Derivational Complexity: TRS Innermost pair #487106676

details

property	value
status	complete
benchmark	136623.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.533 seconds
cpu usage	876.431
user time	868.915
system time	7.51585
max virtual memory	1.888584E7
max residence set size	1.4787592E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 59 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 7 ms]
(12) TRS for Loop Detection
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 15 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1942 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 131 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 107 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2248 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 22 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 7 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 10.0 s]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2729 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2703 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2720 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2720 ms]
    (52) CdtProblem


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(4(4(3(1(3(5(3(5(4(5(x1)))))))))))) -> 4(1(0(0(2(5(4(0(3(2(1(0(5(4(3(x1)))))))))))))))
   0(3(2(0(2(5(3(4(3(3(5(4(x1)))))))))))) -> 5(5(4(0(4(1(2(0(0(1(5(0(4(0(x1))))))))))))))
   0(3(3(4(4(2(0(4(2(4(0(2(x1)))))))))))) -> 1(0(0(5(4(1(1(1(5(5(0(4(2(1(x1))))))))))))))
   0(4(3(1(3(1(2(2(0(3(3(2(x1)))))))))))) -> 3(2(0(0(2(0(0(5(1(4(1(3(0(0(4(1(x1))))))))))))))))
   0(4(5(5(0(2(1(3(4(4(4(1(x1)))))))))))) -> 0(3(0(0(2(1(1(5(0(3(4(1(4(0(x1))))))))))))))
   0(5(2(4(2(3(1(2(2(2(2(1(x1)))))))))))) -> 0(1(0(0(0(2(4(2(2(5(5(4(2(5(1(x1)))))))))))))))
   0(5(3(0(5(3(3(2(3(2(3(4(x1)))))))))))) -> 0(3(5(1(0(3(0(0(0(0(4(4(1(2(x1))))))))))))))
   1(0(2(5(5(3(4(4(2(2(2(2(x1)))))))))))) -> 0(3(1(5(0(5(1(0(5(2(1(2(4(1(1(0(x1))))))))))))))))
   1(1(2(3(5(2(5(3(5(2(2(2(x1)))))))))))) -> 0(2(1(1(5(1(1(5(4(0(2(4(5(4(5(1(1(5(x1))))))))))))))))))
   1(2(2(3(4(1(4(1(0(5(5(1(x1)))))))))))) -> 0(0(3(5(1(0(5(1(0(2(5(0(1(5(x1))))))))))))))
   1(2(4(4(4(4(3(5(5(0(4(5(x1)))))))))))) -> 1(0(0(0(0(4(5(1(5(5(0(2(0(5(2(5(1(x1)))))))))))))))))
   1(3(3(1(2(3(5(5(2(0(4(3(x1)))))))))))) -> 5(5(4(4(0(1(0(5(1(0(2(1(0(4(5(x1)))))))))))))))
   1(3(5(2(0(4(4(3(1(4(4(3(x1)))))))))))) -> 0(0(5(0(0(0(4(2(5(3(5(1(2(1(2(0(x1))))))))))))))))
   1(3(5(4(4(3(1(1(4(2(0(0(x1)))))))))))) -> 4(3(1(0(1(5(2(0(0(0(5(1(0(0(x1))))))))))))))
   1(5(3(4(2(2(4(3(4(5(1(1(x1)))))))))))) -> 0(0(2(0(1(5(0(1(5(4(0(3(5(0(1(0(0(5(x1))))))))))))))))))
   2(0(1(2(4(2(4(1(3(4(4(0(x1)))))))))))) -> 0(0(0(5(0(5(5(5(4(5(1(0(5(4(3(0(x1))))))))))))))))
   2(0(2(1(3(3(5(3(4(2(5(2(x1)))))))))))) -> 4(4(4(0(5(0(1(2(1(4(4(1(0(1(x1))))))))))))))
   2(0(2(2(3(3(3(5(2(3(0(2(x1)))))))))))) -> 5(0(0(4(1(4(5(3(3(4(3(0(5(5(0(x1)))))))))))))))
   2(0(2(4(1(5(2(5(2(5(1(2(x1)))))))))))) -> 0(3(4(5(4(5(0(3(2(1(5(4(2(1(x1))))))))))))))
   2(0(3(4(2(3(5(5(4(3(0(4(x1)))))))))))) -> 4(5(4(0(5(5(4(0(0(1(5(2(0(1(5(x1)))))))))))))))
   2(1(1(1(5(2(5(2(2(3(5(5(x1)))))))))))) -> 4(0(0(0(5(1(0(1(5(1(5(2(0(1(1(5(x1))))))))))))))))
   2(1(5(3(1(3(2(2(4(1(0(0(x1)))))))))))) -> 1(1(0(3(1(1(2(0(2(1(5(1(0(4(x1))))))))))))))
   2(2(1(3(3(5(3(3(2(3(3(1(x1)))))))))))) -> 1(0(5(5(0(0(0(0(3(5(0(5(1(0(0(0(2(0(x1))))))))))))))))))
   2(2(2(3(5(3(2(2(4(5(3(0(x1)))))))))))) -> 3(0(1(0(5(1(5(1(0(2(0(0(4(2(1(1(2(x1)))))))))))))))))
   2(2(3(2(4(2(3(1(1(0(4(5(x1)))))))))))) -> 5(4(2(3(5(1(1(1(5(5(1(0(5(0(0(x1)))))))))))))))
   2(2(3(2(4(2(3(1(2(3(2(4(x1)))))))))))) -> 0(4(4(1(0(2(1(4(0(4(5(0(0(0(2(4(0(x1)))))))))))))))))
   2(2(3(3(3(5(5(3(2(3(1(3(x1)))))))))))) -> 1(5(0(0(4(1(1(3(3(1(0(0(0(4(2(1(5(4(x1))))))))))))))))))
   2(3(0(3(1(5(3(5(5(1(2(2(x1)))))))))))) -> 1(0(4(0(5(4(1(1(5(0(5(4(2(0(4(x1)))))))))))))))
   2(3(1(4(2(4(2(2(3(5(2(3(x1)))))))))))) -> 1(1(2(1(3(4(1(5(0(2(0(2(5(5(x1))))))))))))))

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job log

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actions all output return to Derivational Complexity: TRS Innermost