details

property	value
status	complete
benchmark	2.53.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.577 seconds
cpu usage	324.148
user time	321.521
system time	2.62709
max virtual memory	1.8956068E7
max residence set size	5131208.0

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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 158 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), 1 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), 507 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 276 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 2844 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 5070 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 1097 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 809 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 1242 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 847 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), 428 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), 135 ms] (66) typed CpxTrs (67) RewriteLemmaProof [LOWER BOUND(ID), 77 ms] (68) typed CpxTrs (69) RewriteLemmaProof [LOWER BOUND(ID), 88 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: f(x, y) -> g(x, y) g(h(x), y) -> h(f(x, y)) g(h(x), y) -> h(g(x, 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: popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS