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Compl C Integ Progr 85445 pair #381745818
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
n052.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.06349110603 seconds
cpu usage
3.03854266
max memory
3.14814464E8
stage attributes
key
value
output-size
81991
starexec-result
WORST_CASE(?, O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_c_complexity /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^2)) proof of /export/starexec/sandbox2/output/output_files/bench.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 883 ms] (2) BOUNDS(1, n^2) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 The start-symbols are:[eval_insertsort_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 800*ar_1 + 896*ar_1^2 + 6) Initial complexity problem: 1: T: (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)) (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)) (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 ] (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 ] (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)) (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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)) (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)) (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 ] start location: koat_start leaf cost: 0
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