Derivational Complexity: TRS pair #487103308

details

property	value
status	complete
benchmark	139018.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.137 seconds
cpu usage	963.558
user time	956.345
system time	7.21245
max virtual memory	1.8882592E7
max residence set size	1.483836E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 94 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), 18 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), 1458 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 31 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 1607 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 68 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 48 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 31 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 1010 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 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), 7625 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2296 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2295 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2260 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2191 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5618 ms]
        (56) CdtProblem
        (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 27 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6000 ms]
        (60) CdtProblem
        (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 24 ms]
        (62) 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(1(0(1(2(2(3(3(0(1(3(2(0(2(0(1(3(x1)))))))))))))))))) -> 0(3(2(3(2(2(1(0(0(1(1(1(0(2(0(3(1(3(x1))))))))))))))))))
   0(1(1(2(0(1(3(2(2(1(3(0(1(2(0(3(0(1(x1)))))))))))))))))) -> 0(2(1(0(3(1(2(1(0(0(1(2(3(1(2(3(0(1(x1))))))))))))))))))
   0(1(1(2(2(0(0(1(1(1(1(3(3(0(2(2(2(1(x1)))))))))))))))))) -> 0(0(2(2(0(1(1(2(0(1(1(2(1(2(3(1(3(1(x1))))))))))))))))))
   0(1(3(0(3(1(0(2(1(1(1(3(3(0(3(1(2(3(x1)))))))))))))))))) -> 0(1(3(2(0(1(3(1(0(3(3(2(1(3(1(0(1(3(x1))))))))))))))))))
   0(2(0(2(0(0(1(1(2(0(0(0(1(2(2(2(0(0(x1)))))))))))))))))) -> 0(2(1(0(2(0(1(2(2(2(1(0(2(0(0(0(0(0(x1))))))))))))))))))
   0(2(1(1(3(0(1(0(1(0(0(0(3(1(0(1(1(1(x1)))))))))))))))))) -> 0(0(1(1(3(1(0(3(0(0(2(0(0(1(1(1(1(1(x1))))))))))))))))))
   0(2(2(3(0(1(2(2(2(3(3(3(3(2(2(0(3(3(x1)))))))))))))))))) -> 0(0(1(2(3(3(2(0(3(3(2(2(2(2(3(2(3(3(x1))))))))))))))))))
   0(2(2(3(2(2(2(3(3(0(0(3(3(1(1(0(3(3(x1)))))))))))))))))) -> 0(0(3(1(3(0(2(3(2(1(3(0(2(2(3(2(3(3(x1))))))))))))))))))
   0(3(0(0(1(0(2(3(2(1(3(0(1(1(1(0(2(3(x1)))))))))))))))))) -> 0(0(3(0(1(1(2(1(0(3(2(1(3(1(0(0(2(3(x1))))))))))))))))))
   0(3(0(3(3(1(0(2(2(2(3(3(2(0(3(0(0(1(x1)))))))))))))))))) -> 0(0(2(2(3(3(3(0(0(3(1(0(0(2(3(3(2(1(x1))))))))))))))))))
   0(3(2(1(0(1(2(1(3(2(0(1(0(1(2(3(2(3(x1)))))))))))))))))) -> 0(3(2(0(3(1(1(0(3(2(1(0(2(2(1(2(1(3(x1))))))))))))))))))
   0(3(3(0(3(0(3(2(0(3(3(1(0(0(3(1(1(0(x1)))))))))))))))))) -> 0(0(3(3(0(3(3(3(1(1(3(2(0(0(0(3(1(0(x1))))))))))))))))))
   0(3(3(0(3(2(0(2(0(1(1(3(0(0(0(3(0(3(x1)))))))))))))))))) -> 0(3(0(0(0(0(3(0(0(1(3(2(2(3(1(3(0(3(x1))))))))))))))))))
   1(0(0(1(2(3(1(3(0(1(2(0(1(0(2(1(0(3(x1)))))))))))))))))) -> 1(3(3(2(1(1(0(0(2(0(1(3(1(0(0(0(1(2(x1))))))))))))))))))
   1(0(0(3(3(3(3(2(2(2(3(2(3(3(3(2(3(3(x1)))))))))))))))))) -> 2(3(2(3(1(3(3(2(2(3(2(3(3(0(0(3(3(3(x1))))))))))))))))))
   1(0(1(0(3(3(0(0(2(2(3(1(2(2(2(2(1(2(x1)))))))))))))))))) -> 2(3(2(0(0(2(0(0(2(1(2(1(1(2(3(1(3(2(x1))))))))))))))))))
   1(0(3(0(0(0(1(3(3(1(0(0(2(3(0(1(1(0(x1)))))))))))))))))) -> 1(2(0(0(0(1(0(1(3(1(3(0(1(3(3(0(0(0(x1))))))))))))))))))
   1(0(3(2(0(0(3(3(3(3(3(2(2(1(2(2(1(1(x1)))))))))))))))))) -> 0(3(2(3(1(3(1(2(1(3(1(2(3(2(0(0(3(2(x1))))))))))))))))))
   1(0(3(3(0(2(0(3(2(1(2(3(3(0(0(1(1(2(x1)))))))))))))))))) -> 2(0(1(3(1(0(1(0(0(2(0(3(1(3(2(2(3(3(x1))))))))))))))))))

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actions all output return to Derivational Complexity: TRS