Runtime Complexity: TRS Innermost pair #487112100

details

property	value
status	complete
benchmark	6.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.506 seconds
cpu usage	359.885
user time	357.119
system time	2.76584
max virtual memory	3.8300764E7
max residence set size	5185272.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CdtProblem
    (11) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CdtProblem
    (13) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CdtProblem
    (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CdtProblem
    (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 20 ms]
    (18) CdtProblem
    (19) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CdtProblem
    (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CdtProblem
    (23) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CdtProblem
    (25) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CdtProblem
    (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 12 ms]
    (28) CdtProblem
    (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 15 ms]
    (30) CdtProblem
    (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CdtProblem
    (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 8 ms]
    (36) CdtProblem
    (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 7 ms]
    (56) CdtProblem
    (57) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 9 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 10 ms]
    (64) CdtProblem
    (65) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 0 ms]
    (66) CdtProblem
    (67) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 9 ms]
    (70) CdtProblem
    (71) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 9 ms]
    (76) CdtProblem
    (77) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 30 ms]
    (78) CdtProblem
    (79) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) BOUNDS(1, 1)
(81) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(82) CpxTRS
    (83) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) typed CpxTrs
    (85) OrderProof [LOWER BOUND(ID), 0 ms]
    (86) typed CpxTrs
    (87) RewriteLemmaProof [LOWER BOUND(ID), 248 ms]
    (88) BEST
        (89) proven lower bound
            (90) LowerBoundPropagationProof [FINISHED, 0 ms]
            (91) BOUNDS(n^1, INF)
        (92) typed CpxTrs

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