details

property	value
status	complete
benchmark	realheapsort_step2.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n099.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	37.5803291798 seconds
cpu usage	44.728735475
max memory	4.61180928E8

stage attributes

key	value
output-size	197325
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 1296 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 3169 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realheapsort_step2_start(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb0_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb0_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_0(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_0(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_1(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_1(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_2(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_2(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb1_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: v_N > 2 eval_realheapsort_step2_2(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb12_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: v_N <= 2 eval_realheapsort_step2_bb1_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_3(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_3(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_4(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_4(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_5(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_5(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_6(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_6(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_7(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_7(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_8(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_8(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_9(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_9(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_10(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_10(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_11(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_11(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_12(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_12(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb2_in(v_57, v_N, v_j_0, 0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb2_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb3_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: v_k_0 <= v_N - 2 eval_realheapsort_step2_bb2_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb12_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: v_k_0 > v_N - 2 eval_realheapsort_step2_bb3_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb4_in(v_57, v_N, 0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb4_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb5_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: 2 * v_j_0 + 1 <= v_N - v_k_0 - 2 eval_realheapsort_step2_bb4_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb11_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: 2 * v_j_0 + 1 > v_N - v_k_0 - 2 eval_realheapsort_step2_bb5_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb7_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: 2 * v_j_0 + 1 >= v_N - v_k_0 - 2 && 2 * v_j_0 + 1 <= v_N - v_k_0 - 2 eval_realheapsort_step2_bb5_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb6_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: 2 * v_j_0 + 1 < v_N - v_k_0 - 2 eval_realheapsort_step2_bb5_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb6_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: 2 * v_j_0 + 1 > v_N - v_k_0 - 2 eval_realheapsort_step2_bb6_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb7_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb6_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb8_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb7_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb9_in(v_57, v_N, v_j_0, v_k_0, 2 * v_j_0 + 1)) :|: TRUE eval_realheapsort_step2_bb8_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb9_in(v_57, v_N, v_j_0, v_k_0, 2 * v_j_0 + 2)) :|: TRUE eval_realheapsort_step2_bb9_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb10_in(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb9_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb4_in(v_57, v_N, v_N, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb10_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb4_in(v_57, v_N, v_m_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_bb11_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_58(v_k_0 + 1, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_58(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_59(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE eval_realheapsort_step2_59(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_bb2_in(v_57, v_N, v_j_0, v_57, v_m_0)) :|: TRUE eval_realheapsort_step2_bb12_in(v_57, v_N, v_j_0, v_k_0, v_m_0) -> Com_1(eval_realheapsort_step2_stop(v_57, v_N, v_j_0, v_k_0, v_m_0)) :|: TRUE The start-symbols are:[eval_realheapsort_step2_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 128*ar_0 + 60*ar_0^2 + 89) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealheapsortstep2start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep20(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep21(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep21(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 3 ] (Comp: ?, Cost: 1) evalrealheapsortstep22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep2bb12in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep23(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep23(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep24(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep25(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep26(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep27(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealheapsortstep27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep28(ar_0, ar_1, ar_2, ar_3, ar_4)) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Compl Integ Trans Syste 26843