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Derivational Complexity: TRS Innermost pair #487105498
details
property
value
status
complete
benchmark
06.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
Various_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.558 seconds
cpu usage
322.104
user time
318.791
system time
3.31322
max virtual memory
1.9180704E7
max residence set size
5388284.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 164 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), 570 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 422 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), 249 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 46 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 62 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 229 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 93 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 301 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 63 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 179 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 225 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 137 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 73 ms] (56) CpxRNTS (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 159 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 86 ms] (62) CpxRNTS (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) IntTrsBoundProof [UPPER BOUND(ID), 117 ms] (66) CpxRNTS (67) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (68) CpxRNTS (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (70) CpxRNTS (71) IntTrsBoundProof [UPPER BOUND(ID), 126 ms] (72) CpxRNTS (73) IntTrsBoundProof [UPPER BOUND(ID), 62 ms] (74) CpxRNTS (75) FinalProof [FINISHED, 0 ms] (76) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(x, y) -> g1(x, x, y) f(x, y) -> g1(y, x, x) f(x, y) -> g2(x, y, y) f(x, y) -> g2(y, y, x) g1(x, x, y) -> h(x, y)
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