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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313700
details
property
value
status
complete
benchmark
thiemann03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
16.4179 seconds
cpu usage
60.7593
user time
57.8077
system time
2.9516
max virtual memory
1.905648E7
max residence set size
4401324.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), O(n^3))
output
60.50/16.34 WORST_CASE(Omega(n^3), O(n^3)) 60.50/16.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 60.50/16.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 60.50/16.37 60.50/16.37 60.50/16.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 60.50/16.37 60.50/16.37 (0) CpxTRS 60.50/16.37 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (2) CpxWeightedTrs 60.50/16.37 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (4) CpxTypedWeightedTrs 60.50/16.37 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (6) CpxTypedWeightedCompleteTrs 60.50/16.37 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (8) CpxTypedWeightedCompleteTrs 60.50/16.37 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (10) CpxRNTS 60.50/16.37 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (12) CpxRNTS 60.50/16.37 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (14) CpxRNTS 60.50/16.37 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (16) CpxRNTS 60.50/16.37 (17) IntTrsBoundProof [UPPER BOUND(ID), 193 ms] 60.50/16.37 (18) CpxRNTS 60.50/16.37 (19) IntTrsBoundProof [UPPER BOUND(ID), 8 ms] 60.50/16.37 (20) CpxRNTS 60.50/16.37 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (22) CpxRNTS 60.50/16.37 (23) IntTrsBoundProof [UPPER BOUND(ID), 442 ms] 60.50/16.37 (24) CpxRNTS 60.50/16.37 (25) IntTrsBoundProof [UPPER BOUND(ID), 96 ms] 60.50/16.37 (26) CpxRNTS 60.50/16.37 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (28) CpxRNTS 60.50/16.37 (29) IntTrsBoundProof [UPPER BOUND(ID), 155 ms] 60.50/16.37 (30) CpxRNTS 60.50/16.37 (31) IntTrsBoundProof [UPPER BOUND(ID), 62 ms] 60.50/16.37 (32) CpxRNTS 60.50/16.37 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (34) CpxRNTS 60.50/16.37 (35) IntTrsBoundProof [UPPER BOUND(ID), 170 ms] 60.50/16.37 (36) CpxRNTS 60.50/16.37 (37) IntTrsBoundProof [UPPER BOUND(ID), 42 ms] 60.50/16.37 (38) CpxRNTS 60.50/16.37 (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (40) CpxRNTS 60.50/16.37 (41) IntTrsBoundProof [UPPER BOUND(ID), 353 ms] 60.50/16.37 (42) CpxRNTS 60.50/16.37 (43) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] 60.50/16.37 (44) CpxRNTS 60.50/16.37 (45) ResultPropagationProof [UPPER BOUND(ID), 1 ms] 60.50/16.37 (46) CpxRNTS 60.50/16.37 (47) IntTrsBoundProof [UPPER BOUND(ID), 1871 ms] 60.50/16.37 (48) CpxRNTS 60.50/16.37 (49) IntTrsBoundProof [UPPER BOUND(ID), 272 ms] 60.50/16.37 (50) CpxRNTS 60.50/16.37 (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (52) CpxRNTS 60.50/16.37 (53) IntTrsBoundProof [UPPER BOUND(ID), 639 ms] 60.50/16.37 (54) CpxRNTS 60.50/16.37 (55) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] 60.50/16.37 (56) CpxRNTS 60.50/16.37 (57) FinalProof [FINISHED, 0 ms] 60.50/16.37 (58) BOUNDS(1, n^3) 60.50/16.37 (59) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (60) CpxTRS 60.50/16.37 (61) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 60.50/16.37 (62) typed CpxTrs 60.50/16.37 (63) OrderProof [LOWER BOUND(ID), 0 ms] 60.50/16.37 (64) typed CpxTrs 60.50/16.37 (65) RewriteLemmaProof [LOWER BOUND(ID), 306 ms] 60.50/16.37 (66) BEST 60.50/16.37 (67) proven lower bound 60.50/16.37 (68) LowerBoundPropagationProof [FINISHED, 0 ms] 60.50/16.37 (69) BOUNDS(n^1, INF) 60.50/16.37 (70) typed CpxTrs 60.50/16.37 (71) RewriteLemmaProof [LOWER BOUND(ID), 14 ms] 60.50/16.37 (72) BEST 60.50/16.37 (73) proven lower bound 60.50/16.37 (74) LowerBoundPropagationProof [FINISHED, 0 ms] 60.50/16.37 (75) BOUNDS(n^2, INF) 60.50/16.37 (76) typed CpxTrs 60.50/16.37 (77) RewriteLemmaProof [LOWER BOUND(ID), 797 ms] 60.50/16.37 (78) proven lower bound 60.50/16.37 (79) LowerBoundPropagationProof [FINISHED, 0 ms] 60.50/16.37 (80) BOUNDS(n^3, INF) 60.50/16.37 60.50/16.37 60.50/16.37 ---------------------------------------- 60.50/16.37 60.50/16.37 (0) 60.50/16.37 Obligation: 60.50/16.37 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^3, n^3). 60.50/16.37 60.50/16.37 60.50/16.37 The TRS R consists of the following rules: 60.50/16.37 60.50/16.37 null(nil) -> true
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