details

property	value
status	complete
benchmark	realheapsort_step2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n123.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	30.8046 seconds
cpu usage	36.4839
user time	35.9556
system time	0.528295
max virtual memory	1.8656536E7
max residence set size	233096.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

36.37/30.76 WORST_CASE(Omega(n^1), O(n^2)) 36.37/30.77 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 36.37/30.77 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 36.37/30.77 36.37/30.77 36.37/30.77 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 36.37/30.77 36.37/30.77 (0) CpxIntTrs 36.37/30.77 (1) Koat Proof [FINISHED, 692 ms] 36.37/30.77 (2) BOUNDS(1, n^2) 36.37/30.77 (3) Loat Proof [FINISHED, 2817 ms] 36.37/30.77 (4) BOUNDS(n^1, INF) 36.37/30.77 36.37/30.77 36.37/30.77 ---------------------------------------- 36.37/30.77 36.37/30.77 (0) 36.37/30.77 Obligation: 36.37/30.77 Complexity Int TRS consisting of the following rules: 36.37/30.77 evalrealheapsortstep2start(A, B, C, D) -> Com_1(evalrealheapsortstep2entryin(A, B, C, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2entryin(A, B, C, D) -> Com_1(evalrealheapsortstep2bbin(A, B, C, D)) :|: A >= 3 36.37/30.77 evalrealheapsortstep2entryin(A, B, C, D) -> Com_1(evalrealheapsortstep2returnin(A, B, C, D)) :|: 2 >= A 36.37/30.77 evalrealheapsortstep2bbin(A, B, C, D) -> Com_1(evalrealheapsortstep2bb11in(A, 0, C, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb11in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb1in(A, B, C, D)) :|: A >= 2 + B 36.37/30.77 evalrealheapsortstep2bb11in(A, B, C, D) -> Com_1(evalrealheapsortstep2returnin(A, B, C, D)) :|: B + 1 >= A 36.37/30.77 evalrealheapsortstep2bb1in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, 0, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb9in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb2in(A, B, C, D)) :|: A >= B + 3 + 2 * C 36.37/30.77 evalrealheapsortstep2bb9in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb10in(A, B, C, D)) :|: 2 * C + 2 + B >= A 36.37/30.77 evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb4in(A, B, C, D)) :|: A >= 2 * C + 3 + B && A <= 2 * C + 3 + B 36.37/30.77 evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb3in(A, B, C, D)) :|: A >= B + 4 + 2 * C 36.37/30.77 evalrealheapsortstep2bb2in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb3in(A, B, C, D)) :|: 2 * C + 2 + B >= A 36.37/30.77 evalrealheapsortstep2bb3in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb4in(A, B, C, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb3in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb5in(A, B, C, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb4in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb6in(A, B, C, 2 * C + 1)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb5in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb6in(A, B, C, 2 * C + 2)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb6in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb7in(A, B, C, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb6in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, A, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb7in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb9in(A, B, D, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2bb10in(A, B, C, D) -> Com_1(evalrealheapsortstep2bb11in(A, B + 1, C, D)) :|: TRUE 36.37/30.77 evalrealheapsortstep2returnin(A, B, C, D) -> Com_1(evalrealheapsortstep2stop(A, B, C, D)) :|: TRUE 36.37/30.77 36.37/30.77 The start-symbols are:[evalrealheapsortstep2start_4] 36.37/30.77 36.37/30.77 36.37/30.77 ---------------------------------------- 36.37/30.77 36.37/30.77 (1) Koat Proof (FINISHED) 36.37/30.77 YES(?, 86*ar_0 + 60*ar_0^2 + 34) 36.37/30.77 36.37/30.77 36.37/30.77 36.37/30.77 Initial complexity problem: 36.37/30.77 36.37/30.77 1: T: 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2entryin(ar_0, ar_1, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 3 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2returnin(ar_0, ar_1, ar_2, ar_3)) [ 2 >= ar_0 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb11in(ar_0, 0, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 2 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb11in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 + 1 >= ar_0 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb9in(ar_0, ar_1, 0, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 2*ar_2 + 3 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb9in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb10in(ar_0, ar_1, ar_2, ar_3)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = 2*ar_2 + ar_1 + 3 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 + 2*ar_2 + 4 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3)) [ 2*ar_2 + ar_1 + 2 >= ar_0 ] 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, 2*ar_2 + 1)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, 2*ar_2 + 2)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb7in(ar_0, ar_1, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb9in(ar_0, ar_1, ar_0, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb7in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb9in(ar_0, ar_1, ar_3, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2bb10in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2bb11in(ar_0, ar_1 + 1, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: ?, Cost: 1) evalrealheapsortstep2returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2stop(ar_0, ar_1, ar_2, ar_3)) 36.37/30.77 36.37/30.77 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalrealheapsortstep2start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 36.37/30.77 36.37/30.77 start location: koat_start popout

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

job log

popout

actions

all output return to Complexity_ITS 2019-03-21 04.46