Derivational Complexity: TRS Innermost pair #487106884

details

property	value
status	complete
benchmark	27001.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.82 seconds
cpu usage	860.018
user time	852.073
system time	7.94423
max virtual memory	1.8874852E7
max residence set size	1.4871004E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 41 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), 34 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 4 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (26) CpxRNTS
    (27) CompletionProof [UPPER BOUND(ID), 19 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) NarrowingProof [BOTH BOUNDS(ID, ID), 2016 ms]
        (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 166 ms]
        (32) CpxRNTS
        (33) SimplificationProof [BOTH BOUNDS(ID, ID), 112 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2636 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 393 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 13 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6394 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2666 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2624 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2645 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2672 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2684 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(0(1(0(2(3(4(x1)))))))) -> 0(0(0(1(2(0(3(4(x1))))))))
   2(4(2(3(2(2(5(4(x1)))))))) -> 2(4(3(2(2(5(2(4(x1))))))))
   1(5(2(2(5(3(4(4(5(1(x1)))))))))) -> 1(5(2(2(4(5(3(4(5(1(x1))))))))))
   0(0(4(2(1(3(2(0(4(1(2(x1))))))))))) -> 1(2(2(1(1(5(0(0(3(5(x1))))))))))
   0(2(1(3(4(4(2(3(5(4(4(x1))))))))))) -> 4(1(1(4(2(2(5(0(2(0(x1))))))))))
   0(3(2(0(0(5(5(0(5(0(2(x1))))))))))) -> 5(0(4(0(1(4(0(2(0(0(x1))))))))))
   0(4(1(4(5(4(4(5(2(3(4(x1))))))))))) -> 1(3(4(4(2(2(4(4(5(3(x1))))))))))
   0(4(3(4(3(0(1(0(0(3(2(x1))))))))))) -> 4(3(1(1(4(4(3(0(5(5(x1))))))))))
   0(4(5(1(3(1(1(4(0(2(1(x1))))))))))) -> 4(4(5(0(1(3(1(1(2(3(x1))))))))))
   0(5(0(2(4(5(2(3(2(2(1(x1))))))))))) -> 1(5(5(0(4(5(5(2(3(1(x1))))))))))
   0(5(1(1(4(2(3(0(3(1(3(x1))))))))))) -> 1(3(4(1(3(1(4(0(1(1(x1))))))))))
   0(5(2(3(5(1(4(5(1(1(2(x1))))))))))) -> 3(0(2(4(3(5(5(2(3(0(x1))))))))))
   0(5(4(5(1(0(5(5(2(2(0(x1))))))))))) -> 3(1(2(3(5(4(3(1(0(5(x1))))))))))
   1(0(0(2(0(4(2(4(1(5(3(x1))))))))))) -> 1(4(4(0(1(2(0(3(0(4(x1))))))))))
   1(0(1(1(0(1(4(5(0(3(1(x1))))))))))) -> 0(3(0(3(5(1(2(1(3(0(x1))))))))))
   1(0(3(1(5(2(3(2(0(2(5(x1))))))))))) -> 4(0(3(4(2(2(4(2(5(0(x1))))))))))
   1(2(0(5(5(5(0(5(4(0(2(x1))))))))))) -> 5(5(2(4(3(3(1(4(5(0(x1))))))))))
   1(3(0(4(1(4(4(3(5(5(2(x1))))))))))) -> 1(4(2(0(1(2(5(5(4(0(x1))))))))))
   1(3(4(2(2(3(2(3(5(1(0(x1))))))))))) -> 5(4(3(1(5(3(2(4(4(1(x1))))))))))
   2(0(1(5(3(4(2(3(1(3(1(x1))))))))))) -> 3(0(0(4(4(3(3(4(4(5(x1))))))))))
   2(0(2(4(5(4(5(5(5(0(1(x1))))))))))) -> 3(5(5(5(3(1(0(2(3(2(x1))))))))))
   2(2(4(2(5(4(2(0(4(3(3(x1))))))))))) -> 2(1(1(2(1(5(3(2(1(1(x1))))))))))
   2(4(3(0(4(0(2(1(4(0(5(x1))))))))))) -> 0(4(2(4(1(4(1(5(5(0(x1))))))))))
   2(4(4(2(0(5(5(1(2(2(4(x1))))))))))) -> 2(3(5(5(0(5(5(0(0(1(x1))))))))))
   2(5(5(2(2(3(5(4(0(4(0(x1))))))))))) -> 2(4(3(1(4(3(3(2(2(0(x1))))))))))
   3(1(3(2(5(5(2(2(2(1(3(x1))))))))))) -> 0(2(0(1(3(1(4(4(0(1(x1))))))))))
   3(4(0(5(0(3(5(2(4(4(0(x1))))))))))) -> 3(4(4(3(3(3(5(2(5(1(x1))))))))))

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