 + 1 ] (Comp: 3*ar_1^2 + 11*ar_1, Cost: 1) evaljamaex3bb3in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb2in(ar_0, ar_1, ar_2 + 1)) (Comp: 2*ar_1, Cost: 1) evaljamaex3bb4in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3bb1in(ar_0 + 1, ar_1, ar_2)) (Comp: 2, Cost: 1) evaljamaex3bb5in(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3stop(ar_0, ar_1, ar_2)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2) -> Com_1(evaljamaex3start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 27*ar_1 + 6*ar_1^2 + 6 Time: 0.083 sec (SMT: 0.072 sec) ---------------------------------------- (2) BOUNDS(1, n^2)