Derivational Complexity: TRS pair #487100816

details

property	value
status	complete
benchmark	2.41.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.571 seconds
cpu usage	609.043
user time	605.956
system time	3.0875
max virtual memory	1.9261984E7
max residence set size	5195664.0

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/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 193 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), 40 ms]
    (14) CpxTypedWeightedCompleteTrs
    (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 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), 53 ms]
    (24) CpxRNTS
    (25) IntTrsBoundProof [UPPER BOUND(ID), 14 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 324 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 85 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 322 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 145 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 139 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 15 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 3 ms]
    (50) CpxRNTS
    (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 1069 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 720 ms]
    (56) CpxRNTS
    (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 169 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), 189 ms]
    (66) CpxRNTS
    (67) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (68) CpxRNTS
    (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (70) CpxRNTS
    (71) IntTrsBoundProof [UPPER BOUND(ID), 697 ms]
    (72) CpxRNTS
    (73) IntTrsBoundProof [UPPER BOUND(ID), 248 ms]
    (74) CpxRNTS
    (75) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (76) CpxRNTS
    (77) IntTrsBoundProof [UPPER BOUND(ID), 198 ms]
    (78) CpxRNTS
    (79) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (80) CpxRNTS
    (81) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (82) CpxRNTS
    (83) IntTrsBoundProof [UPPER BOUND(ID), 68 ms]
    (84) CpxRNTS
    (85) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (86) CpxRNTS
    (87) FinalProof [FINISHED, 0 ms]
    (88) BOUNDS(1, n^2)
(89) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(90) CpxRelTRS
    (91) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) typed CpxTrs

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