details

property	value
status	complete
benchmark	jones1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.633 seconds
cpu usage	311.689
user time	309.215
system time	2.47405
max virtual memory	3.7913172E7
max residence set size	5165300.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 166 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 309 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 96 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 56 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 140 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 838 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 460 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 185 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 236 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 117 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 171 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) FinalProof [FINISHED, 0 ms] (62) BOUNDS(1, n^2) (63) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CpxRelTRS (65) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (66) typed CpxTrs (67) OrderProof [LOWER BOUND(ID), 0 ms] (68) typed CpxTrs (69) RewriteLemmaProof [LOWER BOUND(ID), 273 ms] (70) BEST (71) proven lower bound (72) LowerBoundPropagationProof [FINISHED, 0 ms] (73) BOUNDS(n^1, INF) (74) typed CpxTrs (75) RewriteLemmaProof [LOWER BOUND(ID), 29 ms] (76) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: rev(ls) -> r1(ls, empty) r1(empty, a) -> a r1(cons(x, k), a) -> r1(k, cons(x, a)) S is empty. 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