details

property	value
status	complete
benchmark	realshellsort.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n107.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.46240401268 seconds
cpu usage	12.639150987
max memory	3.93699328E8

stage attributes

key	value
output-size	160067
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

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^1), O(n^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^3). (0) CpxIntTrs (1) Koat Proof [FINISHED, 779 ms] (2) BOUNDS(1, n^3) (3) Loat Proof [FINISHED, 3149 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: evalrealshellsortstart(A, B, C, D, E) -> Com_1(evalrealshellsortentryin(A, B, C, D, E)) :|: TRUE evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: A >= 0 && A <= 0 evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: A >= 1 && F >= 0 && A >= 2 * F && 1 + 2 * F >= A evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: 0 >= A + 1 && 0 >= F && 2 * F >= A && 1 + A >= 2 * F evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, 0, D, E)) :|: B >= 1 evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortreturnin(A, B, C, D, E)) :|: 0 >= B evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb1in(A, B, C, D, E)) :|: A >= C + 1 evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb7in(A, B, C, D, E)) :|: C >= A evalrealshellsortbb1in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, F, C)) :|: TRUE evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: B >= E + 1 evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb4in(A, B, C, D, E)) :|: E >= B evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb2in(A, B, C, D, E)) :|: F >= D + 1 evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: D >= F evalrealshellsortbb2in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, D, E - B)) :|: TRUE evalrealshellsortbb5in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, C + 1, D, E)) :|: TRUE evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: B >= 0 && B <= 0 evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: B >= 1 && F >= 0 && B >= 2 * F && 1 + 2 * F >= B evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, F, C, D, E)) :|: 0 >= B + 1 && 0 >= F && 2 * F >= B && 1 + B >= 2 * F evalrealshellsortreturnin(A, B, C, D, E) -> Com_1(evalrealshellsortstop(A, B, C, D, E)) :|: TRUE The start-symbols are:[evalrealshellsortstart_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 73*ar_0 + 65*ar_0^2 + 18*ar_0^3 + 37) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_0 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_0 >= 1 /\ f >= 0 /\ ar_0 >= 2*f /\ 2*f + 1 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 /\ 0 >= f /\ 2*f >= ar_0 /\ ar_0 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, 0, ar_3, ar_4)) [ ar_1 >= 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_2 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 ] (Comp: ?, Cost: 1) evalrealshellsortbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, f, ar_2)) (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_4 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= ar_3 + 1 ] (Comp: ?, Cost: 1) evalrealshellsortbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= f ] (Comp: ?, Cost: 1) evalrealshellsortbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb3in(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_1)) (Comp: ?, Cost: 1) evalrealshellsortbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb6in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, 0, ar_2, ar_3, ar_4)) [ ar_1 = 0 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ ar_1 >= 1 /\ f >= 0 /\ ar_1 >= 2*f /\ 2*f + 1 >= ar_1 ] (Comp: ?, Cost: 1) evalrealshellsortbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortbb8in(ar_0, f, ar_2, ar_3, ar_4)) [ 0 >= ar_1 + 1 /\ 0 >= f /\ 2*f >= ar_1 /\ ar_1 + 1 >= 2*f ] (Comp: ?, Cost: 1) evalrealshellsortreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalrealshellsortstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Compl Integ Trans Syste 26843