details

property	value
status	complete
benchmark	ex1.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	Rank

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.306 seconds
cpu usage	15.3539
user time	14.6942
system time	0.659664
max virtual memory	1.8763428E7
max residence set size	223536.0

stage attributes

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

output

15.24/7.25 WORST_CASE(Omega(n^1), O(n^2)) 15.24/7.26 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 15.24/7.26 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 15.24/7.26 15.24/7.26 15.24/7.26 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 15.24/7.26 15.24/7.26 (0) CpxIntTrs 15.24/7.26 (1) Koat Proof [FINISHED, 3546 ms] 15.24/7.26 (2) BOUNDS(1, n^2) 15.24/7.26 (3) Loat Proof [FINISHED, 2414 ms] 15.24/7.26 (4) BOUNDS(n^1, INF) 15.24/7.26 15.24/7.26 15.24/7.26 ---------------------------------------- 15.24/7.26 15.24/7.26 (0) 15.24/7.26 Obligation: 15.24/7.26 Complexity Int TRS consisting of the following rules: 15.24/7.26 evalfstart(A, B, C, D, E) -> Com_1(evalfentryin(A, B, C, D, E)) :|: TRUE 15.24/7.26 evalfentryin(A, B, C, D, E) -> Com_1(evalfbb7in(B, B, 0, D, E)) :|: TRUE 15.24/7.26 evalfbb7in(A, B, C, D, E) -> Com_1(evalfbbin(A, B, C, D, E)) :|: A >= 0 && C >= 0 15.24/7.26 evalfbb7in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: 0 >= A + 1 15.24/7.26 evalfbb7in(A, B, C, D, E) -> Com_1(evalfreturnin(A, B, C, D, E)) :|: 0 >= C + 1 15.24/7.26 evalfbbin(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, C, E)) :|: 0 >= F + 1 15.24/7.26 evalfbbin(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, C, E)) :|: F >= 1 15.24/7.26 evalfbbin(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, A, C)) :|: TRUE 15.24/7.26 evalfbb3in(A, B, C, D, E) -> Com_1(evalfbb5in(A, B, C, D, E)) :|: D >= B + 1 15.24/7.26 evalfbb3in(A, B, C, D, E) -> Com_1(evalfbb4in(A, B, C, D, E)) :|: B >= D 15.24/7.26 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb2in(A, B, C, D, E)) :|: 0 >= F + 1 15.24/7.26 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb2in(A, B, C, D, E)) :|: F >= 1 15.24/7.26 evalfbb4in(A, B, C, D, E) -> Com_1(evalfbb5in(A, B, C, D, E)) :|: TRUE 15.24/7.26 evalfbb2in(A, B, C, D, E) -> Com_1(evalfbb3in(A, B, C, D + 1, E)) :|: TRUE 15.24/7.26 evalfbb5in(A, B, C, D, E) -> Com_1(evalfbb6in(A, B, C, A - 1, D)) :|: TRUE 15.24/7.26 evalfbb6in(A, B, C, D, E) -> Com_1(evalfbb7in(D, B, E - 1, D, E)) :|: TRUE 15.24/7.26 evalfreturnin(A, B, C, D, E) -> Com_1(evalfstop(A, B, C, D, E)) :|: TRUE 15.24/7.26 15.24/7.26 The start-symbols are:[evalfstart_5] 15.24/7.26 15.24/7.26 15.24/7.26 ---------------------------------------- 15.24/7.26 15.24/7.26 (1) Koat Proof (FINISHED) 15.24/7.26 YES(?, 1650*ar_1 + 432*ar_1^2 + 1246) 15.24/7.26 15.24/7.26 15.24/7.26 15.24/7.26 Initial complexity problem: 15.24/7.26 15.24/7.26 1: T: 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb7in(ar_1, ar_1, 0, ar_3, ar_4)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 0 /\ ar_2 >= 0 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_0 + 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_2, ar_4)) [ 0 >= f + 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_2, ar_4)) [ f >= 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb6in(ar_0, ar_1, ar_2, ar_0, ar_2)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ] 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb5in(ar_0, ar_1, ar_2, ar_3, ar_4)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb6in(ar_0, ar_1, ar_2, ar_0 - 1, ar_3)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb7in(ar_3, ar_1, ar_4 - 1, ar_3, ar_4)) 15.24/7.26 15.24/7.26 (Comp: ?, Cost: 1) evalfreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3, ar_4)) 15.24/7.26 15.24/7.26 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 15.24/7.26 15.24/7.26 start location: koat_start 15.24/7.26 15.24/7.26 leaf cost: 0 15.24/7.26 15.24/7.26 15.24/7.26 15.24/7.26 Repeatedly propagating knowledge in problem 1 produces the following problem: 15.24/7.26 15.24/7.26 2: T: 15.24/7.26 15.24/7.26 (Comp: 1, Cost: 1) evalfstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3, ar_4)) 15.24/7.26 15.24/7.26 (Comp: 1, Cost: 1) evalfentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalfbb7in(ar_1, ar_1, 0, ar_3, ar_4)) 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