Derivational Complexity: TRS Innermost pair #487106880

details

property	value
status	complete
benchmark	165975.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.008 seconds
cpu usage	897.208
user time	891.098
system time	6.11002
max virtual memory	1.886696E7
max residence set size	1.4674624E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) 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), 16 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 48 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 3 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 5067 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 106 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 67 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 39 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 12.8 s]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 225 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 11 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 16.8 s]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2815 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2813 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2796 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5678 ms]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 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(1(x1))) -> 2(1(2(1(x1))))
   0(2(2(1(2(0(x1)))))) -> 2(2(1(2(1(1(1(x1)))))))
   0(1(1(2(2(1(0(x1))))))) -> 1(2(1(2(1(2(2(1(1(1(x1))))))))))
   2(0(1(0(2(2(1(x1))))))) -> 2(0(1(2(1(2(1(1(x1))))))))
   0(1(2(1(1(1(0(1(x1)))))))) -> 2(1(2(2(1(2(1(0(1(x1)))))))))
   2(1(0(2(2(2(2(2(x1)))))))) -> 2(1(2(2(2(0(2(2(x1))))))))
   0(1(1(1(0(2(0(1(2(x1))))))))) -> 1(2(1(2(2(1(1(2(2(1(2(x1)))))))))))
   0(1(2(1(1(1(2(0(0(2(x1)))))))))) -> 2(1(0(0(1(2(1(2(1(1(2(x1)))))))))))
   0(2(0(0(0(2(1(0(1(2(x1)))))))))) -> 2(1(1(0(0(2(0(2(1(2(1(x1)))))))))))
   1(0(2(0(0(2(0(2(0(1(x1)))))))))) -> 1(1(0(1(0(1(2(1(2(1(1(1(0(x1)))))))))))))
   1(2(0(2(2(0(1(2(0(0(x1)))))))))) -> 0(1(2(1(2(1(2(1(2(2(0(x1)))))))))))
   0(0(2(2(2(2(0(0(2(0(0(x1))))))))))) -> 0(2(0(2(1(2(1(1(2(1(1(1(1(1(2(0(2(x1)))))))))))))))))
   2(0(2(2(0(1(2(2(2(2(0(x1))))))))))) -> 2(1(2(2(1(2(1(1(2(2(2(1(1(0(1(2(x1))))))))))))))))
   0(2(2(0(1(2(1(2(0(0(1(1(x1)))))))))))) -> 0(1(1(2(1(2(2(1(1(1(2(2(0(0(x1))))))))))))))
   1(0(2(2(0(2(0(0(0(1(1(1(x1)))))))))))) -> 2(1(2(1(1(0(2(0(1(1(2(2(1(2(1(x1)))))))))))))))
   0(0(0(0(0(2(0(1(2(1(1(1(2(x1))))))))))))) -> 0(0(1(1(1(1(2(2(2(1(2(1(1(1(1(1(x1))))))))))))))))
   0(0(0(0(2(2(0(0(0(1(2(1(0(x1))))))))))))) -> 1(0(0(2(2(2(2(1(2(1(1(2(1(1(x1))))))))))))))
   0(0(2(0(0(1(1(0(0(2(0(1(0(x1))))))))))))) -> 2(0(2(1(1(2(2(1(2(1(2(2(1(1(1(2(2(1(x1))))))))))))))))))
   0(1(0(1(2(0(1(1(2(2(1(0(1(x1))))))))))))) -> 2(1(0(0(1(1(2(2(2(1(2(2(1(1(x1))))))))))))))
   0(1(0(2(0(0(2(0(1(0(2(1(0(x1))))))))))))) -> 2(1(2(1(1(1(0(1(0(0(0(0(2(2(x1))))))))))))))
   0(2(1(1(2(1(1(0(0(2(2(0(2(x1))))))))))))) -> 0(1(0(1(0(1(0(2(1(2(1(1(1(0(2(x1)))))))))))))))
   1(0(1(0(1(2(0(1(1(1(0(2(2(x1))))))))))))) -> 2(1(1(1(0(2(1(1(2(1(2(1(2(2(1(x1)))))))))))))))
   2(0(0(2(1(0(1(1(1(2(0(1(1(x1))))))))))))) -> 2(1(2(1(1(0(1(1(0(1(2(1(0(0(0(x1)))))))))))))))
   0(0(1(2(0(0(1(1(2(1(1(0(2(0(x1)))))))))))))) -> 2(1(0(1(1(1(1(2(1(1(2(1(2(1(1(0(x1))))))))))))))))
   0(1(0(1(2(1(1(1(0(1(2(1(0(0(x1)))))))))))))) -> 2(1(2(2(1(1(1(2(1(1(2(1(2(1(2(x1)))))))))))))))

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