Derivational Complexity: TRS pair #487102732

details

property	value
status	complete
benchmark	26903.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	298.654 seconds
cpu usage	839.683
user time	831.967
system time	7.71555
max virtual memory	1.8786428E7
max residence set size	1.5172048E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 33 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 2 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 5 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 9 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), 1493 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 27 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), 2009 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 194 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 132 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 30 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 856 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 1 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6335 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1851 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1883 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1868 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1805 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1832 ms]
        (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(0(1(2(3(4(2(x1))))))) -> 0(0(1(4(3(2(2(x1)))))))
   0(0(4(0(5(5(2(2(x1)))))))) -> 0(0(4(5(0(5(2(2(x1))))))))
   2(4(2(4(5(5(4(3(x1)))))))) -> 2(4(2(5(4(5(4(3(x1))))))))
   4(5(2(1(1(1(3(5(x1)))))))) -> 4(5(1(2(1(1(3(5(x1))))))))
   3(0(1(0(3(4(0(5(1(x1))))))))) -> 3(0(1(0(0(4(3(5(1(x1)))))))))
   3(0(2(3(5(0(0(3(0(x1))))))))) -> 3(0(2(3(0(0(5(3(0(x1)))))))))
   1(2(0(2(4(1(0(4(4(0(x1)))))))))) -> 1(2(0(2(1(4(0(4(4(0(x1))))))))))
   1(3(1(1(4(0(4(0(5(4(x1)))))))))) -> 1(3(1(5(5(3(2(3(1(3(x1))))))))))
   2(5(5(2(2(2(1(3(4(0(x1)))))))))) -> 2(5(2(5(2(3(2(1(4(0(x1))))))))))
   3(4(0(3(2(5(5(1(3(2(x1)))))))))) -> 3(4(3(0(2(5(5(1(3(2(x1))))))))))
   3(4(4(0(3(4(3(4(1(5(x1)))))))))) -> 3(5(4(4(1(4(3(4(3(0(x1))))))))))
   0(0(4(0(2(1(4(3(3(4(5(x1))))))))))) -> 3(4(3(2(1(3(2(5(5(5(x1))))))))))
   0(1(1(4(4(4(0(5(0(3(5(x1))))))))))) -> 1(3(5(0(2(4(4(0(2(0(x1))))))))))
   0(3(1(3(4(1(3(4(4(3(5(x1))))))))))) -> 0(4(4(2(3(4(1(4(0(4(x1))))))))))
   0(3(5(4(4(5(1(5(4(1(5(x1))))))))))) -> 5(4(1(3(3(4(4(3(1(1(x1))))))))))
   0(5(1(2(5(0(3(5(2(5(1(x1))))))))))) -> 4(2(3(5(2(0(0(3(2(0(x1))))))))))
   1(0(4(5(5(0(0(1(2(5(2(x1))))))))))) -> 4(0(5(0(5(5(5(0(4(0(x1))))))))))
   1(0(5(2(4(4(2(0(2(5(4(x1))))))))))) -> 2(1(0(4(3(2(2(4(2(2(x1))))))))))
   1(1(2(3(1(3(2(1(1(0(5(x1))))))))))) -> 3(1(1(4(2(0(0(0(2(3(x1))))))))))
   1(1(3(0(5(1(5(2(2(3(1(x1))))))))))) -> 0(3(0(3(0(1(2(2(5(2(x1))))))))))
   1(1(4(2(0(1(3(3(4(4(2(x1))))))))))) -> 2(3(5(3(2(4(5(2(1(0(x1))))))))))
   1(2(1(1(1(2(5(2(5(0(2(x1))))))))))) -> 0(2(5(0(2(2(3(2(2(1(x1))))))))))
   1(2(2(3(3(1(3(3(2(0(0(x1))))))))))) -> 1(3(0(2(0(5(5(3(5(0(x1))))))))))
   1(4(0(1(5(3(3(1(1(4(0(x1))))))))))) -> 4(5(5(3(4(4(5(5(1(5(x1))))))))))
   1(4(3(0(2(2(4(4(3(0(1(x1))))))))))) -> 1(3(0(1(0(5(3(4(3(5(x1))))))))))

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actions all output return to Derivational Complexity: TRS