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Complexity_C_Integer 2019-03-21 04.38 pair #429989656
details
property
value
status
complete
benchmark
realshellsort.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
WTC_V2
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
3.47053 seconds
cpu usage
4.77243
user time
4.36851
system time
0.403921
max virtual memory
1.8682972E7
max residence set size
248076.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^3))
output
4.61/3.41 WORST_CASE(?, O(n^3)) 4.61/3.42 proof of /export/starexec/sandbox/output/output_files/bench.koat 4.61/3.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.61/3.42 4.61/3.42 4.61/3.42 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). 4.61/3.42 4.61/3.42 (0) CpxIntTrs 4.61/3.42 (1) Koat Proof [FINISHED, 2187 ms] 4.61/3.42 (2) BOUNDS(1, n^3) 4.61/3.42 4.61/3.42 4.61/3.42 ---------------------------------------- 4.61/3.42 4.61/3.42 (0) 4.61/3.42 Obligation: 4.61/3.42 Complexity Int TRS consisting of the following rules: 4.61/3.42 eval_realshellsort_start(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb0_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 eval_realshellsort_bb0_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, nondef.0, v_j.0)) :|: v_array_size >= 0 && v_array_size <= 0 && nondef.0 >= 0 && nondef.0 <= 0 4.61/3.42 eval_realshellsort_bb0_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, nondef.0, v_j.0)) :|: v_array_size > 0 && nondef.0 >= 0 && nondef.0 < v_array_size 4.61/3.42 eval_realshellsort_bb0_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, nondef.0, v_j.0)) :|: v_array_size < 0 && nondef.0 <= 0 && nondef.0 > v_array_size 4.61/3.42 eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb2_in(v_3, v_5, v_array_size, 0, v_increment.0, v_j.0)) :|: v_increment.0 > 0 4.61/3.42 eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb8_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_increment.0 <= 0 4.61/3.42 eval_realshellsort_bb2_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb3_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_i.0 < v_array_size 4.61/3.42 eval_realshellsort_bb2_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb7_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_i.0 >= v_array_size 4.61/3.42 eval_realshellsort_bb3_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_2(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 eval_realshellsort_2(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_2(eval_nondet_start(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0), eval_realshellsort_3(nondef.1, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 eval_realshellsort_3(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb4_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_i.0)) :|: TRUE 4.61/3.42 eval_realshellsort_bb4_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb5_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_j.0 >= v_increment.0 4.61/3.42 eval_realshellsort_bb4_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_.critedge_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_j.0 < v_increment.0 4.61/3.42 eval_realshellsort_bb5_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_4(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 eval_realshellsort_4(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_2(eval_nondet_start(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0), eval_realshellsort_5(v_3, nondef.2, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 eval_realshellsort_5(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb6_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_5 > v_3 4.61/3.42 eval_realshellsort_5(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_.critedge_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: v_5 <= v_3 4.61/3.42 eval_realshellsort_bb6_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb4_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0 - v_increment.0)) :|: TRUE 4.61/3.42 eval_realshellsort_.critedge_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb2_in(v_3, v_5, v_array_size, v_i.0 + 1, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 eval_realshellsort_bb7_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, nondef.3, v_j.0)) :|: v_increment.0 >= 0 && v_increment.0 <= 0 && nondef.3 >= 0 && nondef.3 <= 0 4.61/3.42 eval_realshellsort_bb7_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, nondef.3, v_j.0)) :|: v_increment.0 > 0 && nondef.3 >= 0 && nondef.3 < v_increment.0 4.61/3.42 eval_realshellsort_bb7_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_bb1_in(v_3, v_5, v_array_size, v_i.0, nondef.3, v_j.0)) :|: v_increment.0 < 0 && nondef.3 <= 0 && nondef.3 > v_increment.0 4.61/3.42 eval_realshellsort_bb8_in(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0) -> Com_1(eval_realshellsort_stop(v_3, v_5, v_array_size, v_i.0, v_increment.0, v_j.0)) :|: TRUE 4.61/3.42 4.61/3.42 The start-symbols are:[eval_realshellsort_start_6] 4.61/3.42 4.61/3.42 4.61/3.42 ---------------------------------------- 4.61/3.42 4.61/3.42 (1) Koat Proof (FINISHED) 4.61/3.42 YES(?, 9*ar_0 + 1392*ar_0^2 + 2352*ar_0^3 + 8) 4.61/3.42 4.61/3.42 4.61/3.42 4.61/3.42 Initial complexity problem: 4.61/3.42 4.61/3.42 1: T: 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb1in(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 = 0 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb1in(ar_0, h, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= 1 /\ h >= 0 /\ ar_0 >= h + 1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb1in(ar_0, h, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_0 + 1 /\ 0 >= h /\ h >= ar_0 + 1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, 0, ar_3, ar_4, ar_5, ar_6)) [ ar_1 >= 1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 >= ar_1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= ar_2 + 1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort3(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrealshellsort20(ar_0, ar_1, ar_2, ar_3, h, ar_5, ar_6), evalrealshellsort21(ar_0, ar_1, ar_2, ar_3, h, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_2, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_1 >= ar_5 + 1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort40(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalnondetstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort41(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_4)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort4(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_2(evalrealshellsort40(ar_0, ar_1, ar_2, ar_3, h, ar_5, ar_6), evalrealshellsort41(ar_0, ar_1, ar_2, ar_3, h, ar_5, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= ar_3 + 1 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_6 ] 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 - ar_1, ar_6)) 4.61/3.42 4.61/3.42 (Comp: ?, Cost: 1) evalrealshellsortcritedgein(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6))
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