Derivational Complexity: TRS pair #487102728

details

property	value
status	complete
benchmark	27026.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	298.041 seconds
cpu usage	789.028
user time	781.347
system time	7.68121
max virtual memory	1.8849676E7
max residence set size	1.49731E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 89 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 3 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 3 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 16 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), 1577 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), 2084 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 67 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 92 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 13 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 32 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 942 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 10 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 18 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6767 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1886 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1905 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1888 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1877 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(2(2(0(3(4(5(1(x1))))))))) -> 0(1(2(2(3(0(4(5(1(x1)))))))))
   1(3(4(5(3(4(5(1(1(x1))))))))) -> 1(5(3(4(4(1(5(3(1(x1)))))))))
   0(3(1(1(1(0(3(4(1(3(x1)))))))))) -> 2(2(2(2(5(2(4(4(0(2(x1))))))))))
   0(4(4(3(3(0(0(0(3(5(x1)))))))))) -> 0(4(3(4(3(0(0(0(3(5(x1))))))))))
   1(0(2(5(1(4(2(5(1(0(x1)))))))))) -> 2(4(2(1(0(3(2(2(5(4(x1))))))))))
   1(1(4(5(1(0(0(5(2(1(x1)))))))))) -> 2(4(3(4(0(2(4(1(5(3(x1))))))))))
   1(2(2(3(3(0(1(5(4(1(x1)))))))))) -> 1(0(2(4(3(1(2(4(2(3(x1))))))))))
   1(2(4(5(1(0(3(1(4(4(x1)))))))))) -> 1(2(4(5(1(3(0(1(4(4(x1))))))))))
   1(2(4(5(1(1(0(1(0(2(x1)))))))))) -> 2(2(4(1(0(1(2(1(5(2(x1))))))))))
   1(3(4(2(0(4(5(0(1(3(x1)))))))))) -> 1(2(4(0(1(0(5(3(4(3(x1))))))))))
   1(5(4(4(4(3(4(3(0(5(x1)))))))))) -> 2(5(1(2(4(2(4(0(2(5(x1))))))))))
   3(0(1(2(1(2(5(0(0(1(x1)))))))))) -> 3(0(1(2(1(5(2(0(0(1(x1))))))))))
   4(0(0(4(5(1(1(5(1(5(x1)))))))))) -> 4(2(5(0(2(4(3(4(4(4(x1))))))))))
   0(0(0(5(4(2(3(3(3(1(0(x1))))))))))) -> 5(2(5(0(0(3(3(2(3(5(x1))))))))))
   0(0(1(0(0(3(2(0(4(1(5(x1))))))))))) -> 3(5(2(3(3(4(3(5(5(1(x1))))))))))
   0(1(0(5(3(5(1(2(1(2(1(x1))))))))))) -> 1(3(5(0(5(1(5(5(2(0(x1))))))))))
   0(1(3(4(5(2(1(3(5(0(4(x1))))))))))) -> 1(4(4(5(1(0(3(5(3(5(x1))))))))))
   0(1(4(1(2(1(4(5(0(2(1(x1))))))))))) -> 2(4(3(4(1(0(5(3(3(4(x1))))))))))
   0(2(2(2(0(2(3(1(5(1(1(x1))))))))))) -> 1(5(0(3(4(4(4(3(1(3(x1))))))))))
   0(2(3(3(0(4(2(4(3(0(1(x1))))))))))) -> 3(4(5(0(2(0(4(0(1(5(x1))))))))))
   0(5(1(2(1(1(2(1(2(1(0(x1))))))))))) -> 1(2(1(2(1(3(0(4(4(3(x1))))))))))
   1(0(0(4(1(1(5(5(4(4(0(x1))))))))))) -> 4(0(4(0(2(5(1(0(3(5(x1))))))))))
   1(0(2(5(1(5(1(3(4(0(0(x1))))))))))) -> 1(0(2(5(5(1(1(3(4(0(0(x1)))))))))))
   1(0(5(1(4(5(3(5(4(4(5(x1))))))))))) -> 1(5(5(5(4(3(0(4(1(4(5(x1)))))))))))
   1(2(5(5(1(4(5(5(1(0(1(x1))))))))))) -> 0(3(5(5(2(3(0(4(2(5(x1))))))))))
   1(3(2(2(0(3(3(5(5(3(1(x1))))))))))) -> 2(3(5(3(1(2(5(1(5(4(x1))))))))))
   1(4(3(5(5(1(0(4(3(2(0(x1))))))))))) -> 3(2(4(3(2(4(0(3(5(4(x1))))))))))

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