Derivational Complexity: TRS pair #487104008

details

property	value
status	complete
benchmark	PEANO_nosorts-noand_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.541 seconds
cpu usage	337.558
user time	334.232
system time	3.32597
max virtual memory	1.9284972E7
max residence set size	5302512.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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^2).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 195 ms]
(4) CpxRelTRS
(5) RcToIrcProof [BOTH BOUNDS(ID, 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), 2896 ms]
    (14) CpxTypedWeightedCompleteTrs
    (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
    (16) CpxRNTS
    (17) InliningProof [UPPER BOUND(ID), 106 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), 23 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 23 ms]
    (28) CpxRNTS
    (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 127 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 42 ms]
    (34) CpxRNTS
    (35) ResultPropagationProof [UPPER BOUND(ID), 1 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 96 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 21 ms]
    (40) CpxRNTS
    (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 752 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 316 ms]
    (46) CpxRNTS
    (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 1270 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 913 ms]
    (52) CpxRNTS
    (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 560 ms]
    (56) CpxRNTS
    (57) IntTrsBoundProof [UPPER BOUND(ID), 9 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), 208 ms]
    (68) CpxRNTS
    (69) IntTrsBoundProof [UPPER BOUND(ID), 2 ms]
    (70) CpxRNTS
    (71) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 238 ms]
    (74) CpxRNTS
    (75) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (76) CpxRNTS
    (77) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 137 ms]
    (80) CpxRNTS
    (81) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (82) CpxRNTS
    (83) FinalProof [FINISHED, 0 ms]
    (84) BOUNDS(1, n^2)
(85) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(86) CpxRelTRS
    (87) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) typed CpxTrs
    (89) OrderProof [LOWER BOUND(ID), 6 ms]
    (90) typed CpxTrs
    (91) RewriteLemmaProof [LOWER BOUND(ID), 263 ms]
    (92) BEST

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