details

property	value
status	complete
benchmark	thiemann31.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.541 seconds
cpu usage	1142.43
user time	1130.61
system time	11.8164
max virtual memory	3.7914364E7
max residence set size	1.096194E7

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 1174 ms] (12) BOUNDS(1, n^2) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) mod(x, 0) -> modZeroErro mod(x, s(y)) -> modIter(x, s(y), 0, 0) modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) if(true, x, y, z, u) -> u if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) if2(false, x, y, z, u) -> modIter(x, y, z, u) if2(true, x, y, z, u) -> modIter(x, y, z, 0) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: modIter([], s(y), z, u) modIter(x, s(y), [], u) if(false, x, [], z, u) if(false, x, y, z, []) The defined contexts are: if2([], x1, x2, s(x3), s(x4)) if([], x1, s(x2), x3, x4) [] just represents basic- or constructor-terms in the following defined contexts: if2([], x1, x2, s(x3), s(x4)) if([], x1, s(x2), x3, x4) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) mod(x, 0) -> modZeroErro mod(x, s(y)) -> modIter(x, s(y), 0, 0) modIter(x, s(y), z, u) -> if(le(x, z), x, s(y), z, u) if(true, x, y, z, u) -> u if(false, x, y, z, u) -> if2(le(y, s(u)), x, y, s(z), s(u)) if2(false, x, y, z, u) -> modIter(x, y, z, u) if2(true, x, y, z, u) -> modIter(x, y, z, 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) popout

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actions

all output return to Runtime Complexity: TRS