Derivational Complexity: TRS Innermost pair #487106314

details

property	value
status	complete
benchmark	142157.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.759 seconds
cpu usage	815.131
user time	807.975
system time	7.15636
max virtual memory	1.8749432E7
max residence set size	1.471638E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 52 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 7 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), 641 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 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), 20 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2213 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 82 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 9275 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2424 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2484 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2414 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8345 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1327 ms]
    (54) 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(0(0(1(0(2(1(2(0(0(1(x1))))))))))))) -> 0(0(0(0(0(2(0(2(0(0(2(0(0(0(0(2(2(x1)))))))))))))))))
   0(0(1(0(0(2(0(1(0(1(2(0(0(x1))))))))))))) -> 0(0(0(2(2(1(0(0(1(2(0(0(0(2(0(0(0(x1)))))))))))))))))
   0(0(1(1(1(0(1(1(0(1(0(0(0(x1))))))))))))) -> 0(1(0(0(0(1(0(1(2(2(2(0(0(0(0(2(0(x1)))))))))))))))))
   0(0(1(2(1(2(0(2(0(0(2(2(2(x1))))))))))))) -> 0(0(0(0(0(1(0(1(0(0(0(0(0(2(1(2(2(x1)))))))))))))))))
   0(0(2(0(0(0(2(1(1(2(1(0(2(x1))))))))))))) -> 0(1(0(2(0(0(0(0(0(2(2(0(0(1(0(0(2(x1)))))))))))))))))
   0(0(2(2(1(2(0(1(2(1(2(2(0(x1))))))))))))) -> 0(0(2(2(0(0(2(0(2(0(2(0(1(1(1(0(0(x1)))))))))))))))))
   0(0(2(2(2(2(2(1(0(0(2(2(0(x1))))))))))))) -> 2(0(0(0(2(0(2(0(1(0(0(0(0(1(2(2(0(x1)))))))))))))))))
   0(1(0(1(1(0(1(0(0(0(2(0(0(x1))))))))))))) -> 0(2(2(0(2(2(0(0(2(0(0(0(0(0(1(0(0(x1)))))))))))))))))
   0(1(0(1(2(1(2(0(0(2(1(0(2(x1))))))))))))) -> 0(1(0(0(0(2(2(1(0(1(2(0(0(0(0(2(2(x1)))))))))))))))))
   0(1(1(0(2(1(0(1(0(0(2(2(0(x1))))))))))))) -> 0(0(2(0(2(1(0(0(0(0(2(1(2(2(1(0(0(x1)))))))))))))))))
   0(1(1(1(2(0(0(2(0(0(1(2(0(x1))))))))))))) -> 1(2(0(0(0(2(0(2(0(0(1(2(0(0(0(2(0(x1)))))))))))))))))
   0(1(2(0(0(0(0(1(0(2(0(1(0(x1))))))))))))) -> 0(0(0(0(0(2(2(0(2(0(0(0(0(1(0(1(0(x1)))))))))))))))))
   0(1(2(0(0(0(0(1(0(2(0(1(0(x1))))))))))))) -> 0(0(2(2(0(0(0(2(2(0(0(0(0(1(2(0(0(x1)))))))))))))))))
   0(1(2(0(0(0(2(1(2(0(1(2(2(x1))))))))))))) -> 0(2(0(0(0(0(2(1(0(0(0(2(0(1(0(2(2(x1)))))))))))))))))
   0(2(0(0(0(0(2(2(1(1(2(1(0(x1))))))))))))) -> 0(2(0(2(0(0(1(0(2(0(0(0(0(2(0(2(0(x1)))))))))))))))))
   0(2(0(0(0(2(2(0(2(1(1(2(2(x1))))))))))))) -> 0(0(0(0(2(2(1(2(0(1(0(0(2(0(0(0(2(x1)))))))))))))))))
   0(2(0(0(1(2(0(1(1(0(1(2(0(x1))))))))))))) -> 0(2(0(1(0(2(1(0(0(2(2(0(0(0(0(2(0(x1)))))))))))))))))
   0(2(0(1(1(1(1(0(2(2(0(0(0(x1))))))))))))) -> 0(0(0(0(0(2(1(1(1(1(2(1(0(0(0(0(0(x1)))))))))))))))))
   0(2(1(1(0(0(2(0(0(1(1(2(0(x1))))))))))))) -> 0(2(0(0(0(0(0(2(0(1(0(0(2(1(0(2(0(x1)))))))))))))))))
   0(2(1(1(1(0(0(2(0(2(2(2(0(x1))))))))))))) -> 0(0(0(0(0(0(0(2(2(0(1(1(1(2(1(2(0(x1)))))))))))))))))
   0(2(1(2(0(0(0(1(1(1(0(2(1(x1))))))))))))) -> 0(0(2(0(2(0(1(0(0(2(1(0(2(0(0(2(1(x1)))))))))))))))))
   0(2(1(2(0(0(2(0(1(2(1(2(0(x1))))))))))))) -> 0(2(0(0(0(0(0(0(1(0(1(2(0(2(1(2(0(x1)))))))))))))))))
   0(2(1(2(2(0(1(0(0(2(2(0(0(x1))))))))))))) -> 0(0(2(1(1(0(1(0(0(1(2(0(0(0(0(0(0(x1)))))))))))))))))
   0(2(1(2(2(1(0(0(2(1(2(2(2(x1))))))))))))) -> 0(0(0(0(1(2(2(2(2(2(1(0(0(1(0(0(2(x1)))))))))))))))))
   0(2(2(0(0(0(1(2(2(2(2(2(0(x1))))))))))))) -> 2(0(0(0(0(0(0(1(1(1(0(1(0(2(0(0(0(x1)))))))))))))))))
   0(2(2(0(0(0(2(2(2(0(1(2(1(x1))))))))))))) -> 0(0(0(0(1(0(0(0(2(2(0(0(2(2(0(0(1(x1)))))))))))))))))
   0(2(2(2(2(0(0(2(0(2(2(2(0(x1))))))))))))) -> 0(0(1(0(1(2(0(2(0(2(0(0(0(0(0(2(0(x1)))))))))))))))))

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actions all output return to Derivational Complexity: TRS Innermost