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	n055.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.53263 seconds
cpu usage	12.5532
user time	12.0217
system time	0.531517
max virtual memory	1.8794312E7
max residence set size	222036.0

stage attributes

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

output

12.45/6.49 WORST_CASE(Omega(n^1), O(n^3)) 12.45/6.50 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 12.45/6.50 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.45/6.50 12.45/6.50 12.45/6.50 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^3). 12.45/6.50 12.45/6.50 (0) CpxIntTrs 12.45/6.50 (1) Koat Proof [FINISHED, 809 ms] 12.45/6.50 (2) BOUNDS(1, n^3) 12.45/6.50 (3) Loat Proof [FINISHED, 3144 ms] 12.45/6.50 (4) BOUNDS(n^1, INF) 12.45/6.50 12.45/6.50 12.45/6.50 ---------------------------------------- 12.45/6.50 12.45/6.50 (0) 12.45/6.50 Obligation: 12.45/6.50 Complexity Int TRS consisting of the following rules: 12.45/6.50 evalrealshellsortstart(A, B, C, D, E) -> Com_1(evalrealshellsortentryin(A, B, C, D, E)) :|: TRUE 12.45/6.50 evalrealshellsortentryin(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: A >= 0 && A <= 0 12.45/6.50 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 12.45/6.50 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 12.45/6.50 evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, 0, D, E)) :|: B >= 1 12.45/6.50 evalrealshellsortbb8in(A, B, C, D, E) -> Com_1(evalrealshellsortreturnin(A, B, C, D, E)) :|: 0 >= B 12.45/6.50 evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb1in(A, B, C, D, E)) :|: A >= C + 1 12.45/6.50 evalrealshellsortbb6in(A, B, C, D, E) -> Com_1(evalrealshellsortbb7in(A, B, C, D, E)) :|: C >= A 12.45/6.50 evalrealshellsortbb1in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, F, C)) :|: TRUE 12.45/6.50 evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: B >= E + 1 12.45/6.50 evalrealshellsortbb3in(A, B, C, D, E) -> Com_1(evalrealshellsortbb4in(A, B, C, D, E)) :|: E >= B 12.45/6.50 evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb2in(A, B, C, D, E)) :|: F >= D + 1 12.45/6.50 evalrealshellsortbb4in(A, B, C, D, E) -> Com_1(evalrealshellsortbb5in(A, B, C, D, E)) :|: D >= F 12.45/6.50 evalrealshellsortbb2in(A, B, C, D, E) -> Com_1(evalrealshellsortbb3in(A, B, C, D, E - B)) :|: TRUE 12.45/6.50 evalrealshellsortbb5in(A, B, C, D, E) -> Com_1(evalrealshellsortbb6in(A, B, C + 1, D, E)) :|: TRUE 12.45/6.50 evalrealshellsortbb7in(A, B, C, D, E) -> Com_1(evalrealshellsortbb8in(A, 0, C, D, E)) :|: B >= 0 && B <= 0 12.45/6.50 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 12.45/6.50 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 12.45/6.50 evalrealshellsortreturnin(A, B, C, D, E) -> Com_1(evalrealshellsortstop(A, B, C, D, E)) :|: TRUE 12.45/6.50 12.45/6.50 The start-symbols are:[evalrealshellsortstart_5] 12.45/6.50 12.45/6.50 12.45/6.50 ---------------------------------------- 12.45/6.50 12.45/6.50 (1) Koat Proof (FINISHED) 12.45/6.50 YES(?, 82*ar_0 + 68*ar_0^2 + 18*ar_0^3 + 43) 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 Initial complexity problem: 12.45/6.50 12.45/6.50 1: T: 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 (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)) 12.45/6.50 12.45/6.50 (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 ] 12.45/6.50 12.45/6.50 start location: koat_start 12.45/6.50 12.45/6.50 leaf cost: 0 12.45/6.50 12.45/6.50 12.45/6.50 12.45/6.50 Repeatedly propagating knowledge in problem 1 produces the following problem: popout

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

job log

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actions

all output return to Complexity_ITS 2019-03-21 04.46