Derivational_Complexity: TRS pair #487531727

details

property	value
status	timeout (wallclock)
benchmark	25734.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	301.008471012 seconds
cpu usage	811.729306921
max memory	1.528111104E10

stage attributes

unavailable

output

/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 53 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 3 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), 1368 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 39 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 15 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 36 ms]
            (28) CpxRNTS
        (29) CompletionProof [UPPER BOUND(ID), 15 ms]
        (30) CpxTypedWeightedCompleteTrs
            (31) NarrowingProof [BOTH BOUNDS(ID, ID), 1887 ms]
            (32) CpxTypedWeightedCompleteTrs
            (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 213 ms]
            (34) CpxRNTS
            (35) SimplificationProof [BOTH BOUNDS(ID, ID), 114 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 856 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 6 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6114 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1785 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1875 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1829 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1822 ms]
        (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(0(2(3(4(x1)))))) -> 0(1(0(3(2(4(x1))))))
   1(0(3(5(4(1(x1)))))) -> 1(1(3(0(5(4(x1))))))
   3(0(0(1(5(1(5(x1))))))) -> 3(0(0(5(1(1(5(x1)))))))
   5(5(1(3(0(4(5(x1))))))) -> 5(5(3(1(0(4(5(x1)))))))
   2(4(3(2(0(1(5(2(x1)))))))) -> 2(4(2(3(1(0(5(2(x1))))))))
   3(0(2(3(3(5(4(5(1(4(x1)))))))))) -> 3(0(3(2(3(5(4(5(1(4(x1))))))))))
   4(3(5(5(1(4(4(0(0(3(x1)))))))))) -> 4(3(5(5(1(4(0(4(0(3(x1))))))))))
   5(5(4(1(2(3(5(3(5(3(x1)))))))))) -> 5(5(1(4(5(2(3(3(5(3(x1))))))))))
   0(1(4(0(4(2(3(4(4(1(3(x1))))))))))) -> 3(1(5(3(2(2(1(1(5(0(x1))))))))))
   0(2(1(3(2(0(5(4(2(0(5(x1))))))))))) -> 2(2(1(1(3(1(4(5(4(0(x1))))))))))
   0(2(1(3(4(3(5(4(3(5(5(x1))))))))))) -> 1(0(0(1(1(4(1(4(1(3(x1))))))))))
   0(2(3(4(1(4(0(2(3(1(0(x1))))))))))) -> 3(1(0(2(2(1(4(1(5(1(x1))))))))))
   0(3(3(0(0(2(0(5(2(4(2(x1))))))))))) -> 5(4(5(0(3(0(3(0(5(0(x1))))))))))
   0(3(3(2(2(2(0(2(4(0(1(x1))))))))))) -> 5(4(3(1(5(0(0(0(4(2(x1))))))))))
   0(5(0(0(2(4(4(1(5(0(3(x1))))))))))) -> 1(4(3(4(3(3(2(4(3(3(x1))))))))))
   0(5(0(4(1(3(4(4(3(3(3(x1))))))))))) -> 0(0(3(0(3(4(0(4(4(4(x1))))))))))
   0(5(0(4(3(2(3(2(4(3(3(x1))))))))))) -> 3(5(0(0(5(5(1(5(0(0(x1))))))))))
   1(0(0(5(4(2(5(2(0(2(0(x1))))))))))) -> 3(0(0(5(4(5(5(4(4(2(x1))))))))))
   1(2(0(3(0(0(4(4(4(1(5(x1))))))))))) -> 1(0(0(2(4(4(0(4(2(3(x1))))))))))
   1(3(1(3(1(2(1(0(1(0(1(x1))))))))))) -> 1(2(0(2(4(5(0(1(5(2(x1))))))))))
   1(4(1(4(0(1(0(1(5(4(1(x1))))))))))) -> 3(0(3(2(2(0(1(3(0(2(x1))))))))))

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