Derivational Complexity: TRS pair #487102912

details

property	value
status	complete
benchmark	167391.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.093 seconds
cpu usage	1156.97
user time	1152.53
system time	4.43727
max virtual memory	1.9058224E7
max residence set size	7114612.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (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), 188 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 9 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) RcToIrcProof [BOTH BOUNDS(ID, ID), 3133 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 48 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), 5607 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 16 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), 2765 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 15 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 21 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 22.8 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7126 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7116 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7172 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20.7 s]
        (54) 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(1(0(x1))) -> 1(1(1(1(0(x1)))))
   1(0(2(x1))) -> 1(1(1(1(2(x1)))))
   2(1(2(0(0(x1))))) -> 1(1(1(0(1(0(x1))))))
   1(0(1(0(2(0(x1)))))) -> 0(0(1(1(1(1(1(x1)))))))
   2(0(2(1(0(0(x1)))))) -> 2(1(1(1(1(2(2(x1)))))))
   2(1(0(2(2(0(x1)))))) -> 1(1(1(1(1(0(0(1(1(x1)))))))))
   2(1(2(2(2(1(x1)))))) -> 2(0(2(1(1(1(1(x1)))))))
   0(0(0(1(1(2(2(0(x1)))))))) -> 0(1(1(1(1(0(0(0(0(1(x1))))))))))
   1(1(0(2(1(1(0(2(0(x1))))))))) -> 1(1(1(1(2(2(1(1(1(1(0(1(x1))))))))))))
   1(2(0(2(0(1(2(2(2(x1))))))))) -> 2(2(1(1(2(0(0(2(2(x1)))))))))
   0(1(2(0(0(0(2(2(0(0(x1)))))))))) -> 0(1(0(0(2(0(2(2(0(0(x1))))))))))
   0(0(0(0(0(2(2(0(1(2(2(x1))))))))))) -> 1(1(1(1(1(2(1(2(1(0(0(1(0(2(x1))))))))))))))
   0(1(2(0(2(1(2(0(2(0(0(x1))))))))))) -> 2(2(1(2(2(1(1(1(1(1(1(0(1(x1)))))))))))))
   2(0(1(2(0(2(1(0(0(1(0(x1))))))))))) -> 2(1(1(1(0(1(0(1(1(0(2(0(x1))))))))))))
   0(0(1(1(0(2(0(2(2(0(0(2(x1)))))))))))) -> 1(1(1(2(1(0(2(2(0(0(1(1(1(1(1(1(x1))))))))))))))))
   0(2(2(1(2(2(2(1(2(1(2(2(x1)))))))))))) -> 1(1(1(0(2(2(1(1(1(0(1(0(2(0(x1))))))))))))))
   0(0(2(2(2(0(1(0(0(0(0(0(2(x1))))))))))))) -> 0(1(0(1(1(1(2(0(2(2(0(0(1(2(x1))))))))))))))
   0(2(0(0(0(2(0(0(2(1(2(2(0(x1))))))))))))) -> 2(1(1(1(1(1(1(0(0(1(2(1(1(2(0(0(0(x1)))))))))))))))))
   2(0(1(0(2(2(2(2(1(1(0(1(2(x1))))))))))))) -> 2(2(1(0(2(2(0(2(2(0(1(1(1(x1)))))))))))))
   2(2(1(0(0(2(2(0(2(1(0(1(0(x1))))))))))))) -> 1(1(1(1(1(0(2(2(0(1(1(1(2(1(0(x1)))))))))))))))
   0(0(0(0(0(0(1(0(2(1(1(2(2(2(x1)))))))))))))) -> 2(0(0(0(2(0(2(1(1(1(0(1(2(1(2(x1)))))))))))))))
   2(2(2(2(2(2(0(0(0(0(0(2(1(0(x1)))))))))))))) -> 0(0(2(2(1(1(1(2(1(2(0(0(1(1(1(1(x1))))))))))))))))
   0(0(2(1(2(1(2(1(1(0(1(1(2(2(0(x1))))))))))))))) -> 2(0(0(1(0(1(0(2(2(1(0(0(1(1(1(1(x1))))))))))))))))
   1(0(1(2(0(2(1(2(1(0(2(1(2(2(0(x1))))))))))))))) -> 2(1(0(2(1(0(0(1(1(1(1(2(2(0(0(0(x1))))))))))))))))
   1(2(2(0(0(2(2(2(1(2(2(0(1(0(2(x1))))))))))))))) -> 1(0(1(0(1(0(1(1(0(1(0(1(0(1(1(2(x1))))))))))))))))
   2(2(0(1(1(2(2(2(2(2(1(0(2(2(2(x1))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(1(1(0(0(0(1(x1))))))))))))))))
   0(2(0(0(0(1(0(1(1(0(0(2(1(0(0(2(x1)))))))))))))))) -> 0(0(2(2(0(0(2(2(1(1(1(1(2(2(1(1(0(x1)))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS