details

property	value
status	complete
benchmark	jones6.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	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.487 seconds
cpu usage	316.388
user time	313.641
system time	2.74706
max virtual memory	1.921532E7
max residence set size	5213552.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 191 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), 13 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), 301 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 89 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 2 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 312 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 370 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 287 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 161 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), 200 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 188 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), 287 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), 48 ms] (76) typed CpxTrs (77) RewriteLemmaProof [LOWER BOUND(ID), 4 ms] (78) 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: f(a, empty) -> g(a, empty) f(a, cons(x, k)) -> f(cons(x, a), k) g(empty, d) -> d 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