Derivational Complexity: TRS pair #487103734

details

property	value
status	complete
benchmark	140659.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.825 seconds
cpu usage	853.75
user time	846.447
system time	7.30326
max virtual memory	3.7111316E7
max residence set size	1.5188716E7

stage attributes

key	value
starexec-result	KILLED

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 46 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) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 580 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 825 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 25 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 19 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 477 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 12 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 3285 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1063 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 995 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1049 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2624 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4377 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5767 ms]
        (58) 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(1(0(2(2(2(2(2(0(0(0(x1))))))))))))) -> 0(1(0(0(0(0(1(2(0(0(0(2(0(1(0(2(0(x1)))))))))))))))))
   0(0(0(1(2(0(2(2(2(2(2(1(0(x1))))))))))))) -> 0(0(1(1(1(2(2(0(1(2(1(0(0(0(0(2(0(x1)))))))))))))))))
   0(0(0(1(2(1(2(1(1(1(0(1(2(x1))))))))))))) -> 0(0(1(2(0(0(0(1(0(2(1(0(0(1(1(0(1(x1)))))))))))))))))
   0(0(0(1(2(1(2(2(2(0(1(2(0(x1))))))))))))) -> 0(0(2(0(1(0(0(1(0(1(0(0(2(0(2(2(0(x1)))))))))))))))))
   0(0(0(2(2(2(0(2(1(2(0(2(1(x1))))))))))))) -> 0(2(0(1(2(0(0(0(2(1(2(1(1(0(0(0(1(x1)))))))))))))))))
   0(0(1(1(0(2(0(0(2(2(0(2(1(x1))))))))))))) -> 0(0(1(0(1(2(0(0(0(1(1(0(0(2(1(0(1(x1)))))))))))))))))
   0(0(1(1(0(2(0(1(1(0(0(1(0(x1))))))))))))) -> 0(0(2(0(0(1(0(1(0(0(0(1(0(0(0(1(0(x1)))))))))))))))))
   0(0(1(1(0(2(2(2(1(1(2(1(0(x1))))))))))))) -> 0(0(0(2(2(0(0(0(0(1(2(2(0(1(1(1(0(x1)))))))))))))))))
   0(0(1(1(2(1(1(1(1(0(2(0(2(x1))))))))))))) -> 0(1(0(2(0(2(0(0(0(0(1(0(0(1(0(1(2(x1)))))))))))))))))
   0(0(1(2(1(2(1(1(1(0(1(0(0(x1))))))))))))) -> 0(2(1(0(1(0(0(0(0(1(0(1(1(2(0(0(0(x1)))))))))))))))))
   0(0(2(1(0(0(1(1(2(0(0(1(0(x1))))))))))))) -> 0(0(0(0(0(0(2(0(1(0(1(1(0(0(0(2(0(x1)))))))))))))))))
   0(0(2(1(0(2(0(1(0(2(0(1(0(x1))))))))))))) -> 0(1(1(1(0(0(0(2(2(0(0(0(1(0(1(0(0(x1)))))))))))))))))
   0(0(2(1(1(2(0(2(1(1(0(2(0(x1))))))))))))) -> 0(0(0(0(0(0(0(0(1(1(2(2(2(2(1(1(0(x1)))))))))))))))))
   0(0(2(1(2(1(1(1(1(2(0(0(1(x1))))))))))))) -> 0(0(0(0(0(2(0(2(2(1(0(0(1(0(2(0(1(x1)))))))))))))))))
   0(0(2(1(2(1(2(0(0(0(2(0(1(x1))))))))))))) -> 0(1(1(0(2(0(0(0(0(0(0(2(1(1(1(0(1(x1)))))))))))))))))
   0(1(0(0(2(0(0(1(1(1(2(1(0(x1))))))))))))) -> 0(0(1(0(0(1(0(1(0(2(1(1(0(1(0(0(0(x1)))))))))))))))))
   0(1(0(1(1(1(0(0(2(2(1(2(0(x1))))))))))))) -> 0(0(1(2(0(0(0(2(1(2(0(0(1(2(0(0(0(x1)))))))))))))))))
   0(1(0(1(2(0(0(1(0(1(1(0(1(x1))))))))))))) -> 0(0(0(0(0(0(0(1(2(0(2(1(0(0(0(2(1(x1)))))))))))))))))
   0(1(0(2(1(2(1(2(1(1(1(0(0(x1))))))))))))) -> 0(1(0(0(2(2(0(2(0(1(0(2(0(0(0(0(0(x1)))))))))))))))))
   0(1(1(0(1(0(2(1(1(0(0(0(2(x1))))))))))))) -> 0(0(0(0(0(1(1(1(2(1(1(0(0(0(0(0(0(x1)))))))))))))))))
   0(1(1(0(2(0(2(2(1(1(2(0(0(x1))))))))))))) -> 0(0(2(0(2(2(0(2(0(0(0(2(0(1(0(0(0(x1)))))))))))))))))
   0(1(1(0(2(1(1(1(2(2(0(2(0(x1))))))))))))) -> 0(0(2(1(2(1(0(0(2(0(1(0(2(2(0(0(0(x1)))))))))))))))))
   0(1(1(0(2(1(2(2(1(1(0(2(1(x1))))))))))))) -> 0(0(2(1(0(0(0(1(2(0(0(2(1(2(1(0(1(x1)))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS