Derivational Complexity: TRS Innermost pair #487106726

details
property	value
status	complete
benchmark	149849.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.075 seconds
cpu usage	1165.25
user time	1160.86
system time	4.39899
max virtual memory	1.9404864E7
max residence set size	6037996.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (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), 39 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), 9 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), 51 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 6 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 4 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1713 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 16 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 7 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 15 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 19.4 s]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 15 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 544 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 3 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 70.5 s]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18.9 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(1(0(1(0(x1))))) -> 0(1(1(0(0(x1)))))
   2(0(2(2(2(2(1(x1))))))) -> 0(2(0(0(0(0(2(1(x1))))))))
   2(0(1(0(1(0(1(2(x1)))))))) -> 0(1(1(2(1(0(0(2(x1))))))))
   1(0(1(1(1(0(1(2(2(x1))))))))) -> 1(0(2(1(2(0(0(0(2(0(x1))))))))))
   1(2(0(1(1(0(2(0(1(2(x1)))))))))) -> 2(0(2(0(0(1(1(1(1(2(x1))))))))))
   0(1(0(1(2(1(0(0(2(2(2(x1))))))))))) -> 2(0(2(2(0(2(0(2(0(2(0(0(0(0(0(x1)))))))))))))))
   2(1(2(2(0(2(1(1(0(1(1(2(x1)))))))))))) -> 0(2(1(1(2(2(0(0(0(0(2(2(0(0(2(0(0(x1)))))))))))))))))
   1(0(0(1(0(1(1(0(2(0(2(1(0(1(x1)))))))))))))) -> 1(0(2(1(2(0(0(0(2(0(2(1(0(1(1(x1)))))))))))))))
   1(2(1(0(1(1(0(2(1(2(2(0(1(2(x1)))))))))))))) -> 0(1(1(1(1(2(0(1(1(0(2(0(0(2(2(x1)))))))))))))))
   1(2(2(1(0(1(0(2(1(1(1(2(1(1(0(1(x1)))))))))))))))) -> 2(1(0(0(2(0(0(0(2(0(1(1(0(2(2(2(0(0(1(x1)))))))))))))))))))
   1(1(2(0(1(1(2(0(2(1(1(1(2(2(1(1(2(0(1(0(0(x1))))))))))))))))))))) -> 1(1(1(0(2(1(2(2(0(2(0(1(0(0(0(1(2(2(0(0(0(0(x1))))))))))))))))))))))
   2(0(1(0(2(0(2(1(0(2(0(2(0(1(2(0(1(2(0(2(1(0(x1)))))))))))))))))))))) -> 0(0(0(2(2(2(2(0(0(0(0(2(2(1(2(2(0(0(2(1(0(0(2(0(x1))))))))))))))))))))))))
   1(2(0(2(0(2(2(2(2(1(2(1(0(2(2(0(2(0(2(2(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(0(2(1(2(0(0(2(2(0(2(0(1(0(0(1(0(2(0(x1))))))))))))))))))))))))
   2(2(1(1(2(1(0(2(0(1(2(2(2(0(1(0(0(2(1(2(0(2(1(x1))))))))))))))))))))))) -> 2(2(2(1(0(2(1(2(1(1(2(0(0(2(1(0(0(2(2(1(0(2(1(x1)))))))))))))))))))))))
   0(0(1(2(0(2(0(2(1(2(0(1(1(2(1(2(1(1(0(0(0(2(2(2(x1)))))))))))))))))))))))) -> 2(0(0(2(2(2(0(1(2(0(2(2(0(1(1(0(1(2(1(0(1(0(1(2(x1))))))))))))))))))))))))
   0(2(1(0(0(1(0(2(1(1(2(0(1(2(2(2(2(0(2(1(2(2(0(2(1(x1))))))))))))))))))))))))) -> 2(0(0(2(0(0(1(1(1(2(1(0(0(2(2(2(0(2(2(0(2(2(1(2(1(0(1(x1)))))))))))))))))))))))))))
   0(2(1(1(1(2(0(2(1(1(2(0(1(1(2(1(1(2(0(0(2(0(2(1(0(x1))))))))))))))))))))))))) -> 2(2(0(2(0(0(0(1(0(0(2(2(0(0(1(2(1(2(1(2(0(0(0(1(0(0(2(1(0(x1)))))))))))))))))))))))))))))
   1(0(1(2(1(2(2(2(1(1(1(2(2(2(0(1(1(0(1(2(1(1(1(0(0(x1))))))))))))))))))))))))) -> 2(0(0(0(0(1(0(2(2(2(2(0(2(0(1(0(2(2(0(1(0(1(1(1(1(1(0(x1)))))))))))))))))))))))))))
   2(0(0(2(2(2(2(1(1(1(2(2(2(0(1(1(0(0(2(1(1(0(0(1(0(x1))))))))))))))))))))))))) -> 2(0(1(0(0(2(2(2(1(0(0(0(0(0(2(1(0(1(1(0(2(2(2(0(0(0(x1))))))))))))))))))))))))))
   1(1(2(2(0(1(0(2(1(2(1(2(0(1(2(1(0(0(0(0(0(0(0(1(2(1(1(x1))))))))))))))))))))))))))) -> 0(2(1(2(0(0(2(0(2(0(2(1(1(1(0(2(2(0(2(0(0(0(2(0(1(1(2(1(0(1(1(x1)))))))))))))))))))))))))))))))
   2(0(1(0(2(0(2(2(1(2(2(0(1(0(0(0(2(1(2(2(0(0(1(0(2(1(0(x1))))))))))))))))))))))))))) -> 0(2(1(0(0(0(2(2(0(0(1(1(1(1(0(2(0(0(2(2(0(2(1(2(2(2(0(x1)))))))))))))))))))))))))))
   0(0(0(1(0(1(0(0(1(2(2(2(0(1(2(1(2(0(2(1(0(2(0(2(1(2(2(1(x1)))))))))))))))))))))))))))) -> 0(1(0(1(1(0(1(2(2(1(2(2(0(0(2(1(2(0(2(2(0(0(1(0(0(0(1(2(1(x1)))))))))))))))))))))))))))))
   1(0(1(2(1(0(2(1(1(1(1(0(1(1(1(2(1(0(2(2(1(2(2(0(2(2(0(1(x1)))))))))))))))))))))))))))) -> 2(1(2(0(2(1(2(0(2(0(1(2(1(2(0(1(1(0(0(1(0(2(0(0(0(0(0(2(2(1(2(1(x1))))))))))))))))))))))))))))))))
   1(1(0(1(1(0(1(0(1(2(1(1(0(1(2(1(0(0(2(2(0(1(2(2(2(2(1(0(x1)))))))))))))))))))))))))))) -> 0(2(0(0(0(2(0(0(2(0(2(0(0(0(2(1(1(2(1(1(2(0(0(2(1(1(0(2(0(1(2(x1)))))))))))))))))))))))))))))))
   1(2(1(1(2(1(1(1(1(1(0(2(2(2(2(2(1(2(1(1(0(1(2(0(1(0(0(0(x1)))))))))))))))))))))))))))) -> 0(1(1(0(2(2(2(2(2(2(0(1(1(0(2(0(2(0(1(1(0(1(1(1(1(0(0(0(0(x1)))))))))))))))))))))))))))))
   2(0(0(1(0(1(0(0(1(2(2(2(0(1(0(2(2(2(1(0(0(0(1(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 2(0(0(2(0(0(1(0(2(2(2(1(1(2(0(2(0(0(1(0(1(0(1(2(2(1(0(2(x1))))))))))))))))))))))))))))
   0(0(2(1(1(2(0(1(2(2(0(1(1(2(2(1(1(2(2(2(0(1(0(1(2(0(0(1(0(x1))))))))))))))))))))))))))))) -> 0(1(2(2(0(2(0(0(0(0(2(0(2(0(2(0(2(2(1(1(1(0(0(1(1(0(1(1(2(2(0(0(1(1(x1))))))))))))))))))))))))))))))))))
   0(2(1(0(2(0(0(2(0(2(2(1(1(2(2(1(0(0(2(0(1(0(2(2(2(0(0(2(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(0(2(0(0(0(1(2(0(0(0(0(1(1(0(0(1(2(0(0(2(0(0(0(0(1(2(x1))))))))))))))))))))))))))))))
   1(2(2(2(1(2(1(1(0(0(1(1(2(1(2(2(1(1(2(2(2(0(1(1(1(2(2(2(1(x1))))))))))))))))))))))))))))) -> 0(1(2(0(2(2(0(0(0(2(2(0(2(2(2(0(0(0(2(1(2(1(2(0(1(1(0(0(0(2(2(1(x1))))))))))))))))))))))))))))))))
   1(2(1(1(1(0(0(0(0(0(2(2(0(0(1(0(2(0(0(2(1(0(2(0(1(1(0(1(1(2(x1)))))))))))))))))))))))))))))) -> 0(1(0(0(2(0(0(0(2(2(0(0(0(2(2(1(0(2(0(2(2(1(1(2(2(1(2(1(1(1(2(2(x1))))))))))))))))))))))))))))))))
   2(1(2(1(2(1(2(0(1(2(2(1(0(1(1(2(0(1(1(2(1(2(0(2(1(1(2(2(2(2(x1)))))))))))))))))))))))))))))) -> 0(1(2(2(2(1(2(1(2(2(0(1(2(0(0(1(0(0(0(0(0(0(2(0(0(2(1(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))))))
   1(1(2(2(1(1(1(1(0(0(2(2(2(2(1(1(2(0(2(2(2(1(0(0(0(1(0(1(1(2(2(x1))))))))))))))))))))))))))))))) -> 1(2(0(1(2(2(1(1(0(1(2(2(1(1(0(2(0(0(0(1(1(1(1(2(0(2(0(0(0(0(1(0(2(0(0(0(x1))))))))))))))))))))))))))))))))))))
   0(2(1(0(1(2(2(2(2(1(2(0(0(0(1(1(1(2(0(2(1(1(1(2(1(1(0(2(2(2(1(2(x1)))))))))))))))))))))))))))))))) -> 2(2(2(0(2(0(2(1(2(2(2(0(2(2(2(2(0(2(0(2(0(0(0(2(0(0(1(2(2(1(1(2(2(x1)))))))))))))))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS Innermost