details

property	value
status	complete
benchmark	02.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	Der95

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	15.8281 seconds
cpu usage	40.7055
user time	38.4933
system time	2.21225
max virtual memory	1.8979408E7
max residence set size	4333856.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 137 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToWeightedTrsProof [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) InliningProof [UPPER BOUND(ID), 1227 ms] (20) CpxRNTS (21) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxRNTS (23) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 487 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 98 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 160 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 47 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 2584 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 930 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 275 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 75 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 1599 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 650 ms] (60) CpxRNTS (61) FinalProof [FINISHED, 0 ms] (62) BOUNDS(1, n^1) (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), 229 ms] (70) proven lower bound (71) LowerBoundPropagationProof [FINISHED, 0 ms] (72) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: .(1, x) -> x .(x, 1) -> x .(i(x), x) -> 1 .(x, i(x)) -> 1 i(1) -> 1 i(i(x)) -> x .(i(y), .(y, z)) -> z .(y, .(i(y), z)) -> z popout

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

job log

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actions

all output return to Derivational Complexity: TRS