/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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, 487 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realheapsort_step1_start(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb0_in(v_33, v_N, v_j_0, v_k_0)) :|: TRUE eval_realheapsort_step1_bb0_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_0(v_33, v_N, v_j_0, v_k_0)) :|: TRUE eval_realheapsort_step1_0(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_1(v_33, v_N, v_j_0, v_k_0)) :|: TRUE eval_realheapsort_step1_1(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0)) :|: TRUE eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, 1)) :|: v_N > 2 eval_realheapsort_step1_2(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0)) :|: v_N <= 2 eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, v_k_0, v_k_0)) :|: v_k_0 <= v_N - 1 eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0)) :|: v_k_0 > v_N - 1 eval_realheapsort_step1_bb2_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 > 0 eval_realheapsort_step1_bb2_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 <= 0 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_0 >= 0 && v_j_0 - 2 * nondef_0 + 1 >= 0 && v_j_0 - 2 * nondef_0 + 1 < 2 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_0 <= 0 && -(v_j_0) + 2 * nondef_0 - 1 >= 0 && -(v_j_0) + 2 * nondef_0 - 1 < 2 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_0 >= 0 && nondef_0 <= 0 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_0 >= 0 && v_j_0 - 2 * nondef_0 + 1 >= 0 && v_j_0 - 2 * nondef_0 + 1 < 2 eval_realheapsort_step1_bb3_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_0 <= 0 && -(v_j_0) + 2 * nondef_0 - 1 >= 0 && -(v_j_0) + 2 * nondef_0 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_1 >= 0 && nondef_1 <= 0 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 < 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 > 0 && nondef_1 >= 0 && v_j_0 - 2 * nondef_1 + 1 >= 0 && v_j_0 - 2 * nondef_1 + 1 < 2 && v_j_0 + 1 < 0 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_2 >= 0 && nondef_2 <= 0 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && v_j_0 + 1 > 0 && nondef_2 >= 0 && v_j_0 - 2 * nondef_2 + 1 >= 0 && v_j_0 - 2 * nondef_2 + 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 >= 0 && v_j_0 + 1 <= 0 && nondef_3 >= 0 && nondef_3 <= 0 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && v_j_0 + 1 > 0 && nondef_3 >= 0 && v_j_0 - 2 * nondef_3 + 1 >= 0 && v_j_0 - 2 * nondef_3 + 1 < 2 eval_realheapsort_step1_bb4_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb2_in(v_33, v_N, nondef_3 - 1, v_k_0)) :|: v_j_0 + 1 < 0 && nondef_1 <= 0 && -(v_j_0) + 2 * nondef_1 - 1 >= 0 && -(v_j_0) + 2 * nondef_1 - 1 < 2 && nondef_2 <= 0 && -(v_j_0) + 2 * nondef_2 - 1 >= 0 && -(v_j_0) + 2 * nondef_2 - 1 < 2 && nondef_3 <= 0 && -(v_j_0) + 2 * nondef_3 - 1 >= 0 && -(v_j_0) + 2 * nondef_3 - 1 < 2 eval_realheapsort_step1__critedge_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_28(v_k_0 + 1, v_N, v_j_0, v_k_0)) :|: TRUE eval_realheapsort_step1_28(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_29(v_33, v_N, v_j_0, v_k_0)) :|: TRUE eval_realheapsort_step1_29(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_bb1_in(v_33, v_N, v_j_0, v_33)) :|: TRUE eval_realheapsort_step1_bb5_in(v_33, v_N, v_j_0, v_k_0) -> Com_1(eval_realheapsort_step1_stop(v_33, v_N, v_j_0, v_k_0)) :|: TRUE The start-symbols are:[eval_realheapsort_step1_start_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 5931*ar_0 + 72*ar_0^2 + 5869) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ 0 >= e /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 + 1 = 0 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= e /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ 0 >= ar_2 + 2 /\ 0 >= g /\ 0 >= e /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ e >= 0 /\ 0 >= 2*e /\ 2*e + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= 1 /\ 0 >= f /\ 0 >= e /\ ar_2 + 1 = 0 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ f >= 0 /\ 0 >= 2*f /\ 2*f + 1 >= 0 /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ ar_2 >= 0 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3)) [ 0 >= 1 /\ 0 >= e /\ 0 >= f /\ ar_2 + 1 = 0 /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g ] evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ 0 >= ar_2 + 2 /\ 0 >= f /\ 0 >= g /\ 0 >= e /\ 2*f >= ar_2 + 1 /\ ar_2 + 2 >= 2*f /\ 2*g >= ar_2 + 1 /\ ar_2 + 2 >= 2*g /\ 2*e >= ar_2 + 1 /\ ar_2 + 2 >= 2*e ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep1bb1in) = 2 Pol(evalrealheapsortstep1bb5in) = 1 Pol(evalrealheapsortstep129) = 2 Pol(evalrealheapsortstep128) = 2 Pol(evalrealheapsortstep1bb4in) = 2 Pol(evalrealheapsortstep1bb2in) = 2 Pol(evalrealheapsortstep1critedgein) = 2 Pol(evalrealheapsortstep1bb3in) = 2 Pol(evalrealheapsortstep1stop) = 0 Pol(evalrealheapsortstep12) = 2 Pol(evalrealheapsortstep11) = 2 Pol(evalrealheapsortstep10) = 2 Pol(evalrealheapsortstep1bb0in) = 2 Pol(evalrealheapsortstep1start) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep1critedgein) = V_1 - V_2 - 1 Pol(evalrealheapsortstep128) = V_1 - V_4 Pol(evalrealheapsortstep1bb4in) = V_1 - V_2 - 1 Pol(evalrealheapsortstep1bb2in) = V_1 - V_2 - 1 Pol(evalrealheapsortstep1bb3in) = V_1 - V_2 - 1 Pol(evalrealheapsortstep1bb1in) = V_1 - V_2 Pol(evalrealheapsortstep129) = V_1 - V_4 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-0) = ar_0 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-1) = 1 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-2) = ar_2 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-3) = ar_3 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ar_0 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ar_2 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ar_3 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ? S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ? S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-0) = ar_0 S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-1) = ? S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-2) = ? S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-3) = ? S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-1) = ? S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-1) = ? S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-2) = ? S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-3) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ? orients the transitions evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) weakly and the transition evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] strictly and produces the following problem: 5: T: (Comp: 2, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: