Derivational Complexity: TRS Innermost pair #487106484

details

property	value
status	complete
benchmark	138477.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)	296.036 seconds
cpu usage	884.813
user time	877.338
system time	7.47561
max virtual memory	1.8687232E7
max residence set size	1.4941888E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 51 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 5 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 5 ms]
    (12) typed CpxTrs
(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), 40 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), 2108 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 178 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 116 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2134 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 50 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 1 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 9947 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2957 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2926 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2926 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2918 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(0(3(3(4(0(0(2(0(5(0(x1)))))))))))) -> 5(1(3(3(1(3(3(5(1(4(4(2(3(5(1(2(5(x1)))))))))))))))))
   0(0(0(5(3(0(2(5(0(0(2(3(x1)))))))))))) -> 3(1(1(0(3(4(5(3(2(1(1(1(4(0(4(1(4(3(x1))))))))))))))))))
   0(0(2(4(4(3(1(0(0(2(5(4(x1)))))))))))) -> 2(5(1(4(5(2(1(5(1(1(2(4(0(1(x1))))))))))))))
   0(0(4(3(3(4(3(4(2(3(4(0(x1)))))))))))) -> 1(2(4(0(2(5(1(1(3(3(3(2(5(4(x1))))))))))))))
   0(1(4(0(0(0(2(3(4(3(4(4(x1)))))))))))) -> 4(5(1(5(1(1(5(5(1(1(3(4(1(3(5(3(1(3(x1))))))))))))))))))
   0(1(5(3(1(5(3(3(0(0(1(2(x1)))))))))))) -> 3(5(1(1(1(5(0(1(1(5(3(1(3(1(2(5(1(x1)))))))))))))))))
   0(2(1(5(4(4(3(4(4(4(4(0(x1)))))))))))) -> 0(1(1(1(1(1(3(1(1(1(0(2(4(1(0(0(5(3(x1))))))))))))))))))
   0(2(3(0(0(5(4(5(0(0(4(5(x1)))))))))))) -> 1(4(2(1(0(1(1(4(5(3(5(3(5(2(1(2(2(3(x1))))))))))))))))))
   0(3(0(2(2(3(3(0(1(4(0(0(x1)))))))))))) -> 4(2(3(1(4(1(1(4(4(2(1(2(2(1(2(5(x1))))))))))))))))
   0(3(1(5(5(4(3(4(0(5(1(4(x1)))))))))))) -> 1(3(5(2(1(1(1(5(5(4(3(1(1(5(1(4(1(3(x1))))))))))))))))))
   0(3(2(0(0(3(2(5(0(1(2(4(x1)))))))))))) -> 1(3(3(2(4(2(5(0(1(1(1(0(1(1(5(x1)))))))))))))))
   0(3(3(4(4(4(0(4(4(4(2(2(x1)))))))))))) -> 5(0(1(2(3(2(4(1(1(5(1(1(3(5(1(5(2(3(x1))))))))))))))))))
   0(4(0(1(4(4(0(0(5(3(2(5(x1)))))))))))) -> 1(1(1(2(4(5(1(3(4(5(2(0(5(3(x1))))))))))))))
   0(4(3(3(0(4(3(1(2(0(0(0(x1)))))))))))) -> 3(1(0(2(5(3(3(1(1(1(1(2(2(1(4(3(4(2(x1))))))))))))))))))
   0(4(4(3(0(2(2(0(5(4(4(1(x1)))))))))))) -> 4(1(3(1(1(4(1(1(1(1(1(5(5(2(4(3(3(x1)))))))))))))))))
   0(4(4(3(1(4(0(3(3(1(5(2(x1)))))))))))) -> 1(0(4(5(1(1(1(1(1(3(2(3(1(1(1(0(5(1(x1))))))))))))))))))
   0(5(0(2(0(5(2(3(3(4(1(5(x1)))))))))))) -> 3(3(3(2(3(1(4(4(5(4(4(1(5(2(1(5(x1))))))))))))))))
   0(5(1(4(4(5(2(0(0(0(4(2(x1)))))))))))) -> 1(3(4(5(2(1(5(1(2(3(2(1(1(3(x1))))))))))))))
   0(5(3(2(4(5(0(3(0(0(5(1(x1)))))))))))) -> 3(1(4(1(3(0(5(3(1(1(1(0(1(1(2(x1)))))))))))))))
   0(5(4(4(0(3(0(3(1(5(2(1(x1)))))))))))) -> 2(2(0(1(1(3(4(5(1(1(0(0(1(1(x1))))))))))))))
   0(5(5(4(5(5(0(2(3(0(4(5(x1)))))))))))) -> 1(1(1(3(5(4(5(0(1(3(3(1(0(4(3(x1)))))))))))))))
   0(5(5(5(1(5(3(3(4(4(3(4(x1)))))))))))) -> 1(0(0(5(1(3(2(1(1(4(1(5(5(4(3(x1)))))))))))))))
   1(0(1(3(4(0(5(5(1(4(3(0(x1)))))))))))) -> 4(1(3(2(1(1(1(1(5(4(1(1(1(3(5(5(3(2(x1))))))))))))))))))
   1(0(3(1(3(0(5(5(0(5(4(0(x1)))))))))))) -> 1(4(5(2(0(1(1(4(2(4(3(1(5(3(5(1(3(5(x1))))))))))))))))))
   1(1(3(5(3(3(5(1(0(0(0(5(x1)))))))))))) -> 1(2(4(1(1(3(2(2(3(2(1(1(1(4(5(x1)))))))))))))))
   1(3(3(0(1(1(0(5(3(5(0(3(x1)))))))))))) -> 4(5(1(5(1(5(5(3(5(2(1(1(2(2(x1))))))))))))))
   1(4(3(0(3(0(4(2(3(0(4(4(x1)))))))))))) -> 5(2(4(5(4(1(3(1(1(1(3(5(1(3(4(5(0(x1)))))))))))))))))
   1(4(4(0(2(2(0(1(5(0(5(0(x1)))))))))))) -> 1(3(5(2(3(1(3(1(0(0(2(5(2(4(x1))))))))))))))
   1(4(4(3(0(3(0(3(4(5(4(1(x1)))))))))))) -> 2(1(1(4(1(2(1(1(2(1(2(1(1(3(1(3(3(x1)))))))))))))))))

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actions all output return to Derivational Complexity: TRS Innermost