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	n049.star.cs.uiowa.edu
space	WTC_V2

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	3.32175517082 seconds
cpu usage	4.679464201
max memory	4.25119744E8

stage attributes

key	value
output-size	310681
starexec-result	WORST_CASE(?, O(n^3))

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^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 2087 ms] (2) BOUNDS(1, n^3) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 The start-symbols are:[eval_realshellsort_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 9*ar_0 + 216*ar_0^2 + 1176*ar_0^3 + 8) Initial complexity problem: 1: T: (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)) (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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 ] (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)) (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)) (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)) (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)) (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)) (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 ] (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 ] (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)) (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)) (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)) (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)) (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 ] popout

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all output return to Compl C Integ Progr 85445