Derivational Complexity: TRS Innermost pair #487106874

details

property	value
status	complete
benchmark	166001.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)	296.904 seconds
cpu usage	1117.89
user time	1114.25
system time	3.63448
max virtual memory	3.7111316E7
max residence set size	6278028.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 51 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 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), 1 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 37 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 31 ms]
        (26) CpxRNTS
    (27) CompletionProof [UPPER BOUND(ID), 0 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) NarrowingProof [BOTH BOUNDS(ID, ID), 5433 ms]
        (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (32) CpxRNTS
        (33) SimplificationProof [BOTH BOUNDS(ID, ID), 21 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 16.0 s]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 4 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 555 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 5 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 79.8 s]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21.7 s]
    (48) 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(1(0(1(0(x1)))))) -> 1(1(2(2(0(0(0(x1)))))))
   0(0(2(1(1(1(x1)))))) -> 2(2(1(1(2(2(2(2(x1))))))))
   0(2(0(0(2(0(x1)))))) -> 1(0(1(1(2(2(1(x1)))))))
   1(1(0(0(2(2(2(1(x1)))))))) -> 1(1(2(2(0(2(0(2(1(1(x1))))))))))
   0(2(0(2(0(2(2(2(0(x1))))))))) -> 0(1(1(1(2(2(1(2(0(0(x1))))))))))
   0(2(0(1(0(2(0(2(1(0(x1)))))))))) -> 0(0(2(2(0(1(1(2(0(0(x1))))))))))
   1(0(2(1(2(2(0(2(1(0(x1)))))))))) -> 0(1(0(1(1(1(2(2(1(1(2(x1)))))))))))
   0(1(2(1(1(1(1(0(1(2(2(x1))))))))))) -> 0(1(2(1(2(1(1(1(1(0(2(x1)))))))))))
   2(0(2(1(2(0(1(1(0(0(0(x1))))))))))) -> 1(2(1(1(2(2(2(0(0(1(0(2(2(x1)))))))))))))
   2(2(0(2(0(2(2(0(0(2(0(x1))))))))))) -> 1(2(2(2(2(2(2(1(1(2(2(0(2(x1)))))))))))))
   2(2(1(1(1(1(1(1(0(1(0(x1))))))))))) -> 0(2(0(1(1(1(1(1(2(1(2(0(x1))))))))))))
   0(0(0(0(0(2(0(2(2(0(1(0(x1)))))))))))) -> 1(0(0(2(1(0(1(1(1(2(2(2(2(1(x1))))))))))))))
   0(0(0(0(0(2(1(2(1(0(1(2(x1)))))))))))) -> 1(1(2(2(0(0(1(2(2(2(2(2(1(x1)))))))))))))
   0(0(2(0(2(0(0(2(0(1(0(2(x1)))))))))))) -> 1(1(2(1(2(2(0(2(0(2(2(2(1(x1)))))))))))))
   0(2(2(2(0(2(1(2(0(1(0(2(x1)))))))))))) -> 2(0(0(0(2(1(0(2(1(1(2(2(1(x1)))))))))))))
   2(0(1(2(0(2(2(2(0(2(0(2(x1)))))))))))) -> 2(2(1(1(1(1(1(2(1(1(2(2(0(x1)))))))))))))
   2(2(0(2(0(2(1(2(0(2(2(2(x1)))))))))))) -> 2(0(2(1(1(1(2(1(1(2(2(1(0(2(1(1(2(2(x1))))))))))))))))))
   0(0(0(2(2(0(0(2(1(2(2(0(1(x1))))))))))))) -> 1(2(0(2(1(1(2(2(2(0(1(1(2(1(2(2(1(x1)))))))))))))))))
   0(0(2(0(0(0(0(1(0(0(0(1(0(x1))))))))))))) -> 1(0(1(1(2(2(2(2(1(2(1(0(0(1(2(0(x1))))))))))))))))
   0(1(2(0(1(2(0(1(1(0(1(1(1(x1))))))))))))) -> 0(0(1(2(0(0(0(1(1(1(2(2(2(1(1(2(2(x1)))))))))))))))))
   0(1(2(2(1(2(2(1(0(2(1(2(0(x1))))))))))))) -> 1(1(1(2(1(0(0(2(1(1(2(1(1(0(0(x1)))))))))))))))
   0(2(0(0(0(1(0(1(0(0(1(1(0(x1))))))))))))) -> 0(2(1(0(2(0(1(1(1(2(2(2(1(2(2(2(0(x1)))))))))))))))))
   0(0(0(0(2(1(1(0(2(2(1(0(2(0(x1)))))))))))))) -> 0(2(0(0(0(0(1(2(1(1(2(0(2(0(x1))))))))))))))
   0(0(2(0(2(1(1(1(0(0(1(0(2(0(x1)))))))))))))) -> 0(0(1(1(1(1(2(1(1(1(1(1(1(2(2(2(x1))))))))))))))))
   0(1(2(0(1(0(2(1(2(0(2(2(2(0(x1)))))))))))))) -> 1(1(0(1(1(1(2(1(2(1(0(0(1(2(2(x1)))))))))))))))
   2(0(0(2(2(2(0(2(2(2(2(0(1(2(x1)))))))))))))) -> 2(0(0(2(0(0(1(2(0(1(1(1(2(2(0(1(x1))))))))))))))))
   0(2(2(1(2(2(2(1(2(0(2(1(2(0(0(x1))))))))))))))) -> 0(1(1(2(0(1(0(1(1(0(0(0(2(1(2(2(x1))))))))))))))))
   1(1(2(0(1(2(2(0(0(0(0(1(0(2(2(x1))))))))))))))) -> 1(0(1(1(2(1(1(1(1(2(1(2(2(0(1(1(x1))))))))))))))))
   2(0(0(0(1(0(2(0(2(1(2(1(2(1(0(x1))))))))))))))) -> 1(2(1(0(2(2(0(1(0(0(0(2(2(1(0(x1)))))))))))))))
   2(0(1(1(0(0(0(1(0(2(1(0(2(2(0(x1))))))))))))))) -> 2(1(1(2(2(1(1(2(2(2(0(0(0(0(0(1(2(x1)))))))))))))))))
   0(0(0(2(0(1(0(2(0(0(1(0(0(1(1(1(x1)))))))))))))))) -> 1(0(2(1(1(0(1(0(1(1(2(2(2(1(2(0(1(1(1(x1)))))))))))))))))))
   0(2(1(2(1(0(2(2(1(0(1(1(1(0(1(0(x1)))))))))))))))) -> 1(1(2(2(1(2(2(2(2(2(1(2(2(2(2(2(2(x1)))))))))))))))))
   1(0(1(2(1(2(2(0(2(2(1(0(0(0(0(2(x1)))))))))))))))) -> 0(1(1(2(2(2(1(0(0(2(1(2(2(0(0(0(x1))))))))))))))))

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actions all output return to Derivational Complexity: TRS Innermost