details

property	value
status	complete
benchmark	realshellsort.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	13.6604847908 seconds
cpu usage	20.496211417
max memory	5.0130944E8

stage attributes

key	value
output-size	251771
starexec-result	WORST_CASE(?, O(n^3))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^3).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, 1510 ms] (2) BOUNDS(1, n^3) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_realshellsort_start(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb0_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_bb0_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_0(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_0(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_1(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_1(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_2(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_2(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_3(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_3(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_4(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_4(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_5(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_5(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_6(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_6(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_7(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_7(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb2_in(nondef_0, v_21, v_5, v_array_size, v_array_size_sink, 0, v_j_0)) :|: v_array_size_sink >= 0 && v_array_size_sink <= 0 && nondef_0 >= 0 && nondef_0 <= 0 && nondef_0 > 0 eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb2_in(nondef_0, v_21, v_5, v_array_size, v_array_size_sink, 0, v_j_0)) :|: v_array_size_sink > 0 && nondef_0 >= 0 && v_array_size_sink - 2 * nondef_0 >= 0 && v_array_size_sink - 2 * nondef_0 < 2 && nondef_0 > 0 eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb2_in(nondef_0, v_21, v_5, v_array_size, v_array_size_sink, 0, v_j_0)) :|: v_array_size_sink < 0 && nondef_0 <= 0 && -(v_array_size_sink) + 2 * nondef_0 >= 0 && -(v_array_size_sink) + 2 * nondef_0 < 2 && nondef_0 > 0 eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb7_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: v_array_size_sink >= 0 && v_array_size_sink <= 0 && nondef_0 >= 0 && nondef_0 <= 0 eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb7_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: v_array_size_sink > 0 && nondef_0 >= 0 && v_array_size_sink - 2 * nondef_0 >= 0 && v_array_size_sink - 2 * nondef_0 < 2 && nondef_0 <= 0 eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb7_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: v_array_size_sink < 0 && nondef_0 <= 0 && -(v_array_size_sink) + 2 * nondef_0 >= 0 && -(v_array_size_sink) + 2 * nondef_0 < 2 eval_realshellsort_bb2_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb3_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: v_i_0 < v_array_size eval_realshellsort_bb2_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb1_in(v_0, v_21, v_5, v_array_size, v_0, v_i_0, v_j_0)) :|: v_i_0 >= v_array_size eval_realshellsort_bb3_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb4_in(v_0, v_21, nondef_1, v_array_size, v_array_size_sink, v_i_0, v_i_0)) :|: TRUE eval_realshellsort_bb4_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb5_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: v_j_0 >= v_0 eval_realshellsort_bb4_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort__critedge_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: v_j_0 < v_0 eval_realshellsort_bb5_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb6_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: nondef_2 > v_5 eval_realshellsort_bb5_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort__critedge_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: nondef_2 <= v_5 eval_realshellsort_bb6_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb4_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0 - v_0)) :|: TRUE eval_realshellsort__critedge_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_27(v_0, v_i_0 + 1, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_27(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_28(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE eval_realshellsort_28(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_bb2_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_21, v_j_0)) :|: TRUE eval_realshellsort_bb7_in(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0) -> Com_1(eval_realshellsort_stop(v_0, v_21, v_5, v_array_size, v_array_size_sink, v_i_0, v_j_0)) :|: TRUE The start-symbols are:[eval_realshellsort_start_7] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_1 + 31*ar_1^2 + 18*ar_1^3 + 18) 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(evalrealshellsort0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealshellsort0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealshellsort1(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) evalrealshellsort2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealshellsort3(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) evalrealshellsort4(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_6)) (Comp: ?, Cost: 1) evalrealshellsort5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealshellsort6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsort7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (Comp: ?, Cost: 1) evalrealshellsort7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evalrealshellsortbb1in(ar_1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) (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, 0, ar_4, ar_5, ar_6)) [ 0 >= 1 /\ ar_0 = 0 ] (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, h, 0, ar_4, ar_5, ar_6)) [ ar_0 >= 1 /\ h >= 0 /\ ar_0 >= 2*h /\ 2*h + 1 >= ar_0 /\ h >= 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, h, 0, ar_4, ar_5, ar_6)) [ 0 >= ar_0 + 1 /\ 0 >= h /\ h >= 1 /\ 2*h >= ar_0 /\ ar_0 + 1 >= 2*h ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(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_0 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(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_0 = 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(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)) [ 0 >= ar_0 + 1 /\ 0 >= h /\ 2*h >= ar_0 /\ ar_0 + 1 >= 2*h ] (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_1 >= ar_3 + 1 ] popout

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actions

all output return to Compl Integ Trans Syste 26843