Derivational Complexity: TRS Innermost pair #487106718

details

property	value
status	complete
benchmark	25734.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	295.239 seconds
cpu usage	820.292
user time	811.985
system time	8.30705
max virtual memory	1.8848448E7
max residence set size	1.5158468E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 50 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 6 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), 43 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), 1935 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 142 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 113 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2675 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 315 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), 5472 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2400 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2414 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2364 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2378 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2378 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(0(2(3(4(x1)))))) -> 0(1(0(3(2(4(x1))))))
   1(0(3(5(4(1(x1)))))) -> 1(1(3(0(5(4(x1))))))
   3(0(0(1(5(1(5(x1))))))) -> 3(0(0(5(1(1(5(x1)))))))
   5(5(1(3(0(4(5(x1))))))) -> 5(5(3(1(0(4(5(x1)))))))
   2(4(3(2(0(1(5(2(x1)))))))) -> 2(4(2(3(1(0(5(2(x1))))))))
   3(0(2(3(3(5(4(5(1(4(x1)))))))))) -> 3(0(3(2(3(5(4(5(1(4(x1))))))))))
   4(3(5(5(1(4(4(0(0(3(x1)))))))))) -> 4(3(5(5(1(4(0(4(0(3(x1))))))))))
   5(5(4(1(2(3(5(3(5(3(x1)))))))))) -> 5(5(1(4(5(2(3(3(5(3(x1))))))))))
   0(1(4(0(4(2(3(4(4(1(3(x1))))))))))) -> 3(1(5(3(2(2(1(1(5(0(x1))))))))))
   0(2(1(3(2(0(5(4(2(0(5(x1))))))))))) -> 2(2(1(1(3(1(4(5(4(0(x1))))))))))
   0(2(1(3(4(3(5(4(3(5(5(x1))))))))))) -> 1(0(0(1(1(4(1(4(1(3(x1))))))))))
   0(2(3(4(1(4(0(2(3(1(0(x1))))))))))) -> 3(1(0(2(2(1(4(1(5(1(x1))))))))))
   0(3(3(0(0(2(0(5(2(4(2(x1))))))))))) -> 5(4(5(0(3(0(3(0(5(0(x1))))))))))
   0(3(3(2(2(2(0(2(4(0(1(x1))))))))))) -> 5(4(3(1(5(0(0(0(4(2(x1))))))))))
   0(5(0(0(2(4(4(1(5(0(3(x1))))))))))) -> 1(4(3(4(3(3(2(4(3(3(x1))))))))))
   0(5(0(4(1(3(4(4(3(3(3(x1))))))))))) -> 0(0(3(0(3(4(0(4(4(4(x1))))))))))
   0(5(0(4(3(2(3(2(4(3(3(x1))))))))))) -> 3(5(0(0(5(5(1(5(0(0(x1))))))))))
   1(0(0(5(4(2(5(2(0(2(0(x1))))))))))) -> 3(0(0(5(4(5(5(4(4(2(x1))))))))))
   1(2(0(3(0(0(4(4(4(1(5(x1))))))))))) -> 1(0(0(2(4(4(0(4(2(3(x1))))))))))
   1(3(1(3(1(2(1(0(1(0(1(x1))))))))))) -> 1(2(0(2(4(5(0(1(5(2(x1))))))))))
   1(4(1(4(0(1(0(1(5(4(1(x1))))))))))) -> 3(0(3(2(2(0(1(3(0(2(x1))))))))))
   1(4(4(2(1(2(2(3(2(5(5(x1))))))))))) -> 1(1(1(5(1(0(1(5(4(2(x1))))))))))
   1(5(3(5(1(1(4(4(3(0(2(x1))))))))))) -> 0(5(0(0(0(0(2(0(1(3(x1))))))))))
   2(0(2(1(1(2(4(4(1(2(4(x1))))))))))) -> 5(5(3(1(0(5(5(5(3(0(x1))))))))))
   2(0(3(1(3(1(5(0(5(1(5(x1))))))))))) -> 5(3(1(3(5(2(4(0(4(4(x1))))))))))
   2(0(5(2(1(1(3(1(3(4(1(x1))))))))))) -> 2(3(1(3(1(4(0(3(1(3(x1))))))))))
   2(2(1(2(0(0(1(1(0(2(4(x1))))))))))) -> 0(1(5(1(5(0(2(5(4(0(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost