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Compl Integ Trans Syste 26843 pair #381744589
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
n048.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.18315696716 seconds
cpu usage
6.890663768
max memory
3.23293184E8
stage attributes
key
value
output-size
74768
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 213 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 1405 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 The start-symbols are:[eval_insertsort_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 229*ar_1 + 12*ar_1^2 + 13) Initial complexity problem: 1: T: (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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 ] (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 ] (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 ] (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 ] (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)) (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)) (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)) (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))
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