details

property	value
status	complete
benchmark	4.11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.555 seconds
cpu usage	317.715
user time	314.834
system time	2.88127
max virtual memory	3.7708676E7
max residence set size	5223248.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^3))

output

WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 155 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxWeightedTrs (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedTrs (13) CompletionProof [UPPER BOUND(ID), 0 ms] (14) CpxTypedWeightedCompleteTrs (15) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxTypedWeightedCompleteTrs (17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 43 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 14 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 193 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 13 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 761 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 313 ms] (40) CpxRNTS (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 2039 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 915 ms] (46) CpxRNTS (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 283 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (52) CpxRNTS (53) ResultPropagationProof [UPPER BOUND(ID), 2 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 1315 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 712 ms] (58) CpxRNTS (59) FinalProof [FINISHED, 0 ms] (60) BOUNDS(1, n^3) (61) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CpxRelTRS (63) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (64) typed CpxTrs (65) OrderProof [LOWER BOUND(ID), 0 ms] (66) typed CpxTrs (67) RewriteLemmaProof [LOWER BOUND(ID), 226 ms] (68) proven lower bound (69) LowerBoundPropagationProof [FINISHED, 0 ms] (70) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) +(0, s(y)) -> s(y) s(+(0, y)) -> s(y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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

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actions

all output return to Derivational Complexity: TRS Innermost