/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 349 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, Fresh_17 - 1, Ar_3)) [ 0 >= 1 /\ Fresh_17 >= 0 /\ 0 >= 2*Fresh_17 /\ 2*Fresh_17 + 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, Fresh_16 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= Fresh_16 /\ Ar_2 + 1 = 0 /\ 2*Fresh_16 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_16 ] (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, Fresh_15 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ Fresh_15 >= 0 /\ 0 >= 2*Fresh_15 /\ 2*Fresh_15 + 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, Fresh_14 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ 0 >= Fresh_14 /\ Ar_2 + 1 = 0 /\ 2*Fresh_14 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_14 ] (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, Fresh_13 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ Fresh_13 >= 0 /\ 0 >= 2*Fresh_13 /\ 2*Fresh_13 + 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, Fresh_12 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ 0 >= Fresh_12 /\ Ar_2 + 1 = 0 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*Fresh_12 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_12 ] (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, Fresh_11 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ Fresh_11 >= 0 /\ 0 >= 2*Fresh_11 /\ 2*Fresh_11 + 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, Fresh_10 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ 0 >= Fresh_10 /\ Ar_2 + 1 = 0 /\ 2*Fresh_10 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_10 ] (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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= Ar_2 ] (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_8 - 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 >= Fresh_8 /\ 2*Fresh_8 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_8 ] (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, Fresh_7 - 1, Ar_3)) [ Ar_2 >= 0 /\ F >= 0 /\ Ar_2 + 1 >= 2*F /\ 2*F >= Ar_2 /\ 0 >= Ar_2 + 2 /\ 0 >= G /\ Fresh_7 >= 0 /\ Ar_2 + 1 >= 2*Fresh_7 /\ 2*Fresh_7 >= 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, Fresh_6 - 1, Ar_3)) [ Ar_2 >= 0 /\ F >= 0 /\ Ar_2 + 1 >= 2*F /\ 2*F >= Ar_2 /\ 0 >= Ar_2 + 2 /\ 0 >= G /\ 0 >= Fresh_6 /\ 2*G >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*G /\ 2*Fresh_6 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_6 ] (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, Fresh_5 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ Fresh_5 >= 0 /\ 0 >= 2*Fresh_5 /\ 2*Fresh_5 + 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, Fresh_4 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ 0 >= Fresh_4 /\ Ar_2 + 1 = 0 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*Fresh_4 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_4 ] (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, Fresh_3 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ Ar_2 >= 0 /\ G >= 0 /\ Ar_2 + 1 >= 2*G /\ 2*G >= Ar_2 /\ Fresh_3 >= 0 /\ Ar_2 + 1 >= 2*Fresh_3 /\ 2*Fresh_3 >= 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, Fresh_2 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ Ar_2 >= 0 /\ G >= 0 /\ Ar_2 + 1 >= 2*G /\ 2*G >= Ar_2 /\ 0 >= Fresh_2 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*Fresh_2 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_2 ] (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, Fresh_1 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ 0 >= G /\ Ar_2 >= 0 /\ Fresh_1 >= 0 /\ Ar_2 + 1 >= 2*Fresh_1 /\ 2*Fresh_1 >= 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, Fresh_0 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ 0 >= G /\ 0 >= Fresh_0 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*G >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*G /\ 2*Fresh_0 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_0 ] (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, Fresh_17 - 1, Ar_3)) [ 0 >= 1 /\ Fresh_17 >= 0 /\ 0 >= 2*Fresh_17 /\ 2*Fresh_17 + 1 >= 0 /\ Ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_16 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= Fresh_16 /\ Ar_2 + 1 = 0 /\ 2*Fresh_16 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_16 ] 