ar_0 + 1, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep1critedgein) = 3 Pol(evalrealheapsortstep128) = 2 Pol(evalrealheapsortstep1bb4in) = 4 Pol(evalrealheapsortstep1bb2in) = 4 Pol(evalrealheapsortstep1bb3in) = 4 Pol(evalrealheapsortstep129) = 1 Pol(evalrealheapsortstep1bb1in) = 0 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-0) = ar_0 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-1) = 1 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-2) = ar_2 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-3) = ar_3 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ar_0 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ar_2 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ar_3 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ? S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ? S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-0) = ar_0 S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-1) = ? S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-2) = ? S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-3) = ? S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = ? S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-1) = ? S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-2) = ? S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-3) = ? S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-1) = ? S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-2) = ? S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-3) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = ? S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = ? orients the transitions evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) weakly and the transitions evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) strictly and produces the following problem: 6: T: (Comp: 2, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: ar_0 + 1, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalrealheapsortstep1bb4in) = 3*V_3 + 1 Pol(evalrealheapsortstep1bb2in) = 6*V_3 + 2 Pol(evalrealheapsortstep1bb3in) = 3*V_3 + 3 and size complexities S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2 S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2 S("evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-0) = ar_0 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-1) = 1 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-2) = ar_2 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ]", 0-3) = ar_3 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-0) = ar_0 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-1) = ar_1 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-2) = ar_2 S("evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ]", 0-3) = ar_3 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 4*ar_0 + 324 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 1280 S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = 4*ar_0 + 4*ar_1 + 1280 S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 4*ar_0 + 4*ar_2 + 5373952 S("evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_0 + 4*ar_3 + 5120 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-2) = 4*ar_0 + 1312 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]", 0-3) = 4*ar_0 + 4*ar_3 + 5120 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-2) = 4*ar_0 + 5248 S("evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 20480 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = 4*ar_0 + 1312 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 5120 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = 4*ar_0 + 5248 S("evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 20480 S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-0) = ar_0 S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-1) = 4*ar_0 + 320 S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-2) = 4*ar_0 + 20992 S("evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1))", 0-3) = 4*ar_0 + 80 S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-2) = 4*ar_0 + 1312 S("evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\\ f >= 0 /\\ ar_2 + 1 >= 2*f /\\ 2*f >= ar_2 /\\ g >= 0 /\\ ar_2 + 1 >= 2*g /\\ 2*g >= ar_2 /\\ e >= 0 /\\ ar_2 + 1 >= 2*e /\\ 2*e >= ar_2 ]", 0-3) = 4*ar_0 + 4*ar_3 + 5120 S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-1) = 4*ar_0 + 1280 S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-2) = 4*ar_0 + 83968 S("evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3))", 0-3) = 4*ar_0 + 80 S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-0) = ar_0 S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-1) = 4*ar_0 + 80 S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-2) = 4*ar_0 + 335872 S("evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3))", 0-3) = 4*ar_0 + 320 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-1) = 4*ar_0 + 320 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-2) = 4*ar_0 + 1343488 S("evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ]", 0-3) = 4*ar_0 + 1280 orients the transitions evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] weakly and the transitions evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] strictly and produces the following problem: 7: T: (Comp: 2, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 ] (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_3, ar_2, ar_3)) (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep129(ar_0, ar_1, ar_2, ar_3)) (Comp: 24*ar_0^2 + 1970*ar_0 + 1946, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, e - 1, ar_3)) [ ar_2 >= 0 /\ f >= 0 /\ ar_2 + 1 >= 2*f /\ 2*f >= ar_2 /\ g >= 0 /\ ar_2 + 1 >= 2*g /\ 2*g >= ar_2 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep128(ar_0, ar_1, ar_2, ar_1 + 1)) (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: 24*ar_0^2 + 1970*ar_0 + 1946, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 0 /\ e >= 0 /\ ar_2 + 1 >= 2*e /\ 2*e >= ar_2 ] (Comp: 4*ar_0 + 4, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] (Comp: 24*ar_0^2 + 1970*ar_0 + 1946, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ] (Comp: 2, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3)) (Comp: ar_0 + 1, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3)) [ ar_0 >= ar_1 + 1 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] (Comp: 1, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3)) [ ar_0 >= 3 ] (Comp: 1, Cost: 1) evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep11(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep10(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 5931*ar_0 + 72*ar_0^2 + 5869 Time: 0.375 sec (SMT: 0.273 sec) ---------------------------------------- (2) BOUNDS(1, n^2)