Derivational Complexity: TRS pair #487103452

details

property	value
status	complete
benchmark	166001.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)	297.418 seconds
cpu usage	1166.22
user time	1160.07
system time	6.1546
max virtual memory	1.8867656E7
max residence set size	1.18755E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 63 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), 4 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), 3088 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 17 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), 5404 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 23 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 24 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 2940 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 19 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 13 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 21.4 s]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6396 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6504 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6457 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19.2 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(0(1(0(1(0(x1)))))) -> 1(1(2(2(0(0(0(x1)))))))
   0(0(2(1(1(1(x1)))))) -> 2(2(1(1(2(2(2(2(x1))))))))
   0(2(0(0(2(0(x1)))))) -> 1(0(1(1(2(2(1(x1)))))))
   1(1(0(0(2(2(2(1(x1)))))))) -> 1(1(2(2(0(2(0(2(1(1(x1))))))))))
   0(2(0(2(0(2(2(2(0(x1))))))))) -> 0(1(1(1(2(2(1(2(0(0(x1))))))))))
   0(2(0(1(0(2(0(2(1(0(x1)))))))))) -> 0(0(2(2(0(1(1(2(0(0(x1))))))))))
   1(0(2(1(2(2(0(2(1(0(x1)))))))))) -> 0(1(0(1(1(1(2(2(1(1(2(x1)))))))))))
   0(1(2(1(1(1(1(0(1(2(2(x1))))))))))) -> 0(1(2(1(2(1(1(1(1(0(2(x1)))))))))))
   2(0(2(1(2(0(1(1(0(0(0(x1))))))))))) -> 1(2(1(1(2(2(2(0(0(1(0(2(2(x1)))))))))))))
   2(2(0(2(0(2(2(0(0(2(0(x1))))))))))) -> 1(2(2(2(2(2(2(1(1(2(2(0(2(x1)))))))))))))
   2(2(1(1(1(1(1(1(0(1(0(x1))))))))))) -> 0(2(0(1(1(1(1(1(2(1(2(0(x1))))))))))))
   0(0(0(0(0(2(0(2(2(0(1(0(x1)))))))))))) -> 1(0(0(2(1(0(1(1(1(2(2(2(2(1(x1))))))))))))))
   0(0(0(0(0(2(1(2(1(0(1(2(x1)))))))))))) -> 1(1(2(2(0(0(1(2(2(2(2(2(1(x1)))))))))))))
   0(0(2(0(2(0(0(2(0(1(0(2(x1)))))))))))) -> 1(1(2(1(2(2(0(2(0(2(2(2(1(x1)))))))))))))
   0(2(2(2(0(2(1(2(0(1(0(2(x1)))))))))))) -> 2(0(0(0(2(1(0(2(1(1(2(2(1(x1)))))))))))))
   2(0(1(2(0(2(2(2(0(2(0(2(x1)))))))))))) -> 2(2(1(1(1(1(1(2(1(1(2(2(0(x1)))))))))))))
   2(2(0(2(0(2(1(2(0(2(2(2(x1)))))))))))) -> 2(0(2(1(1(1(2(1(1(2(2(1(0(2(1(1(2(2(x1))))))))))))))))))
   0(0(0(2(2(0(0(2(1(2(2(0(1(x1))))))))))))) -> 1(2(0(2(1(1(2(2(2(0(1(1(2(1(2(2(1(x1)))))))))))))))))
   0(0(2(0(0(0(0(1(0(0(0(1(0(x1))))))))))))) -> 1(0(1(1(2(2(2(2(1(2(1(0(0(1(2(0(x1))))))))))))))))
   0(1(2(0(1(2(0(1(1(0(1(1(1(x1))))))))))))) -> 0(0(1(2(0(0(0(1(1(1(2(2(2(1(1(2(2(x1)))))))))))))))))
   0(1(2(2(1(2(2(1(0(2(1(2(0(x1))))))))))))) -> 1(1(1(2(1(0(0(2(1(1(2(1(1(0(0(x1)))))))))))))))
   0(2(0(0(0(1(0(1(0(0(1(1(0(x1))))))))))))) -> 0(2(1(0(2(0(1(1(1(2(2(2(1(2(2(2(0(x1)))))))))))))))))
   0(0(0(0(2(1(1(0(2(2(1(0(2(0(x1)))))))))))))) -> 0(2(0(0(0(0(1(2(1(1(2(0(2(0(x1))))))))))))))
   0(0(2(0(2(1(1(1(0(0(1(0(2(0(x1)))))))))))))) -> 0(0(1(1(1(1(2(1(1(1(1(1(1(2(2(2(x1))))))))))))))))
   0(1(2(0(1(0(2(1(2(0(2(2(2(0(x1)))))))))))))) -> 1(1(0(1(1(1(2(1(2(1(0(0(1(2(2(x1)))))))))))))))
   2(0(0(2(2(2(0(2(2(2(2(0(1(2(x1)))))))))))))) -> 2(0(0(2(0(0(1(2(0(1(1(1(2(2(0(1(x1))))))))))))))))
   0(2(2(1(2(2(2(1(2(0(2(1(2(0(0(x1))))))))))))))) -> 0(1(1(2(0(1(0(1(1(0(0(0(2(1(2(2(x1))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS