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Derivational Complexity: TRS Innermost pair #487105694
details
property
value
status
complete
benchmark
2.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.508 seconds
cpu usage
312.671
user time
309.676
system time
2.99448
max virtual memory
3.8178152E7
max residence set size
5177084.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 171 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [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) InliningProof [UPPER BOUND(ID), 327 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), 215 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 35 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 912 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 280 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 148 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 67 ms] (46) CpxRNTS (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 851 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 371 ms] (52) CpxRNTS (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 338 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 36 ms] (58) CpxRNTS (59) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 189 ms] (62) CpxRNTS (63) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (66) CpxRNTS (67) IntTrsBoundProof [UPPER BOUND(ID), 189 ms] (68) CpxRNTS (69) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (70) CpxRNTS (71) FinalProof [FINISHED, 0 ms] (72) BOUNDS(1, n^2) (73) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CpxRelTRS (75) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (76) typed CpxTrs (77) OrderProof [LOWER BOUND(ID), 0 ms] (78) typed CpxTrs (79) RewriteLemmaProof [LOWER BOUND(ID), 222 ms] (80) proven lower bound (81) LowerBoundPropagationProof [FINISHED, 0 ms] (82) BOUNDS(n^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:
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