Derivational Complexity: TRS pair #487102906

details

property	value
status	complete
benchmark	133159.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	299.041 seconds
cpu usage	892.499
user time	884.829
system time	7.67065
max virtual memory	1.8952184E7
max residence set size	1.4889368E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 45 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), 1037 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), 5 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2383 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 193 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 129 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 993 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 7 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 7267 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2094 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2058 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2034 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2022 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2088 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(0(0(2(0(4(3(0(3(4(4(x1)))))))))))) -> 4(3(3(0(0(1(5(0(1(5(5(4(3(5(x1))))))))))))))
   0(0(0(1(0(0(2(2(0(1(4(1(x1)))))))))))) -> 1(2(3(1(3(3(1(0(5(5(2(5(2(3(5(5(5(5(x1))))))))))))))))))
   0(0(1(1(2(0(0(2(2(2(2(2(x1)))))))))))) -> 1(5(1(1(3(2(5(1(4(5(3(1(3(4(5(0(4(5(x1))))))))))))))))))
   0(0(1(1(2(1(1(3(0(0(1(2(x1)))))))))))) -> 3(0(2(4(2(5(2(2(3(1(0(1(5(0(x1))))))))))))))
   0(0(1(2(1(1(1(2(0(2(0(0(x1)))))))))))) -> 2(0(5(2(5(5(5(0(5(0(3(5(4(0(2(2(0(x1)))))))))))))))))
   0(0(1(2(4(2(1(1(2(1(2(4(x1)))))))))))) -> 3(2(5(0(4(4(1(3(1(0(4(1(5(5(0(5(5(5(x1))))))))))))))))))
   0(0(2(0(0(1(4(3(2(0(0(3(x1)))))))))))) -> 2(5(0(4(4(4(2(2(0(5(3(2(5(0(4(2(4(x1)))))))))))))))))
   0(0(2(0(2(2(2(2(5(3(4(0(x1)))))))))))) -> 2(5(4(1(5(4(0(3(3(3(3(3(0(5(2(5(3(x1)))))))))))))))))
   0(1(0(1(4(4(3(1(2(1(1(0(x1)))))))))))) -> 3(5(3(1(5(4(5(5(4(3(5(3(3(0(4(4(x1))))))))))))))))
   0(1(0(2(4(2(0(0(1(2(1(1(x1)))))))))))) -> 2(0(4(5(3(5(4(4(5(0(0(1(1(5(x1))))))))))))))
   0(1(2(1(2(1(0(2(2(0(2(0(x1)))))))))))) -> 2(5(1(5(2(0(0(4(4(0(2(4(2(5(1(1(3(0(x1))))))))))))))))))
   0(2(0(2(1(5(3(2(1(4(4(5(x1)))))))))))) -> 0(3(1(4(5(3(5(5(2(0(5(3(0(5(4(x1)))))))))))))))
   0(2(0(3(4(2(2(2(4(4(5(4(x1)))))))))))) -> 3(5(5(5(1(1(5(3(4(2(4(5(4(3(x1))))))))))))))
   0(2(2(2(3(4(4(4(5(5(1(2(x1)))))))))))) -> 2(0(4(5(4(1(4(5(1(2(4(4(1(2(4(x1)))))))))))))))
   0(2(2(3(4(2(1(2(0(2(3(0(x1)))))))))))) -> 3(1(5(0(4(2(2(5(5(5(1(3(5(5(5(3(0(1(x1))))))))))))))))))
   0(2(5(1(2(5(0(2(2(0(3(5(x1)))))))))))) -> 1(5(3(4(3(4(4(3(4(1(3(5(5(1(x1))))))))))))))
   0(3(1(0(0(1(2(0(0(0(0(5(x1)))))))))))) -> 1(1(5(1(0(1(4(2(0(2(4(5(1(3(x1))))))))))))))
   1(0(0(0(0(3(3(4(4(0(0(3(x1)))))))))))) -> 4(5(4(2(5(0(5(3(3(5(0(4(3(0(5(0(x1))))))))))))))))
   1(0(0(2(0(3(4(4(4(1(1(2(x1)))))))))))) -> 1(5(2(2(5(2(2(5(2(5(4(5(4(0(5(0(x1))))))))))))))))
   1(1(0(1(1(0(2(3(1(3(1(5(x1)))))))))))) -> 4(5(4(1(5(5(4(1(4(4(1(4(1(1(x1))))))))))))))
   1(1(0(4(0(2(3(4(3(2(2(2(x1)))))))))))) -> 0(5(5(0(5(3(2(2(4(3(2(4(4(4(x1))))))))))))))
   1(1(2(0(2(3(4(1(1(4(1(0(x1)))))))))))) -> 1(2(1(5(2(4(2(5(4(3(5(1(3(5(1(5(x1))))))))))))))))
   1(2(2(1(0(0(3(5(3(4(1(2(x1)))))))))))) -> 3(5(5(5(1(4(3(0(0(4(5(5(4(2(x1))))))))))))))
   1(2(2(1(1(4(1(0(0(1(5(0(x1)))))))))))) -> 5(1(5(5(4(5(3(1(0(5(5(2(5(0(5(0(5(x1)))))))))))))))))
   1(2(2(2(3(4(3(2(0(3(5(1(x1)))))))))))) -> 5(0(5(2(4(0(4(1(5(2(5(4(0(5(1(3(5(3(x1))))))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS