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Complexity_ITS 2019-03-21 04.46 pair #429989982
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
n167.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
37.9276 seconds
cpu usage
45.1133
user time
43.9479
system time
1.16547
max virtual memory
1.8917304E7
max residence set size
247844.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
44.95/37.88 WORST_CASE(Omega(n^1), O(n^2)) 44.95/37.89 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 44.95/37.89 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 44.95/37.89 44.95/37.89 44.95/37.89 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 44.95/37.89 44.95/37.89 (0) CpxIntTrs 44.95/37.89 (1) Koat Proof [FINISHED, 1319 ms] 44.95/37.89 (2) BOUNDS(1, n^2) 44.95/37.89 (3) Loat Proof [FINISHED, 3334 ms] 44.95/37.89 (4) BOUNDS(n^1, INF) 44.95/37.89 44.95/37.89 44.95/37.89 ---------------------------------------- 44.95/37.89 44.95/37.89 (0) 44.95/37.89 Obligation: 44.95/37.89 Complexity Int TRS consisting of the following rules: 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 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 44.95/37.89 44.95/37.89 The start-symbols are:[eval_realheapsort_step2_start_5] 44.95/37.89 44.95/37.89 44.95/37.89 ---------------------------------------- 44.95/37.89 44.95/37.89 (1) Koat Proof (FINISHED) 44.95/37.89 YES(?, 128*ar_0 + 60*ar_0^2 + 89) 44.95/37.89 44.95/37.89 44.95/37.89 44.95/37.89 Initial complexity problem: 44.95/37.89 44.95/37.89 1: T: 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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 ] 44.95/37.89 44.95/37.89 (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 ] 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (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)) 44.95/37.89 44.95/37.89 (Comp: ?, Cost: 1) evalrealheapsortstep28(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep29(ar_0, ar_1, ar_2, ar_3, ar_4)) 44.95/37.89 44.95/37.89 (Comp: ?, Cost: 1) evalrealheapsortstep29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep210(ar_0, ar_1, ar_2, ar_3, ar_4)) 44.95/37.89 44.95/37.89 (Comp: ?, Cost: 1) evalrealheapsortstep210(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealheapsortstep211(ar_0, ar_1, ar_2, ar_3, ar_4)) 44.95/37.89
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