Derivational Complexity: TRS pair #487103406

details
property	value
status	complete
benchmark	151247.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	ICFP_2010
run statistics
property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.286 seconds
cpu usage	1164.82
user time	1160.03
system time	4.7876
max virtual memory	1.914916E7
max residence set size	6690372.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) 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), 46 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) RcToIrcProof [BOTH BOUNDS(ID, ID), 3627 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 24 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1575 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 146 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 70 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 3108 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 8 ms]
        (44) CdtProblem
        (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8034 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 26.5 s]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7998 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8035 ms]
        (52) CdtProblem


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

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


The TRS R consists of the following rules:

   0(0(0(1(2(2(1(2(2(x1))))))))) -> 1(2(1(1(2(1(0(1(1(1(x1))))))))))
   0(0(0(2(2(1(1(0(1(0(1(x1))))))))))) -> 1(1(2(1(1(2(2(1(2(2(2(1(x1))))))))))))
   0(0(2(0(2(1(1(0(1(0(1(0(1(0(2(x1))))))))))))))) -> 1(1(2(1(2(2(2(1(2(2(2(2(2(0(2(2(2(x1)))))))))))))))))
   0(1(2(0(0(1(1(1(1(0(1(2(2(1(1(0(2(x1))))))))))))))))) -> 0(2(1(1(1(0(0(1(2(1(0(0(2(1(2(0(2(1(1(x1)))))))))))))))))))
   0(1(0(2(2(0(0(1(1(0(0(0(2(1(2(2(0(0(x1)))))))))))))))))) -> 2(1(2(1(0(2(1(0(2(2(2(1(0(2(1(0(2(1(1(0(x1))))))))))))))))))))
   2(0(1(0(0(1(1(0(2(0(2(0(0(2(1(1(1(0(x1)))))))))))))))))) -> 2(1(0(2(1(0(2(2(0(1(1(2(0(2(1(0(1(2(1(2(x1))))))))))))))))))))
   0(0(2(2(2(0(0(0(0(1(1(0(2(1(1(1(2(0(2(x1))))))))))))))))))) -> 2(2(1(2(1(0(0(0(2(0(2(1(0(0(2(1(1(2(1(1(x1))))))))))))))))))))
   0(0(1(0(0(0(1(0(1(1(0(2(0(2(2(2(2(2(2(0(x1)))))))))))))))))))) -> 0(2(1(0(2(1(1(2(2(0(2(0(0(2(2(1(0(1(2(1(2(1(x1))))))))))))))))))))))
   0(2(1(0(2(2(2(1(1(1(1(1(0(1(0(0(2(1(1(1(x1)))))))))))))))))))) -> 0(2(1(2(1(1(0(2(2(2(1(1(2(1(2(2(0(1(2(2(1(x1)))))))))))))))))))))
   2(0(1(2(2(1(1(0(0(1(2(0(1(1(2(2(2(0(0(0(x1)))))))))))))))))))) -> 2(1(2(1(1(2(0(2(1(2(2(0(1(2(1(0(2(0(2(0(1(2(x1))))))))))))))))))))))
   1(2(1(2(2(0(0(2(1(1(1(2(2(1(0(2(2(2(1(1(0(x1))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(0(2(0(1(2(1(0(2(1(x1)))))))))))))))))))))
   2(0(2(2(1(0(2(1(2(2(2(0(2(0(0(2(1(2(0(0(0(x1))))))))))))))))))))) -> 0(1(2(1(2(1(2(0(1(1(2(2(0(2(0(1(2(2(2(2(2(0(x1))))))))))))))))))))))
   0(0(2(0(2(2(2(0(0(1(1(2(2(2(2(1(1(1(1(1(1(0(x1)))))))))))))))))))))) -> 2(1(2(1(2(2(1(2(2(1(2(2(2(0(2(2(1(0(1(0(1(2(2(0(x1))))))))))))))))))))))))
