Derivational Complexity: TRS pair #487102658

details

property	value
status	complete
benchmark	160475.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.195 seconds
cpu usage	1163.68
user time	1158.29
system time	5.38531
max virtual memory	1.8903928E7
max residence set size	9801752.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 55 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), 19 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), 3023 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 2 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms]
            (28) CpxRNTS
        (29) CompletionProof [UPPER BOUND(ID), 0 ms]
        (30) CpxTypedWeightedCompleteTrs
            (31) NarrowingProof [BOTH BOUNDS(ID, ID), 5246 ms]
            (32) CpxTypedWeightedCompleteTrs
            (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 12 ms]
            (34) CpxRNTS
            (35) SimplificationProof [BOTH BOUNDS(ID, ID), 8 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 2616 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 18 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 19.1 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5643 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5644 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5614 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13.4 s]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15.7 s]
        (56) 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(2(1(x1)))) -> 2(1(2(1(2(1(x1))))))
   2(2(0(1(1(1(x1)))))) -> 2(2(1(0(1(2(1(x1)))))))
   2(2(0(1(1(0(0(x1))))))) -> 2(1(0(2(2(0(2(1(x1))))))))
   0(0(0(0(1(0(1(2(x1)))))))) -> 2(0(2(1(2(1(0(1(2(x1)))))))))
   2(0(1(2(0(1(0(0(x1)))))))) -> 1(2(2(1(2(1(0(0(1(x1)))))))))
   0(0(1(2(0(1(2(2(0(x1))))))))) -> 2(1(2(1(1(2(2(0(1(2(x1))))))))))
   1(1(2(0(1(1(0(1(1(x1))))))))) -> 2(2(1(2(1(1(2(0(0(1(x1))))))))))
   1(2(2(0(0(1(0(0(0(x1))))))))) -> 1(2(1(2(1(2(1(0(0(2(0(x1)))))))))))
   2(1(1(1(2(0(2(0(2(x1))))))))) -> 2(2(1(0(0(2(1(2(0(2(x1))))))))))
   0(1(1(1(2(0(1(1(1(0(x1)))))))))) -> 2(1(1(2(1(2(1(0(0(0(2(x1)))))))))))
   1(1(0(2(0(1(0(2(0(0(x1)))))))))) -> 2(1(2(1(1(2(2(1(0(1(2(x1)))))))))))
   1(2(0(0(2(2(2(0(1(2(x1)))))))))) -> 1(0(1(2(0(2(2(0(2(2(x1))))))))))
   0(1(0(2(2(1(1(2(0(2(0(x1))))))))))) -> 2(1(2(1(2(1(2(2(0(0(1(0(1(x1)))))))))))))
   1(2(0(2(1(0(1(1(1(2(0(x1))))))))))) -> 1(2(1(2(1(2(0(2(1(1(1(2(x1))))))))))))
   2(0(0(2(2(2(0(0(2(0(1(x1))))))))))) -> 1(1(2(0(0(2(2(1(2(2(2(1(x1))))))))))))
   2(2(0(0(1(1(0(1(2(2(1(x1))))))))))) -> 1(0(2(1(2(1(1(2(2(0(2(1(x1))))))))))))
   0(0(2(1(2(2(1(0(2(0(0(0(x1)))))))))))) -> 2(1(2(2(1(0(1(0(1(2(1(0(0(x1)))))))))))))
   2(0(0(0(0(2(1(2(0(2(0(1(x1)))))))))))) -> 0(2(2(1(1(2(2(2(2(1(2(1(1(x1)))))))))))))
   0(0(0(0(1(2(0(2(0(2(1(2(0(x1))))))))))))) -> 0(1(2(2(0(0(0(0(1(2(0(0(2(x1)))))))))))))
   0(0(0(1(2(1(0(0(0(1(0(1(0(x1))))))))))))) -> 2(0(2(1(2(1(0(2(0(1(2(1(2(2(x1))))))))))))))
   0(1(2(2(0(0(0(1(2(1(2(2(0(x1))))))))))))) -> 2(1(2(1(2(1(1(1(0(1(1(0(2(0(x1))))))))))))))
   1(0(0(1(2(0(2(0(0(0(2(1(2(x1))))))))))))) -> 2(2(1(0(2(0(2(2(1(2(1(0(1(2(2(x1)))))))))))))))
   1(1(0(0(0(2(1(1(0(1(0(2(0(x1))))))))))))) -> 2(1(0(0(1(2(2(2(2(2(1(2(1(1(x1))))))))))))))
   1(2(2(0(2(0(0(1(1(1(1(0(2(x1))))))))))))) -> 2(2(2(1(2(2(1(2(0(0(2(2(0(2(x1))))))))))))))
   2(0(1(0(1(0(0(1(1(0(2(0(0(x1))))))))))))) -> 2(1(1(0(1(2(0(1(2(2(1(2(1(2(x1))))))))))))))

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