Derivational Complexity: TRS pair #487102814

details

property	value
status	complete
benchmark	91218.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.209 seconds
cpu usage	1165.75
user time	1158.61
system time	7.13651
max virtual memory	1.901506E7
max residence set size	1.3208988E7

stage attributes

key	value
starexec-result	KILLED

output

KILLED
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 35 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 10.6 s]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 674 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms]
    (22) CpxWeightedTrs
        (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxWeightedTrs
        (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedTrs
        (27) CompletionProof [UPPER BOUND(ID), 0 ms]
        (28) CpxTypedWeightedCompleteTrs
            (29) NarrowingProof [BOTH BOUNDS(ID, ID), 333 ms]
            (30) CpxTypedWeightedCompleteTrs
            (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 196 ms]
            (32) CpxRNTS
            (33) SimplificationProof [BOTH BOUNDS(ID, ID), 74 ms]
            (34) CpxRNTS
        (35) CompletionProof [UPPER BOUND(ID), 0 ms]
        (36) CpxTypedWeightedCompleteTrs
            (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (38) CpxRNTS
    (39) CpxTrsToCdtProof [UPPER BOUND(ID), 724 ms]
    (40) CdtProblem
        (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 6 ms]
        (44) CdtProblem
        (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 4039 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1214 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1159 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1190 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4160 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5148 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6305 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7162 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7772 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9209 ms]
        (66) CdtProblem


----------------------------------------

(0)
Obligation:
The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(0(0(0(0(1(1(1(1(2(2(1(2(1(2(2(1(2(2(1(2(1(x1))))))))))))))))))))))) -> 1(0(0(2(1(2(1(1(1(0(0(1(1(2(1(0(1(1(0(1(2(1(1(0(0(2(1(x1)))))))))))))))))))))))))))
   0(0(0(1(2(2(0(0(0(1(2(1(0(1(1(0(2(0(1(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(0(1(1(1(2(1(1(0(2(0(2(1(2(0(1(0(2(2(0(1(1(0(1(0(2(x1)))))))))))))))))))))))))))
   0(0(0(2(1(1(2(0(2(0(1(1(1(0(0(1(1(2(2(0(2(1(1(x1))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(0(1(1(1(1(0(1(1(0(1(1(0(2(1(0(0(2(1(1(x1)))))))))))))))))))))))))))
   0(0(1(0(0(1(0(1(0(2(0(1(1(0(0(2(2(1(0(0(1(2(2(x1))))))))))))))))))))))) -> 2(0(1(1(2(2(1(1(0(1(0(2(1(1(2(1(1(2(2(1(0(1(1(1(0(0(1(x1)))))))))))))))))))))))))))
   0(0(2(1(0(0(1(2(1(0(0(0(1(1(1(0(0(2(2(0(0(0(0(x1))))))))))))))))))))))) -> 0(2(1(0(1(1(1(2(0(2(2(0(0(1(1(2(1(1(0(0(1(1(1(2(1(2(1(x1)))))))))))))))))))))))))))
   0(0(2(1(0(1(0(0(1(2(1(2(1(1(2(0(1(2(2(0(1(0(1(x1))))))))))))))))))))))) -> 0(0(2(1(1(2(0(0(0(1(2(2(0(1(2(0(2(1(0(1(1(1(1(2(1(1(1(x1)))))))))))))))))))))))))))
   0(0(2(1(1(2(0(1(2(2(0(1(0(2(2(1(2(0(1(1(0(1(1(x1))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(1(1(1(2(2(1(0(2(0(1(0(0(1(0(2(1(0(1(1(x1)))))))))))))))))))))))))))
   0(1(2(0(1(0(2(0(1(1(0(2(1(1(0(2(0(0(1(1(2(2(1(x1))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(1(0(0(2(2(1(1(0(0(1(0(0(1(1(0(1(2(1(1(x1)))))))))))))))))))))))))))
   0(2(0(1(0(0(1(2(0(1(2(1(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))) -> 0(2(2(1(1(0(0(1(1(1(1(2(1(0(0(1(1(1(2(0(0(1(0(1(1(0(1(x1)))))))))))))))))))))))))))
   0(2(0(1(2(2(0(0(0(2(0(0(0(0(1(1(0(0(2(1(2(1(1(x1))))))))))))))))))))))) -> 2(0(0(2(2(2(2(1(1(2(1(1(2(0(0(0(0(1(1(0(0(0(1(1(0(1(1(x1)))))))))))))))))))))))))))
   0(2(1(1(2(2(1(2(1(2(0(0(0(1(2(1(0(1(2(1(1(1(0(x1))))))))))))))))))))))) -> 0(0(1(0(1(0(2(1(1(1(0(1(0(2(1(1(2(2(1(2(1(1(1(1(1(1(0(x1)))))))))))))))))))))))))))
   0(2(2(0(1(0(1(0(0(0(1(1(1(0(0(2(2(1(2(1(0(1(0(x1))))))))))))))))))))))) -> 0(2(0(1(1(1(1(1(1(1(2(2(1(1(1(2(2(1(1(1(0(2(1(0(2(1(1(x1)))))))))))))))))))))))))))
   0(2(2(0(1(1(0(1(0(1(1(0(0(2(2(2(1(0(1(2(1(2(1(x1))))))))))))))))))))))) -> 0(2(1(2(1(1(1(1(0(0(2(1(1(2(1(0(1(1(2(1(1(2(2(1(2(1(1(x1)))))))))))))))))))))))))))
   0(2(2(0(2(0(2(1(1(2(1(0(1(0(1(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(2(2(2(1(1(2(1(0(1(1(1(0(1(1(0(1(2(1(0(1(1(1(0(2(1(x1)))))))))))))))))))))))))))
   0(2(2(1(1(0(2(0(0(0(2(1(1(1(2(0(0(2(2(2(1(1(1(x1))))))))))))))))))))))) -> 1(1(0(1(0(2(2(0(2(1(2(1(0(1(2(1(1(0(1(0(1(1(0(2(0(1(1(x1)))))))))))))))))))))))))))

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actions all output return to Derivational Complexity: TRS