Derivational Complexity: TRS pair #487103704

details

property	value
status	complete
benchmark	142142.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)	292.995 seconds
cpu usage	947.495
user time	939.195
system time	8.30082
max virtual memory	1.8749272E7
max residence set size	1.5223816E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 64 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), 313 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 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), 28 ms]
            (28) CpxRNTS
        (29) CompletionProof [UPPER BOUND(ID), 0 ms]
        (30) CpxTypedWeightedCompleteTrs
            (31) NarrowingProof [BOTH BOUNDS(ID, ID), 320 ms]
            (32) CpxTypedWeightedCompleteTrs
            (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 72 ms]
            (34) CpxRNTS
            (35) SimplificationProof [BOTH BOUNDS(ID, ID), 70 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 391 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 3 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 1913 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 582 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 562 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 549 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1677 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1926 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2623 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2523 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2812 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3024 ms]
        (64) 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(0(1(1(0(0(0(0(1(2(0(1(x1))))))))))))) -> 1(1(1(1(0(0(0(1(0(0(1(1(0(1(1(0(0(x1)))))))))))))))))
   0(0(0(1(1(2(2(1(1(0(0(1(1(x1))))))))))))) -> 0(1(1(0(2(0(0(0(1(0(1(1(0(0(0(1(0(x1)))))))))))))))))
   0(1(0(0(2(1(0(0(1(0(0(1(0(x1))))))))))))) -> 0(1(1(0(0(0(1(1(0(1(0(0(1(1(1(0(0(x1)))))))))))))))))
   0(1(0(1(1(0(0(0(0(2(0(1(2(x1))))))))))))) -> 1(1(1(0(0(0(1(0(1(1(0(1(1(1(0(0(2(x1)))))))))))))))))
   0(1(0(1(1(0(2(1(0(1(0(0(0(x1))))))))))))) -> 0(1(1(0(1(1(0(0(1(0(0(1(0(1(1(1(0(x1)))))))))))))))))
   0(1(1(0(0(1(0(2(0(0(0(2(1(x1))))))))))))) -> 0(0(1(1(0(1(0(1(1(0(0(1(1(2(1(1(1(x1)))))))))))))))))
   0(1(2(1(0(0(0(0(0(2(1(1(1(x1))))))))))))) -> 0(1(0(1(1(2(0(1(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))
   0(2(0(0(2(1(0(0(0(0(0(0(1(x1))))))))))))) -> 1(0(0(1(0(1(1(1(0(0(0(1(0(0(0(0(1(x1)))))))))))))))))
   0(2(1(0(1(2(1(2(2(0(1(1(1(x1))))))))))))) -> 0(2(1(1(0(0(2(1(1(0(0(1(2(1(1(1(1(x1)))))))))))))))))
   0(2(1(0(2(1(0(1(2(0(0(0(1(x1))))))))))))) -> 0(0(2(1(1(1(1(0(0(1(0(2(0(0(0(1(0(x1)))))))))))))))))
   0(2(1(1(0(0(0(0(2(1(0(1(1(x1))))))))))))) -> 0(0(1(0(1(0(1(0(2(1(1(1(0(0(0(0(0(x1)))))))))))))))))
   0(2(2(0(0(1(1(0(1(0(1(0(1(x1))))))))))))) -> 0(0(2(1(0(0(0(1(1(0(1(1(0(1(1(0(0(x1)))))))))))))))))
   1(0(0(0(0(1(1(1(0(0(2(1(1(x1))))))))))))) -> 1(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(x1)))))))))))))))))
   1(0(0(0(1(1(1(2(0(0(1(0(2(x1))))))))))))) -> 0(1(1(0(1(0(0(1(0(0(0(0(0(2(0(1(2(x1)))))))))))))))))
   1(0(0(0(1(2(0(1(0(0(0(1(0(x1))))))))))))) -> 1(1(1(0(0(0(1(1(0(1(1(0(1(1(1(0(1(x1)))))))))))))))))
   1(0(0(0(2(1(0(0(2(0(1(0(1(x1))))))))))))) -> 2(1(0(0(1(1(0(1(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))
   1(0(0(1(0(1(2(1(0(2(1(1(0(x1))))))))))))) -> 0(1(1(1(0(0(0(0(0(2(1(1(1(1(1(1(0(x1)))))))))))))))))

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actions all output return to Derivational Complexity: TRS