Derivational Complexity: TRS pair #487103302

details

property	value
status	complete
benchmark	161917.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.154 seconds
cpu usage	1165.41
user time	1158.85
system time	6.5652
max virtual memory	3.7110172E7
max residence set size	1.348374E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 73 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), 2635 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 22 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), 4935 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 23 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 39 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 2387 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 32 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 21.0 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6492 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6556 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6317 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15.2 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(2(2(1(2(x1)))))) -> 0(0(1(1(0(1(1(0(0(0(1(0(1(0(x1))))))))))))))
   1(0(2(0(0(2(1(x1))))))) -> 0(0(1(2(0(1(1(1(1(0(1(0(x1))))))))))))
   1(0(1(2(2(1(2(1(x1)))))))) -> 1(0(0(0(1(0(1(0(1(0(1(2(1(0(x1))))))))))))))
   1(2(2(2(0(1(1(2(x1)))))))) -> 0(0(0(1(1(0(0(0(1(2(0(0(0(1(0(x1)))))))))))))))
   2(0(0(1(1(0(2(2(x1)))))))) -> 1(0(1(0(2(0(2(2(x1))))))))
   1(0(0(1(1(2(0(0(0(x1))))))))) -> 1(0(0(1(1(0(0(1(0(1(0(1(0(1(x1))))))))))))))
   0(0(0(1(2(0(2(1(2(1(x1)))))))))) -> 2(0(0(0(0(1(2(1(0(0(1(x1)))))))))))
   2(1(1(2(2(0(1(0(2(2(x1)))))))))) -> 0(1(2(2(2(1(0(1(0(1(0(x1)))))))))))
   0(2(2(0(2(1(2(1(1(0(0(x1))))))))))) -> 0(0(0(2(0(0(0(1(1(0(1(0(x1))))))))))))
   1(0(1(1(2(0(1(1(1(0(2(x1))))))))))) -> 1(2(1(2(0(1(1(0(0(1(2(1(0(1(x1))))))))))))))
   2(2(0(0(2(0(1(2(1(2(0(x1))))))))))) -> 1(1(0(0(1(0(1(0(0(0(0(0(0(1(0(2(0(x1)))))))))))))))))
   2(2(1(0(2(1(2(0(0(2(2(x1))))))))))) -> 1(1(1(0(2(2(0(1(0(1(1(0(1(0(2(x1)))))))))))))))
   2(0(0(2(1(1(1(0(2(2(1(2(x1)))))))))))) -> 0(1(0(1(0(2(0(1(1(1(0(2(2(x1)))))))))))))
   2(2(1(1(1(2(2(0(0(0(2(0(x1)))))))))))) -> 1(1(1(2(2(1(2(0(1(1(1(1(0(1(0(x1)))))))))))))))
   2(2(2(0(0(1(1(0(2(1(2(1(x1)))))))))))) -> 1(1(0(0(1(0(2(0(0(1(0(2(1(0(0(x1)))))))))))))))
   1(0(1(1(0(2(2(1(1(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(0(1(0(1(2(0(1(2(1(0(1(2(1(x1))))))))))))))))))
   1(2(2(2(2(1(1(1(2(2(0(2(2(x1))))))))))))) -> 0(1(2(2(0(1(1(1(1(0(0(0(0(1(0(2(x1))))))))))))))))
   2(0(2(1(2(0(1(1(0(2(2(1(0(x1))))))))))))) -> 1(1(2(1(2(0(1(1(1(0(0(1(0(2(0(1(x1))))))))))))))))
   2(1(2(2(0(0(1(1(1(0(2(2(0(x1))))))))))))) -> 2(1(0(2(2(1(0(2(2(1(0(1(0(1(0(x1)))))))))))))))
   2(2(0(2(0(1(2(0(0(2(0(2(2(x1))))))))))))) -> 2(1(0(2(0(2(0(2(2(0(2(2(0(x1)))))))))))))
   2(2(1(1(2(0(0(1(2(0(0(0(2(x1))))))))))))) -> 2(0(0(0(0(1(1(1(0(1(0(0(0(1(0(x1)))))))))))))))
   0(2(1(1(1(0(2(0(0(1(1(2(1(1(x1)))))))))))))) -> 0(1(2(2(0(0(1(0(0(0(1(1(1(0(0(x1)))))))))))))))
   0(1(1(2(2(2(2(0(2(2(0(1(2(2(2(x1))))))))))))))) -> 1(1(0(1(0(1(2(2(2(0(0(0(0(2(0(0(0(x1)))))))))))))))))
   0(1(2(0(1(1(2(1(1(1(1(1(1(2(0(x1))))))))))))))) -> 0(2(2(2(2(2(1(2(1(0(1(0(2(1(1(0(x1))))))))))))))))
   1(1(2(2(2(0(0(1(2(1(0(1(2(0(0(x1))))))))))))))) -> 1(0(2(0(0(0(0(0(2(0(1(0(0(0(1(0(x1))))))))))))))))
   2(0(1(2(0(1(2(0(2(2(2(0(2(2(0(x1))))))))))))))) -> 0(2(2(2(1(2(0(1(0(0(1(0(2(1(0(2(x1))))))))))))))))
   2(0(2(1(1(1(1(2(2(2(1(0(2(2(2(x1))))))))))))))) -> 1(1(1(1(0(0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(0(2(2(0(0(x1)))))))))))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS