details

property	value
status	complete
benchmark	t011.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.53 seconds
cpu usage	324.916
user time	322.395
system time	2.52088
max virtual memory	1.888848E7
max residence set size	5178272.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 182 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTypedWeightedCompleteTrs (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 282 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 72 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 2812 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 5116 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 1197 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 838 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 127 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 1249 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 815 ms] (50) CpxRNTS (51) FinalProof [FINISHED, 0 ms] (52) BOUNDS(1, n^2) (53) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CpxRelTRS (55) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (56) typed CpxTrs (57) OrderProof [LOWER BOUND(ID), 0 ms] (58) typed CpxTrs (59) RewriteLemmaProof [LOWER BOUND(ID), 395 ms] (60) BEST (61) proven lower bound (62) LowerBoundPropagationProof [FINISHED, 0 ms] (63) BOUNDS(n^1, INF) (64) typed CpxTrs (65) RewriteLemmaProof [LOWER BOUND(ID), 141 ms] (66) typed CpxTrs (67) RewriteLemmaProof [LOWER BOUND(ID), 158 ms] (68) typed CpxTrs (69) RewriteLemmaProof [LOWER BOUND(ID), 71 ms] (70) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: g(f(x), y) -> f(h(x, y)) h(x, y) -> g(x, f(y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(f(x_1)) -> f(encArg(x_1)) popout

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job log

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actions

all output return to Derivational Complexity: TRS