Runtime Complexity: TRS pair #487111290

details

property	value
status	complete
benchmark	IJCAR_26a.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.941 seconds
cpu usage	1111.22
user time	1097.89
system time	13.3311
max virtual memory	5.6602984E7
max residence set size	1.50769E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^3), O(n^4))

output

WORST_CASE(Omega(n^3), O(n^4))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, n^4).

(0) CpxTRS
(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
(2) CpxTRS
    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CpxTRS
    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
    (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
    (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (14) CpxRNTS
    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (16) CpxRNTS
    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxRNTS
    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) IntTrsBoundProof [UPPER BOUND(ID), 309 ms]
    (22) CpxRNTS
    (23) IntTrsBoundProof [UPPER BOUND(ID), 119 ms]
    (24) CpxRNTS
    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (26) CpxRNTS
    (27) IntTrsBoundProof [UPPER BOUND(ID), 1027 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 394 ms]
    (30) CpxRNTS
    (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (32) CpxRNTS
    (33) IntTrsBoundProof [UPPER BOUND(ID), 412 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 236 ms]
    (36) CpxRNTS
    (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (38) CpxRNTS
    (39) IntTrsBoundProof [UPPER BOUND(ID), 177 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
    (42) CpxRNTS
    (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (44) CpxRNTS
    (45) IntTrsBoundProof [UPPER BOUND(ID), 602 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 5 ms]
    (48) CpxRNTS
    (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (50) CpxRNTS
    (51) IntTrsBoundProof [UPPER BOUND(ID), 231 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 29 ms]
    (54) CpxRNTS
    (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (56) CpxRNTS
    (57) IntTrsBoundProof [UPPER BOUND(ID), 189 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 0 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), 0 ms]
    (66) CpxRNTS
    (67) FinalProof [FINISHED, 0 ms]
    (68) BOUNDS(1, n^4)
(69) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(70) CpxTRS
    (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), 251 ms]
    (76) BEST
        (77) proven lower bound
            (78) LowerBoundPropagationProof [FINISHED, 0 ms]
            (79) BOUNDS(n^1, INF)
        (80) typed CpxTrs
            (81) RewriteLemmaProof [LOWER BOUND(ID), 59 ms]
            (82) BEST
                (83) proven lower bound
                    (84) LowerBoundPropagationProof [FINISHED, 0 ms]
                    (85) BOUNDS(n^3, INF)
                (86) typed CpxTrs
                    (87) RewriteLemmaProof [LOWER BOUND(ID), 55 ms]
                    (88) typed CpxTrs
                    (89) RewriteLemmaProof [LOWER BOUND(ID), 43 ms]
                    (90) typed CpxTrs

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