Derivational Complexity: TRS pair #487100874

details

property	value
status	complete
benchmark	01.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	Der95

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	14.4269 seconds
cpu usage	32.0277
user time	30.0244
system time	2.00331
max virtual memory	1.9215652E7
max residence set size	3999224.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 205 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
    (7) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxWeightedTrs
    (11) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxWeightedTrs
    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxTypedWeightedTrs
    (15) CompletionProof [UPPER BOUND(ID), 0 ms]
    (16) CpxTypedWeightedCompleteTrs
    (17) NarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
    (18) CpxTypedWeightedCompleteTrs
    (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) InliningProof [UPPER BOUND(ID), 0 ms]
    (22) CpxRNTS
    (23) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CpxRNTS
    (25) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 38 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 4 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 405 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 5 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 334 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 434 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
    (50) CpxRNTS
    (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 211 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), 63 ms]
    (62) CpxRNTS
    (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (64) CpxRNTS
    (65) IntTrsBoundProof [UPPER BOUND(ID), 188 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
    (68) CpxRNTS
    (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (70) CpxRNTS
    (71) IntTrsBoundProof [UPPER BOUND(ID), 158 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 63 ms]
    (74) CpxRNTS
    (75) FinalProof [FINISHED, 0 ms]
    (76) BOUNDS(1, n^1)
(77) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(78) CpxRelTRS
    (79) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) typed CpxTrs
    (81) OrderProof [LOWER BOUND(ID), 0 ms]
    (82) typed CpxTrs
    (83) RewriteLemmaProof [LOWER BOUND(ID), 206 ms]
    (84) proven lower bound
    (85) LowerBoundPropagationProof [FINISHED, 0 ms]
    (86) BOUNDS(n^1, INF)


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(0)
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