Runtime Complexity: TRS Innermost pair #487111644

details

property	value
status	complete
benchmark	minsort.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.58 seconds
cpu usage	354.452
user time	348.161
system time	6.29133
max virtual memory	1.9249212E7
max residence set size	8846624.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 157 ms]
(2) CpxRelTRS
(3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CpxWeightedTrs
    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxTypedWeightedTrs
    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
    (8) CpxTypedWeightedCompleteTrs
    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (12) CpxRNTS
    (13) InliningProof [UPPER BOUND(ID), 972 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 3 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 846 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 168 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 273 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 82 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 199 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (36) CpxRNTS
    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 535 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 82 ms]
    (42) CpxRNTS
    (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 249 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 62 ms]
    (48) CpxRNTS
    (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 186 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
    (54) CpxRNTS
    (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (56) CpxRNTS
    (57) IntTrsBoundProof [UPPER BOUND(ID), 407 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 98 ms]
    (60) CpxRNTS
    (61) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (62) CpxRNTS
    (63) IntTrsBoundProof [UPPER BOUND(ID), 116 ms]
    (64) CpxRNTS
    (65) IntTrsBoundProof [UPPER BOUND(ID), 54 ms]
    (66) CpxRNTS
    (67) FinalProof [FINISHED, 0 ms]
    (68) BOUNDS(1, n^2)
(69) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(70) CpxRelTRS
    (71) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) typed CpxTrs
    (73) OrderProof [LOWER BOUND(ID), 0 ms]
    (74) typed CpxTrs
    (75) RewriteLemmaProof [LOWER BOUND(ID), 1958 ms]
    (76) typed CpxTrs
    (77) RewriteLemmaProof [LOWER BOUND(ID), 360 ms]
    (78) BEST
        (79) proven lower bound
            (80) LowerBoundPropagationProof [FINISHED, 0 ms]
            (81) BOUNDS(n^1, INF)
        (82) typed CpxTrs
            (83) RewriteLemmaProof [LOWER BOUND(ID), 406 ms]
            (84) typed CpxTrs
            (85) RewriteLemmaProof [LOWER BOUND(ID), 353 ms]
            (86) typed CpxTrs


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