   0(0(1(1(0(2(0(2(1(0(2(2(0(1(1(0(0(1(2(0(2(1(1(1(1(x1))))))))))))))))))))))))) -> 1(2(2(0(2(2(1(0(2(1(1(2(2(0(1(2(2(2(2(0(0(0(1(2(1(1(x1))))))))))))))))))))))))))
   2(0(1(1(1(1(2(0(0(0(0(2(1(1(0(0(2(2(1(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))) -> 2(1(2(1(0(0(0(1(1(0(1(2(1(0(1(0(1(2(1(1(1(2(2(1(0(0(2(x1)))))))))))))))))))))))))))
   0(1(1(0(0(2(1(0(2(0(2(1(1(0(2(2(1(0(1(1(1(1(1(1(1(0(2(x1))))))))))))))))))))))))))) -> 1(0(0(0(1(2(2(1(2(1(0(1(0(2(0(2(0(2(2(0(1(2(0(0(2(1(2(1(x1))))))))))))))))))))))))))))
   0(2(1(1(2(0(1(0(2(0(0(1(2(2(0(0(0(0(2(0(0(2(0(1(0(0(2(x1))))))))))))))))))))))))))) -> 2(2(1(2(1(2(2(1(2(1(1(0(0(0(1(2(0(2(1(1(1(2(2(0(1(2(0(2(1(x1)))))))))))))))))))))))))))))
   2(0(0(2(1(2(2(0(2(1(1(1(1(2(0(0(1(2(0(0(0(2(0(0(0(2(0(x1))))))))))))))))))))))))))) -> 2(2(2(1(2(0(1(1(0(0(1(2(1(1(2(1(2(0(1(1(0(2(0(1(0(2(1(1(x1))))))))))))))))))))))))))))
   2(2(1(2(2(1(2(0(1(2(0(1(1(1(2(2(1(0(2(2(0(0(2(2(1(0(0(x1))))))))))))))))))))))))))) -> 2(2(1(2(1(2(0(2(1(1(2(1(2(0(2(0(0(0(2(2(0(2(1(2(1(1(0(x1)))))))))))))))))))))))))))
   0(0(2(1(1(1(1(0(1(0(0(0(0(0(1(0(0(2(0(2(0(2(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) -> 1(0(1(1(1(0(0(0(2(0(1(2(2(2(2(1(2(1(2(0(2(0(2(0(2(0(2(2(2(x1)))))))))))))))))))))))))))))
   0(2(1(2(0(2(2(0(2(1(2(2(2(0(0(2(0(0(2(2(1(0(0(2(2(0(1(1(x1)))))))))))))))))))))))))))) -> 1(0(1(2(1(2(1(0(0(1(1(0(1(2(2(2(2(1(1(2(0(1(1(0(2(2(1(2(1(x1)))))))))))))))))))))))))))))
   2(0(0(0(2(2(2(0(1(2(1(1(0(0(0(1(0(2(2(2(0(0(1(1(2(1(2(2(x1)))))))))))))))))))))))))))) -> 0(1(1(2(1(2(1(0(0(0(2(0(1(2(1(2(2(1(0(0(1(2(1(2(1(2(0(1(0(x1)))))))))))))))))))))))))))))
   0(1(1(2(0(1(0(1(1(2(2(0(0(2(0(2(1(2(2(2(2(0(2(0(1(1(0(0(2(x1))))))))))))))))))))))))))))) -> 1(2(2(1(1(0(2(0(0(0(0(2(1(1(0(2(0(2(1(2(2(0(2(1(1(2(1(1(2(2(x1))))))))))))))))))))))))))))))
   2(0(2(2(0(0(0(1(0(1(0(2(0(2(0(0(0(2(1(1(1(0(0(0(2(1(2(0(0(x1))))))))))))))))))))))))))))) -> 1(0(0(0(1(2(2(2(2(1(1(2(2(1(2(2(2(1(1(1(1(1(0(2(2(2(1(2(1(0(x1))))))))))))))))))))))))))))))
   0(1(1(0(0(1(0(1(2(2(2(1(1(0(0(1(2(2(0(0(2(0(1(2(2(2(1(1(2(0(x1)))))))))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(1(0(1(2(2(0(0(1(0(2(1(2(2(2(1(1(1(2(0(0(1(2(1(x1))))))))))))))))))))))))))))))))
   2(0(0(0(1(1(0(0(1(0(0(1(1(0(2(2(1(1(1(2(1(0(0(0(2(2(2(0(0(2(x1)))))))))))))))))))))))))))))) -> 1(2(1(1(0(2(2(1(1(1(0(0(2(2(2(2(1(1(2(1(2(2(2(1(2(1(1(2(1(2(0(x1)))))))))))))))))))))))))))))))
   1(2(0(2(0(1(0(0(2(1(1(1(0(0(1(2(0(2(1(1(1(1(2(0(2(2(0(1(0(1(0(2(x1)))))))))))))))))))))))))))))))) -> 1(1(0(0(1(1(2(1(0(1(2(2(0(1(1(2(1(2(0(1(2(1(1(2(1(2(2(1(2(1(2(1(0(2(x1))))))))))))))))))))))))))))))))))
   2(0(0(2(0(1(2(2(2(2(1(2(0(0(1(2(1(2(1(0(1(1(1(0(0(0(2(0(1(0(2(0(x1)))))))))))))))))))))))))))))))) -> 2(1(2(1(0(0(2(1(0(1(2(1(2(2(0(2(0(1(1(2(2(2(0(1(1(2(1(2(0(1(2(0(1(x1)))))))))))))))))))))))))))))))))
   2(0(2(0(0(1(0(2(2(2(1(1(1(0(0(1(1(1(0(0(0(0(1(0(1(2(0(2(2(0(0(1(x1)))))))))))))))))))))))))))))))) -> 2(0(2(2(2(0(0(2(1(0(1(1(1(1(2(1(2(1(1(0(0(2(2(2(2(0(0(1(1(1(0(0(1(x1)))))))))))))))))))))))))))))))))
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actions all output return to Derivational Complexity: TRS