Derivational Complexity: TRS Innermost pair #487106740

details

property	value
status	complete
benchmark	26741.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)	296.697 seconds
cpu usage	850.849
user time	842.716
system time	8.13244
max virtual memory	1.8746628E7
max residence set size	1.4788696E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 43 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 7 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 16 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), 24 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 10 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 2031 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 149 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 134 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 1 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2824 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 320 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), 5732 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2728 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2736 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2746 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2754 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2751 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(0(1(2(3(2(4(x1))))))) -> 0(0(2(1(3(2(4(x1)))))))
   2(3(0(3(2(5(2(4(3(x1))))))))) -> 2(3(4(2(0(3(5(2(3(x1)))))))))
   1(2(4(3(0(3(2(2(1(3(x1)))))))))) -> 3(1(4(1(4(3(0(0(0(2(x1))))))))))
   2(1(5(1(5(3(2(5(5(1(x1)))))))))) -> 5(2(2(2(5(4(5(1(4(1(x1))))))))))
   2(2(3(2(0(5(1(2(1(5(x1)))))))))) -> 2(0(3(2(4(4(3(4(4(5(x1))))))))))
   2(5(5(1(5(5(0(4(1(5(x1)))))))))) -> 4(3(4(0(1(1(2(0(0(2(x1))))))))))
   3(2(3(1(2(3(3(3(0(4(x1)))))))))) -> 3(2(0(0(1(4(3(1(2(2(x1))))))))))
   0(0(1(0(4(1(3(3(0(0(1(x1))))))))))) -> 4(3(4(4(1(4(1(0(2(5(x1))))))))))
   0(1(1(1(1(4(0(2(2(0(5(x1))))))))))) -> 0(5(3(2(5(3(5(4(4(1(x1))))))))))
   0(1(1(1(4(2(4(4(2(0(1(x1))))))))))) -> 2(1(4(1(4(2(0(4(1(0(1(x1)))))))))))
   0(1(5(1(2(5(4(3(4(0(2(x1))))))))))) -> 5(1(1(3(5(4(5(4(0(5(x1))))))))))
   1(1(3(3(5(5(2(1(3(3(5(x1))))))))))) -> 4(3(1(4(3(3(3(0(2(2(x1))))))))))
   1(2(3(2(2(2(0(3(4(0(4(x1))))))))))) -> 1(4(2(4(2(1(2(0(3(4(x1))))))))))
   1(3(4(3(1(4(5(5(4(2(0(x1))))))))))) -> 0(5(0(2(2(0(4(0(5(2(x1))))))))))
   1(4(1(3(1(4(5(2(2(4(4(x1))))))))))) -> 2(4(3(0(4(0(5(0(0(4(x1))))))))))
   1(5(3(4(1(3(5(4(4(5(4(x1))))))))))) -> 5(3(2(4(4(1(5(0(3(5(x1))))))))))
   2(0(2(1(1(4(3(2(3(3(1(x1))))))))))) -> 4(0(5(3(1(0(5(5(4(4(x1))))))))))
   2(1(0(2(1(3(1(5(3(0(1(x1))))))))))) -> 5(3(4(3(2(5(4(5(0(2(x1))))))))))
   2(1(0(5(1(5(1(1(5(2(1(x1))))))))))) -> 3(3(3(5(2(1(0(2(3(5(x1))))))))))
   2(1(1(5(1(3(4(4(4(1(0(x1))))))))))) -> 3(1(3(4(1(0(2(1(5(1(x1))))))))))
   2(1(2(0(3(5(1(0(1(4(2(x1))))))))))) -> 4(5(0(4(0(1(2(0(3(4(x1))))))))))
   2(2(2(0(3(4(2(4(2(2(2(x1))))))))))) -> 4(0(3(1(0(0(4(3(4(1(x1))))))))))
   2(3(2(0(2(4(1(5(5(1(1(x1))))))))))) -> 4(3(2(3(3(3(5(5(5(5(x1))))))))))
   2(3(2(2(1(4(1(3(0(3(2(x1))))))))))) -> 1(0(1(2(0(3(4(2(5(0(x1))))))))))
   3(0(4(2(1(1(2(5(5(1(4(x1))))))))))) -> 4(2(3(4(3(2(0(3(4(1(x1))))))))))
   3(1(0(1(0(4(0(5(4(5(5(x1))))))))))) -> 4(4(5(1(5(4(0(0(2(0(x1))))))))))
   3(1(5(4(4(1(2(5(1(4(1(x1))))))))))) -> 3(2(0(5(5(5(2(2(1(1(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost