details

property	value
status	complete
benchmark	perfect.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n017.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.86258 seconds
cpu usage	9.17848
user time	8.73956
system time	0.438916
max virtual memory	1.8733852E7
max residence set size	226356.0

stage attributes

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

output

9.08/4.82 WORST_CASE(Omega(n^1), O(n^2)) 9.08/4.83 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 9.08/4.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.08/4.83 9.08/4.83 9.08/4.83 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(4, -2 + 3 * Arg_0) * nat(Arg_0) + max(4, -2 + 3 * Arg_0) * nat(Arg_0)^2 + max(2, -2 + 2 * Arg_0) + nat(-1 + Arg_0) + max(-6 + 6 * Arg_0, 6) + max(7 + 3 * Arg_0, 13)). 9.08/4.83 9.08/4.83 (0) CpxIntTrs 9.08/4.83 (1) Loat Proof [FINISHED, 1617 ms] 9.08/4.83 (2) BOUNDS(n^1, INF) 9.08/4.83 9.08/4.83 9.08/4.83 ---------------------------------------- 9.08/4.83 9.08/4.83 (0) 9.08/4.83 Obligation: 9.08/4.83 Complexity Int TRS consisting of the following rules: 9.08/4.83 evalperfectstart(A, B, C, D) -> Com_1(evalperfectentryin(A, B, C, D)) :|: TRUE 9.08/4.83 evalperfectentryin(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: 1 >= A 9.08/4.83 evalperfectentryin(A, B, C, D) -> Com_1(evalperfectbb1in(A, B, C, D)) :|: A >= 2 9.08/4.83 evalperfectbb1in(A, B, C, D) -> Com_1(evalperfectbb8in(A, A, A - 1, D)) :|: TRUE 9.08/4.83 evalperfectbb8in(A, B, C, D) -> Com_1(evalperfectbb4in(A, B, C, A)) :|: C >= 1 9.08/4.83 evalperfectbb8in(A, B, C, D) -> Com_1(evalperfectbb9in(B, B, C, D)) :|: 0 >= C 9.08/4.83 evalperfectbb4in(A, B, C, D) -> Com_1(evalperfectbb3in(A, B, C, D)) :|: D >= C 9.08/4.83 evalperfectbb4in(A, B, C, D) -> Com_1(evalperfectbb5in(A, B, C, D)) :|: C >= D + 1 9.08/4.83 evalperfectbb3in(A, B, C, D) -> Com_1(evalperfectbb4in(A, B, C, D - C)) :|: TRUE 9.08/4.83 evalperfectbb5in(A, B, C, D) -> Com_1(evalperfectbb8in(A, B - C, C - 1, D)) :|: D >= 0 && D <= 0 9.08/4.83 evalperfectbb5in(A, B, C, D) -> Com_1(evalperfectbb8in(A, B, C - 1, D)) :|: 0 >= D + 1 9.08/4.83 evalperfectbb5in(A, B, C, D) -> Com_1(evalperfectbb8in(A, B, C - 1, D)) :|: D >= 1 9.08/4.83 evalperfectbb9in(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: 0 >= A + 1 9.08/4.83 evalperfectbb9in(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: A >= 1 9.08/4.83 evalperfectbb9in(A, B, C, D) -> Com_1(evalperfectreturnin(A, B, C, D)) :|: A >= 0 && A <= 0 9.08/4.83 evalperfectreturnin(A, B, C, D) -> Com_1(evalperfectstop(A, B, C, D)) :|: TRUE 9.08/4.83 9.08/4.83 The start-symbols are:[evalperfectstart_4] 9.08/4.83 9.08/4.83 9.08/4.83 ---------------------------------------- 9.08/4.83 9.08/4.83 (1) Loat Proof (FINISHED) 9.08/4.83 9.08/4.83 9.08/4.83 ### Pre-processing the ITS problem ### 9.08/4.83 9.08/4.83 9.08/4.83 9.08/4.83 Initial linear ITS problem 9.08/4.83 9.08/4.83 Start location: evalperfectstart 9.08/4.83 9.08/4.83 0: evalperfectstart -> evalperfectentryin : [], cost: 1 9.08/4.83 9.08/4.83 1: evalperfectentryin -> evalperfectreturnin : [ 1>=A ], cost: 1 9.08/4.83 9.08/4.83 2: evalperfectentryin -> evalperfectbb1in : [ A>=2 ], cost: 1 9.08/4.83 9.08/4.83 3: evalperfectbb1in -> evalperfectbb8in : B'=A, C'=-1+A, [], cost: 1 9.08/4.83 9.08/4.83 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 9.08/4.83 9.08/4.83 5: evalperfectbb8in -> evalperfectbb9in : A'=B, [ 0>=C ], cost: 1 9.08/4.83 9.08/4.83 6: evalperfectbb4in -> evalperfectbb3in : [ D>=C ], cost: 1 9.08/4.83 9.08/4.83 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 9.08/4.83 9.08/4.83 8: evalperfectbb3in -> evalperfectbb4in : D'=-C+D, [], cost: 1 9.08/4.83 9.08/4.83 9: evalperfectbb5in -> evalperfectbb8in : B'=-C+B, C'=-1+C, [ D==0 ], cost: 1 9.08/4.83 9.08/4.83 10: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ 0>=1+D ], cost: 1 9.08/4.83 9.08/4.83 11: evalperfectbb5in -> evalperfectbb8in : C'=-1+C, [ D>=1 ], cost: 1 9.08/4.83 9.08/4.83 12: evalperfectbb9in -> evalperfectreturnin : [ 0>=1+A ], cost: 1 9.08/4.83 9.08/4.83 13: evalperfectbb9in -> evalperfectreturnin : [ A>=1 ], cost: 1 9.08/4.83 9.08/4.83 14: evalperfectbb9in -> evalperfectreturnin : [ A==0 ], cost: 1 9.08/4.83 9.08/4.83 15: evalperfectreturnin -> evalperfectstop : [], cost: 1 9.08/4.83 9.08/4.83 9.08/4.83 9.08/4.83 Removed unreachable and leaf rules: 9.08/4.83 9.08/4.83 Start location: evalperfectstart 9.08/4.83 9.08/4.83 0: evalperfectstart -> evalperfectentryin : [], cost: 1 9.08/4.83 9.08/4.83 2: evalperfectentryin -> evalperfectbb1in : [ A>=2 ], cost: 1 9.08/4.83 9.08/4.83 3: evalperfectbb1in -> evalperfectbb8in : B'=A, C'=-1+A, [], cost: 1 9.08/4.83 9.08/4.83 4: evalperfectbb8in -> evalperfectbb4in : D'=A, [ C>=1 ], cost: 1 9.08/4.83 9.08/4.83 6: evalperfectbb4in -> evalperfectbb3in : [ D>=C ], cost: 1 9.08/4.83 9.08/4.83 7: evalperfectbb4in -> evalperfectbb5in : [ C>=1+D ], cost: 1 9.08/4.83 popout

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all output return to Complexity_ITS 2019-03-21 04.46