Derivational Complexity: TRS Innermost pair #487106186

details

property	value
status	complete
benchmark	26132.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.464 seconds
cpu usage	868.125
user time	859.659
system time	8.46603
max virtual memory	1.8721536E7
max residence set size	1.5046512E7

stage attributes

key	value
starexec-result	KILLED

output

KILLED
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 84 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) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 37 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 4 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 17 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2622 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 268 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 232 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 33 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 3565 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 393 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6037 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3005 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2960 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3011 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2996 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2936 ms]
    (54) 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(1(2(3(3(4(x1)))))) -> 0(2(1(3(3(4(x1))))))
   4(4(3(0(4(2(4(x1))))))) -> 4(4(3(4(0(2(4(x1)))))))
   3(1(2(0(0(4(3(2(x1)))))))) -> 3(1(0(2(0(4(3(2(x1))))))))
   0(1(2(4(3(0(2(0(3(x1))))))))) -> 0(2(1(4(3(0(2(0(3(x1)))))))))
   0(5(5(3(5(3(0(5(3(3(x1)))))))))) -> 0(5(5(3(3(5(0(5(3(3(x1))))))))))
   2(1(2(4(5(4(1(2(5(0(x1)))))))))) -> 3(1(1(1(0(1(4(1(5(0(x1))))))))))
   2(4(4(2(0(2(1(5(4(5(x1)))))))))) -> 1(1(2(1(5(5(5(2(4(5(x1))))))))))
   4(1(1(1(0(0(0(0(2(0(x1)))))))))) -> 4(1(1(0(1(0(0(0(2(0(x1))))))))))
   4(4(1(5(1(1(0(0(4(3(x1)))))))))) -> 4(2(1(3(2(1(0(0(4(3(x1))))))))))
   0(0(5(3(1(3(0(2(2(2(3(x1))))))))))) -> 4(1(2(0(2(3(1(4(3(0(x1))))))))))
   0(5(1(0(4(5(5(3(4(1(3(x1))))))))))) -> 1(3(2(2(1(3(0(0(0(3(x1))))))))))
   0(5(1(4(5(2(2(4(4(5(1(x1))))))))))) -> 1(0(1(2(5(0(1(0(0(4(x1))))))))))
   0(5(3(2(4(4(3(1(1(5(0(x1))))))))))) -> 3(5(0(3(0(5(1(0(4(1(x1))))))))))
   1(1(4(5(3(4(5(5(3(2(0(x1))))))))))) -> 5(3(0(2(1(5(1(0(3(3(x1))))))))))
   1(2(4(3(0(2(3(0(0(5(1(x1))))))))))) -> 1(1(3(1(5(2(5(0(4(3(x1))))))))))
   1(5(1(3(4(4(3(3(5(4(2(x1))))))))))) -> 3(4(0(0(2(1(3(3(2(0(x1))))))))))
   2(0(0(0(4(1(1(2(4(3(3(x1))))))))))) -> 5(5(2(2(2(4(5(0(1(5(x1))))))))))
   2(0(4(5(4(4(4(5(3(2(4(x1))))))))))) -> 3(4(0(0(3(4(2(3(0(1(x1))))))))))
   2(2(3(1(1(4(4(5(5(3(5(x1))))))))))) -> 1(2(1(0(3(4(4(3(1(5(x1))))))))))
   2(5(5(1(4(4(0(2(0(4(2(x1))))))))))) -> 5(4(0(1(3(3(4(5(5(4(x1))))))))))
   3(0(0(4(3(1(5(4(2(2(1(x1))))))))))) -> 3(4(2(3(4(0(1(4(2(5(x1))))))))))
   3(0(5(5(1(4(5(1(0(2(2(x1))))))))))) -> 5(4(1(4(5(2(0(4(0(3(x1))))))))))
   3(1(0(2(2(5(0(0(2(3(2(x1))))))))))) -> 4(0(5(2(4(0(5(3(1(2(x1))))))))))
   3(1(3(5(3(3(5(1(2(2(5(x1))))))))))) -> 1(4(2(1(5(3(3(1(0(2(x1))))))))))
   3(2(1(2(4(3(4(2(5(0(1(x1))))))))))) -> 5(1(3(5(1(1(0(4(2(3(x1))))))))))
   3(3(1(5(4(5(1(2(4(4(3(x1))))))))))) -> 2(3(3(5(2(4(2(1(0(2(x1))))))))))
   3(4(4(2(0(1(1(4(0(2(3(x1))))))))))) -> 5(5(2(2(2(0(4(5(5(2(x1))))))))))

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