details

property	value
status	complete
benchmark	realheapsort_step1.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	2.58805 seconds
cpu usage	3.77183
user time	3.45822
system time	0.313613
max virtual memory	1.861248E7
max residence set size	190164.0

stage attributes

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

output

3.62/2.55 WORST_CASE(?, O(n^2)) 3.62/2.56 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.62/2.56 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.62/2.56 3.62/2.56 3.62/2.56 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.62/2.56 3.62/2.56 (0) CpxIntTrs 3.62/2.56 (1) Koat Proof [FINISHED, 1282 ms] 3.62/2.56 (2) BOUNDS(1, n^2) 3.62/2.56 3.62/2.56 3.62/2.56 ---------------------------------------- 3.62/2.56 3.62/2.56 (0) 3.62/2.56 Obligation: 3.62/2.56 Complexity Int TRS consisting of the following rules: 3.62/2.56 eval_realheapsort_step1_start(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb0_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_bb0_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, 1)) :|: v_N > 2 3.62/2.56 eval_realheapsort_step1_bb0_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb5_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_N <= 2 3.62/2.56 eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, v_k.0, v_k.0)) :|: v_k.0 <= v_N - 1 3.62/2.56 eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb5_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_k.0 > v_N - 1 3.62/2.56 eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb3_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_j.0 > 0 3.62/2.56 eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_.critedge_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_j.0 <= 0 3.62/2.56 eval_realheapsort_step1_bb3_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_2(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_2(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_2(eval_nondet_start(v_4, v_5, v_N, v_j.0, v_k.0), eval_realheapsort_step1_3(nondef.0, v_5, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_3(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_2(eval_nondet_start(v_4, v_5, v_N, v_j.0, v_k.0), eval_realheapsort_step1_4(v_4, nondef.1, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_4(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb4_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_4 > v_5 3.62/2.56 eval_realheapsort_step1_4(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_.critedge_in(v_4, v_5, v_N, v_j.0, v_k.0)) :|: v_4 <= v_5 3.62/2.56 eval_realheapsort_step1_bb4_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_5(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_5(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_2(eval_nondet_start(v_4, v_5, v_N, v_j.0, v_k.0), eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, nondef.3 - 1, v_k.0)) :|: v_j.0 + 1 >= 0 && v_j.0 + 1 <= 0 && nondef.3 >= 0 && nondef.3 <= 0 3.62/2.56 eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, nondef.3 - 1, v_k.0)) :|: v_j.0 + 1 > 0 && nondef.3 >= 0 && nondef.3 < v_j.0 + 1 3.62/2.56 eval_realheapsort_step1_6(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb2_in(v_4, v_5, v_N, nondef.3 - 1, v_k.0)) :|: v_j.0 + 1 < 0 && nondef.3 <= 0 && nondef.3 > v_j.0 + 1 3.62/2.56 eval_realheapsort_step1_.critedge_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_bb1_in(v_4, v_5, v_N, v_j.0, v_k.0 + 1)) :|: TRUE 3.62/2.56 eval_realheapsort_step1_bb5_in(v_4, v_5, v_N, v_j.0, v_k.0) -> Com_1(eval_realheapsort_step1_stop(v_4, v_5, v_N, v_j.0, v_k.0)) :|: TRUE 3.62/2.56 3.62/2.56 The start-symbols are:[eval_realheapsort_step1_start_5] 3.62/2.56 3.62/2.56 3.62/2.56 ---------------------------------------- 3.62/2.56 3.62/2.56 (1) Koat Proof (FINISHED) 3.62/2.56 YES(?, 876*ar_0 + 432*ar_0^2 + 451) 3.62/2.56 3.62/2.56 3.62/2.56 3.62/2.56 Initial complexity problem: 3.62/2.56 3.62/2.56 1: T: 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb1in(ar_0, 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 3 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 2 >= ar_0 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, ar_1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 + 1 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= 1 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_2 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep120(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep13(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalrealheapsortstep120(ar_0, ar_1, ar_2, ar_3, g, ar_5), evalrealheapsortstep121(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep130(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep13(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalrealheapsortstep130(ar_0, ar_1, ar_2, ar_3, g, ar_5), evalrealheapsortstep131(ar_0, ar_1, ar_2, ar_3, g, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_3 >= ar_5 + 1 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep14(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_3 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep15(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5), evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, -1, ar_3, ar_4, ar_5)) [ ar_2 + 1 = 0 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, g - 1, ar_3, ar_4, ar_5)) [ ar_2 >= 0 /\ g >= 0 /\ ar_2 >= g ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep16(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb2in(ar_0, ar_1, g - 1, ar_3, ar_4, ar_5)) [ 0 >= ar_2 + 2 /\ 0 >= g /\ g >= ar_2 + 2 ] 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1critedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1bb1in(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: ?, Cost: 1) evalrealheapsortstep1bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.62/2.56 3.62/2.56 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalrealheapsortstep1start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.62/2.56 3.62/2.56 start location: koat_start popout

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all output return to Complexity_C_Integer 2019-03-21 04.38