details

property	value
status	complete
benchmark	realheapsort_step1.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	17.5429871082 seconds
cpu usage	24.646463176
max memory	4.22907904E8

stage attributes

key	value
output-size	88399
starexec-result	WORST_CASE(?, O(n^2))

output

/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2).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 ] popout

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all output return to Compl Integ Trans Syste 26843