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Derivational Complexity: TRS Innermost pair #487105732
details
property
value
status
complete
benchmark
2.11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.56 seconds
cpu usage
314.707
user time
311.868
system time
2.83927
max virtual memory
1.9081696E7
max residence set size
5361196.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 198 ms] (4) CpxRelTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) CpxWeightedTrsRenamingProof [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), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 322 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 128 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 1 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 279 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 115 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 423 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 157 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 137 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 2 ms] (62) CpxRNTS (63) FinalProof [FINISHED, 0 ms] (64) BOUNDS(1, n^2) (65) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CpxRelTRS (67) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (68) typed CpxTrs (69) OrderProof [LOWER BOUND(ID), 0 ms] (70) typed CpxTrs (71) RewriteLemmaProof [LOWER BOUND(ID), 306 ms] (72) BEST (73) proven lower bound (74) LowerBoundPropagationProof [FINISHED, 0 ms] (75) BOUNDS(n^1, INF) (76) typed CpxTrs (77) RewriteLemmaProof [LOWER BOUND(ID), 20 ms] (78) typed CpxTrs (79) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (80) 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: +(0, y) -> y
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