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Complexity_C_Integer 2019-03-21 04.38 pair #429989652
details
property
value
status
complete
benchmark
insertsort.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n081.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.16022 seconds
cpu usage
3.33705
user time
3.08105
system time
0.255998
max virtual memory
1.8480724E7
max residence set size
189284.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^2))
output
3.24/2.12 WORST_CASE(?, O(n^2)) 3.24/2.13 proof of /export/starexec/sandbox/output/output_files/bench.koat 3.24/2.13 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.24/2.13 3.24/2.13 3.24/2.13 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). 3.24/2.13 3.24/2.13 (0) CpxIntTrs 3.24/2.13 (1) Koat Proof [FINISHED, 894 ms] 3.24/2.13 (2) BOUNDS(1, n^2) 3.24/2.13 3.24/2.13 3.24/2.13 ---------------------------------------- 3.24/2.13 3.24/2.13 (0) 3.24/2.13 Obligation: 3.24/2.13 Complexity Int TRS consisting of the following rules: 3.24/2.13 eval_insertsort_start(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb0_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_bb0_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb1_in(v_1, v_4, 1, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_bb1_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb2_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: v_i.0 < v_length 3.24/2.13 eval_insertsort_bb1_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb6_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: v_i.0 >= v_length 3.24/2.13 eval_insertsort_bb2_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_0(v_1, v_4, v_i.0, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_0(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_2(eval_nondet_start(v_1, v_4, v_i.0, v_j.0, v_length), eval_insertsort_1(nondef.0, v_4, v_i.0, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_1(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb3_in(v_1, v_4, v_i.0, v_i.0 - 1, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_bb3_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb4_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: v_j.0 >= 0 3.24/2.13 eval_insertsort_bb3_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_.critedge_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: v_j.0 < 0 3.24/2.13 eval_insertsort_bb4_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_3(v_1, v_4, v_i.0, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_3(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_2(eval_nondet_start(v_1, v_4, v_i.0, v_j.0, v_length), eval_insertsort_4(v_1, nondef.1, v_i.0, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_4(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb5_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: v_4 > v_1 3.24/2.13 eval_insertsort_4(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_.critedge_in(v_1, v_4, v_i.0, v_j.0, v_length)) :|: v_4 <= v_1 3.24/2.13 eval_insertsort_bb5_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb3_in(v_1, v_4, v_i.0, v_j.0 - 1, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_.critedge_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_bb1_in(v_1, v_4, v_i.0 + 1, v_j.0, v_length)) :|: TRUE 3.24/2.13 eval_insertsort_bb6_in(v_1, v_4, v_i.0, v_j.0, v_length) -> Com_1(eval_insertsort_stop(v_1, v_4, v_i.0, v_j.0, v_length)) :|: TRUE 3.24/2.13 3.24/2.13 The start-symbols are:[eval_insertsort_start_5] 3.24/2.13 3.24/2.13 3.24/2.13 ---------------------------------------- 3.24/2.13 3.24/2.13 (1) Koat Proof (FINISHED) 3.24/2.13 YES(?, 800*ar_1 + 896*ar_1^2 + 6) 3.24/2.13 3.24/2.13 3.24/2.13 3.24/2.13 Initial complexity problem: 3.24/2.13 3.24/2.13 1: T: 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb1in(1, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= ar_0 + 1 ] 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= ar_1 ] 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort00(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)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort01(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsort1(ar_0, ar_1, ar_3, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalinsertsort00(ar_0, ar_1, ar_2, g, ar_4, ar_5), evalinsertsort01(ar_0, ar_1, ar_2, g, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_0 - 1, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_4 >= 0 ] 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_4 + 1 ] 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort30(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)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort31(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_2(evalinsertsort30(ar_0, ar_1, ar_2, g, ar_4, ar_5), evalinsertsort31(ar_0, ar_1, ar_2, g, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_5 >= ar_2 + 1 ] 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_5 ] 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortbb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: ?, Cost: 1) evalinsertsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) 3.24/2.13 3.24/2.13 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 3.24/2.13 3.24/2.13 start location: koat_start 3.24/2.13 3.24/2.13 leaf cost: 0 3.24/2.13 3.24/2.13 3.24/2.13 3.24/2.13 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.24/2.13 3.24/2.13 2: T: 3.24/2.13
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