Derivational Complexity: TRS pair #487102940

details

property	value
status	complete
benchmark	161593.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)	297.328 seconds
cpu usage	1165.64
user time	1159.66
system time	5.98659
max virtual memory	1.9182448E7
max residence set size	1.1635972E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 37 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 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), 2377 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 58 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), 4519 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 198 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 101 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), 2191 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 28 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 17.8 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5250 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5254 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5271 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11.1 s]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13.9 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(0(x1))) -> 2(2(1(1(x1))))
   1(0(0(x1))) -> 2(0(2(2(2(0(2(2(0(1(0(2(x1))))))))))))
   1(0(0(1(x1)))) -> 2(2(1(0(1(x1)))))
   1(0(0(1(x1)))) -> 1(2(0(2(2(0(0(2(2(0(0(2(0(1(x1))))))))))))))
   1(0(2(1(x1)))) -> 2(2(0(0(2(x1)))))
   0(0(1(1(0(x1))))) -> 0(1(1(1(2(2(2(1(2(2(0(2(2(x1)))))))))))))
   0(1(0(1(0(x1))))) -> 2(1(1(2(2(2(x1))))))
   0(1(2(2(0(x1))))) -> 2(2(2(0(2(2(2(0(2(1(2(0(x1))))))))))))
   2(2(1(1(1(x1))))) -> 2(2(1(2(2(2(1(1(x1))))))))
   2(2(1(0(0(0(x1)))))) -> 2(0(2(1(2(2(0(0(0(2(2(1(2(0(x1))))))))))))))
   0(2(0(1(1(1(0(x1))))))) -> 2(0(1(2(1(0(2(2(2(x1)))))))))
   0(0(1(2(2(0(1(1(x1)))))))) -> 2(2(1(0(0(1(2(0(2(2(1(x1)))))))))))
   0(1(2(1(2(2(2(1(x1)))))))) -> 2(2(2(2(1(1(2(2(1(x1)))))))))
   1(1(0(0(0(0(1(1(x1)))))))) -> 0(2(0(1(1(2(2(1(2(1(x1))))))))))
   1(1(0(2(1(1(0(0(x1)))))))) -> 1(1(2(1(2(2(0(0(2(0(x1))))))))))
   2(1(2(0(0(1(0(0(x1)))))))) -> 2(0(2(1(1(0(2(1(1(2(x1))))))))))
   0(2(1(1(1(2(0(1(1(x1))))))))) -> 2(0(1(0(2(2(1(0(2(2(1(1(2(0(x1))))))))))))))
   0(2(2(2(2(0(1(1(1(x1))))))))) -> 0(2(0(0(2(2(2(1(0(2(1(1(x1))))))))))))
   0(0(0(0(2(0(1(0(0(0(x1)))))))))) -> 0(2(1(1(2(1(2(2(2(2(0(0(2(0(1(2(x1))))))))))))))))
   0(1(1(0(1(2(1(2(2(0(x1)))))))))) -> 0(2(2(1(1(1(0(0(2(2(2(2(1(2(x1))))))))))))))
   0(2(2(0(1(0(1(2(1(1(x1)))))))))) -> 2(0(0(2(2(0(2(2(2(2(1(x1)))))))))))
   2(0(2(1(1(0(0(1(0(0(x1)))))))))) -> 2(2(1(2(2(0(0(0(2(2(2(2(0(2(2(2(0(2(1(2(0(2(1(x1)))))))))))))))))))))))
   2(0(2(1(2(1(0(1(0(0(x1)))))))))) -> 2(0(0(2(2(1(1(0(1(0(2(2(x1))))))))))))
   2(1(0(2(0(1(2(0(1(1(x1)))))))))) -> 2(0(0(0(0(1(0(2(1(2(2(2(2(0(1(2(1(0(2(2(x1))))))))))))))))))))
   0(1(2(1(1(1(1(0(0(0(1(x1))))))))))) -> 0(2(0(1(1(1(1(0(0(0(2(0(2(0(0(0(2(1(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))

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