Derivational Complexity: TRS Innermost pair #487107014

details

property	value
status	complete
benchmark	25736.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.834 seconds
cpu usage	820.26
user time	812.229
system time	8.03072
max virtual memory	1.8719328E7
max residence set size	1.4847348E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 42 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), 1 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), 28 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 9 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 22 ms]
        (26) CpxRNTS
    (27) CompletionProof [UPPER BOUND(ID), 8 ms]
    (28) CpxTypedWeightedCompleteTrs
        (29) NarrowingProof [BOTH BOUNDS(ID, ID), 2320 ms]
        (30) CpxTypedWeightedCompleteTrs
        (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 188 ms]
        (32) CpxRNTS
        (33) SimplificationProof [BOTH BOUNDS(ID, ID), 141 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2761 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 353 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), 4963 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2447 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2400 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2424 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2369 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2359 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(1(2(0(3(x1)))))) -> 0(1(2(1(0(3(x1))))))
   4(3(1(2(1(4(2(x1))))))) -> 4(3(1(1(2(4(2(x1)))))))
   2(2(0(0(1(2(3(4(x1)))))))) -> 2(2(0(1(3(0(2(4(x1))))))))
   0(5(5(2(3(5(0(3(1(x1))))))))) -> 0(5(2(5(3(5(0(3(1(x1)))))))))
   3(5(2(1(1(0(0(1(2(x1))))))))) -> 3(5(1(0(2(1(0(1(2(x1)))))))))
   5(2(5(3(4(1(2(4(4(x1))))))))) -> 5(2(5(3(1(2(4(4(4(x1)))))))))
   0(1(0(3(2(3(4(0(4(3(x1)))))))))) -> 0(4(1(0(4(5(0(3(0(5(x1))))))))))
   2(2(2(4(1(3(3(2(3(3(x1)))))))))) -> 0(2(3(4(1(3(5(5(1(2(x1))))))))))
   2(3(2(2(0(3(5(2(2(2(x1)))))))))) -> 1(2(4(1(1(5(3(3(1(2(x1))))))))))
   3(3(3(3(3(2(3(4(3(4(x1)))))))))) -> 1(1(2(4(3(4(3(0(4(5(x1))))))))))
   3(5(5(2(5(1(3(0(3(5(x1)))))))))) -> 3(2(4(5(1(0(4(5(0(0(x1))))))))))
   4(3(4(5(0(3(2(0(5(5(x1)))))))))) -> 4(3(4(0(5(2(3(0(5(5(x1))))))))))
   5(2(1(5(3(1(0(1(3(4(x1)))))))))) -> 4(4(4(4(0(4(0(2(2(2(x1))))))))))
   5(2(1(5(5(3(2(3(3(3(x1)))))))))) -> 1(1(1(2(3(5(1(5(0(4(x1))))))))))
   0(0(0(1(5(3(2(2(0(1(0(x1))))))))))) -> 1(1(3(3(5(1(5(1(4(4(x1))))))))))
   0(0(1(4(3(1(0(3(3(0(2(x1))))))))))) -> 0(2(4(0(1(1(4(0(3(5(x1))))))))))
   0(1(5(5(4(3(0(4(1(1(0(x1))))))))))) -> 0(2(4(2(5(0(0(0(0(1(x1))))))))))
   0(2(0(2(1(1(4(2(5(5(3(x1))))))))))) -> 0(3(2(5(4(0(2(5(4(1(x1))))))))))
   0(3(0(5(3(5(3(3(2(0(3(x1))))))))))) -> 3(4(3(3(1(5(1(4(2(2(x1))))))))))
   0(5(4(0(3(0(2(5(1(2(3(x1))))))))))) -> 1(3(0(0(5(1(0(1(3(0(x1))))))))))
   0(5(5(2(1(5(1(0(0(4(1(x1))))))))))) -> 0(3(0(0(5(3(1(3(3(0(x1))))))))))
   1(2(0(2(5(3(3(2(4(4(0(x1))))))))))) -> 5(5(1(4(3(5(5(0(4(3(x1))))))))))
   1(3(2(0(4(5(0(2(5(5(0(x1))))))))))) -> 3(2(4(4(0(2(4(3(5(5(x1))))))))))
   1(4(0(0(0(5(2(1(3(5(5(x1))))))))))) -> 1(1(2(3(0(2(4(0(3(1(x1))))))))))
   1(4(2(2(3(0(5(1(2(0(4(x1))))))))))) -> 4(5(3(4(0(2(5(0(4(2(x1))))))))))
   1(5(2(0(3(2(0(5(4(2(0(x1))))))))))) -> 1(5(2(0(2(3(0(5(4(2(0(x1)))))))))))
   1(5(5(5(4(4(2(0(4(2(3(x1))))))))))) -> 2(0(0(2(3(5(1(0(4(4(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost