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Derivational Complexity: TRS Innermost pair #487104226
details
property
value
status
complete
benchmark
#3.53b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.027 seconds
cpu usage
1098.76
user time
1085.96
system time
12.7999
max virtual memory
3.7773052E7
max residence set size
1.4925132E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 197 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), 146 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 2 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 152 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 34 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 8 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 32 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 95 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 1 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 352 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 77 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 413 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 241 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 200 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (56) CpxRNTS (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 167 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) IntTrsBoundProof [UPPER BOUND(ID), 147 ms] (66) CpxRNTS (67) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) FinalProof [FINISHED, 0 ms] (70) BOUNDS(1, n^2) (71) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (72) TRS for Loop Detection (73) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (74) BEST (75) proven lower bound (76) LowerBoundPropagationProof [FINISHED, 0 ms] (77) BOUNDS(n^1, INF) (78) TRS for Loop Detection ---------------------------------------- (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: g(x, y) -> x g(x, y) -> y f(0, 1, x) -> f(s(x), x, x)
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