Derivational Complexity: TRS Innermost pair #487106600

details

property	value
status	complete
benchmark	167452.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)	297.007 seconds
cpu usage	1160.14
user time	1153.48
system time	6.66
max virtual memory	1.9050428E7
max residence set size	1.3784884E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 70 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 18 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 32 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 5329 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 19 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 23 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 13.1 s]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 691 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 20 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 29.7 s]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6512 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6451 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6462 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13.8 s]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 403 ms]
    (56) CdtProblem


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

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


The TRS R consists of the following rules:

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

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