details

property	value
status	complete
benchmark	insertsort.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.28753 seconds
cpu usage	6.91465
user time	6.58711
system time	0.327538
max virtual memory	1.8633612E7
max residence set size	223612.0

stage attributes

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

output

6.76/3.24 WORST_CASE(Omega(n^2), O(n^2)) 6.76/3.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 6.76/3.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.76/3.25 6.76/3.25 6.76/3.25 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 6.76/3.25 6.76/3.25 (0) CpxIntTrs 6.76/3.25 (1) Koat Proof [FINISHED, 221 ms] 6.76/3.25 (2) BOUNDS(1, n^2) 6.76/3.25 (3) Loat Proof [FINISHED, 1422 ms] 6.76/3.25 (4) BOUNDS(n^2, INF) 6.76/3.25 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (0) 6.76/3.25 Obligation: 6.76/3.25 Complexity Int TRS consisting of the following rules: 6.76/3.25 eval_insertsort_start(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb0_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb0_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_0(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_0(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_1(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_1(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_2(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_2(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_3(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_3(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_4(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_4(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_5(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_5(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_6(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_6(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb1_in(v_20, v_3, 1, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb1_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb2_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_i_0 < v_length 6.76/3.25 eval_insertsort_bb1_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb7_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_i_0 >= v_length 6.76/3.25 eval_insertsort_bb2_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb3_in(v_20, nondef_0, v_i_0, v_i_0 - 1, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb3_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb4_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_j_0 >= 0 6.76/3.25 eval_insertsort_bb3_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb6_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: v_j_0 < 0 6.76/3.25 eval_insertsort_bb4_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb5_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: nondef_1 > v_3 6.76/3.25 eval_insertsort_bb4_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb6_in(v_20, v_3, v_i_0, v_j_0, v_length)) :|: nondef_1 <= v_3 6.76/3.25 eval_insertsort_bb5_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb3_in(v_20, v_3, v_i_0, v_j_0 - 1, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb6_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_25(v_i_0 + 1, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_25(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_26(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_26(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_bb1_in(v_20, v_3, v_20, v_j_0, v_length)) :|: TRUE 6.76/3.25 eval_insertsort_bb7_in(v_20, v_3, v_i_0, v_j_0, v_length) -> Com_1(eval_insertsort_stop(v_20, v_3, v_i_0, v_j_0, v_length)) :|: TRUE 6.76/3.25 6.76/3.25 The start-symbols are:[eval_insertsort_start_5] 6.76/3.25 6.76/3.25 6.76/3.25 ---------------------------------------- 6.76/3.25 6.76/3.25 (1) Koat Proof (FINISHED) 6.76/3.25 YES(?, 229*ar_1 + 12*ar_1^2 + 13) 6.76/3.25 6.76/3.25 6.76/3.25 6.76/3.25 Initial complexity problem: 6.76/3.25 6.76/3.25 1: T: 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort5(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort6(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, f, ar_0 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= 0 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_3 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_2 + 1 ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= f ] 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3 - 1, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_0 + 1)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsort26(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortbb1in(ar_4, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: ?, Cost: 1) evalinsertsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 6.76/3.25 6.76/3.25 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 6.76/3.25 6.76/3.25 start location: koat_start popout

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all output return to Complexity_ITS 2019-03-21 04.46