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, Fresh_15 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ Fresh_15 >= 0 /\ 0 >= 2*Fresh_15 /\ 2*Fresh_15 + 1 >= 0 /\ Ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_14 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ 0 >= Fresh_14 /\ Ar_2 + 1 = 0 /\ 2*Fresh_14 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_14 ] 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, Fresh_13 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ Fresh_13 >= 0 /\ 0 >= 2*Fresh_13 /\ 2*Fresh_13 + 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, Fresh_12 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ 0 >= Fresh_12 /\ Ar_2 + 1 = 0 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*Fresh_12 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_12 ] 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, Fresh_11 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ Fresh_11 >= 0 /\ 0 >= 2*Fresh_11 /\ 2*Fresh_11 + 1 >= 0 /\ Ar_2 + 1 = 0 ] evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_10 - 1, Ar_3)) [ 0 >= 1 /\ F >= 0 /\ 0 >= 2*F /\ 2*F + 1 >= 0 /\ 0 >= Fresh_10 /\ Ar_2 + 1 = 0 /\ 2*Fresh_10 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_10 ] 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, Fresh_8 - 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 >= Fresh_8 /\ 2*Fresh_8 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_8 ] 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, Fresh_7 - 1, Ar_3)) [ Ar_2 >= 0 /\ F >= 0 /\ Ar_2 + 1 >= 2*F /\ 2*F >= Ar_2 /\ 0 >= Ar_2 + 2 /\ 0 >= G /\ Fresh_7 >= 0 /\ Ar_2 + 1 >= 2*Fresh_7 /\ 2*Fresh_7 >= 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, Fresh_6 - 1, Ar_3)) [ Ar_2 >= 0 /\ F >= 0 /\ Ar_2 + 1 >= 2*F /\ 2*F >= Ar_2 /\ 0 >= Ar_2 + 2 /\ 0 >= G /\ 0 >= Fresh_6 /\ 2*G >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*G /\ 2*Fresh_6 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_6 ] 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, Fresh_5 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ Fresh_5 >= 0 /\ 0 >= 2*Fresh_5 /\ 2*Fresh_5 + 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, Fresh_4 - 1, Ar_3)) [ 0 >= 1 /\ 0 >= F /\ 0 >= Fresh_4 /\ Ar_2 + 1 = 0 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*Fresh_4 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_4 ] 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, Fresh_3 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ Ar_2 >= 0 /\ G >= 0 /\ Ar_2 + 1 >= 2*G /\ 2*G >= Ar_2 /\ Fresh_3 >= 0 /\ Ar_2 + 1 >= 2*Fresh_3 /\ 2*Fresh_3 >= 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, Fresh_2 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ Ar_2 >= 0 /\ G >= 0 /\ Ar_2 + 1 >= 2*G /\ 2*G >= Ar_2 /\ 0 >= Fresh_2 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*Fresh_2 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_2 ] 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, Fresh_1 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ 0 >= G /\ Ar_2 >= 0 /\ Fresh_1 >= 0 /\ Ar_2 + 1 >= 2*Fresh_1 /\ 2*Fresh_1 >= 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, Fresh_0 - 1, Ar_3)) [ 0 >= Ar_2 + 2 /\ 0 >= F /\ 0 >= G /\ 0 >= Fresh_0 /\ 2*F >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*F /\ 2*G >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*G /\ 2*Fresh_0 >= Ar_2 + 1 /\ Ar_2 + 2 >= 2*Fresh_0 ] 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-0) = Ar_0 S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-0) = Ar_0 S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-1) = ? S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-2) = ? S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= Ar_2 ]", 0-0) = Ar_0 S("evalrealheapsortstep1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalrealheapsortstep1bb2in(Ar_0, Ar_1, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\\ Fresh_9 >= 0 /\\ Ar_2 + 1 >= 2*Fresh_9 /\\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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, Fresh_9 - 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 /\ Fresh_9 >= 0 /\ Ar_2 + 1 >= 2*Fresh_9 /\ 2*Fresh_9 >= 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: 0.298 sec (SMT: 0.198 sec) ---------------------------------------- (2) BOUNDS(1, n^2)