Derivational Complexity: TRS Innermost pair #487107046

details

property	value
status	complete
benchmark	26933.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.602 seconds
cpu usage	979.005
user time	971.185
system time	7.81913
max virtual memory	1.8850692E7
max residence set size	1.525898E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 40 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), 9 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), 2 ms]
    (18) CpxWeightedTrs
    (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 25 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), 2342 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 158 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 121 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 28 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2875 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 321 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 16 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 5852 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2730 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2744 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2757 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2660 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2699 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2648 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5716 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 270 ms]
    (60) 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(3(1(x1))))))) -> 0(0(2(1(3(3(1(x1)))))))
   2(1(1(0(3(1(0(x1))))))) -> 2(0(1(1(3(1(0(x1)))))))
   1(3(2(0(0(4(1(4(0(x1))))))))) -> 1(3(2(0(1(0(4(4(0(x1)))))))))
   1(5(0(2(3(3(2(2(1(x1))))))))) -> 1(0(3(5(2(2(3(2(1(x1)))))))))
   2(5(2(1(5(4(2(4(0(x1))))))))) -> 2(5(2(5(1(4(2(4(0(x1)))))))))
   5(2(0(4(2(5(4(5(2(x1))))))))) -> 5(2(0(4(5(2(4(5(2(x1)))))))))
   0(3(2(4(3(2(2(0(4(2(x1)))))))))) -> 5(1(4(2(3(4(5(1(0(5(x1))))))))))
   3(0(4(3(0(1(4(4(4(2(x1)))))))))) -> 4(5(0(0(2(1(0(5(5(2(x1))))))))))
   0(0(4(4(0(0(3(4(5(4(2(x1))))))))))) -> 4(1(5(3(1(0(5(3(1(1(x1))))))))))
   0(1(4(4(3(1(1(1(2(2(4(x1))))))))))) -> 3(3(1(3(4(3(1(1(0(0(x1))))))))))
   0(2(3(4(1(5(5(0(0(1(1(x1))))))))))) -> 1(1(4(3(4(3(5(5(4(4(x1))))))))))
   0(3(0(4(3(3(3(0(5(3(4(x1))))))))))) -> 4(3(4(0(2(4(4(5(4(4(x1))))))))))
   0(3(1(4(0(0(2(2(4(4(0(x1))))))))))) -> 5(5(3(3(3(3(3(2(0(0(x1))))))))))
   0(3(3(0(5(5(5(2(2(3(4(x1))))))))))) -> 0(3(5(4(4(3(4(3(2(4(x1))))))))))
   0(4(3(5(3(3(5(4(0(0(4(x1))))))))))) -> 5(2(5(0(4(4(1(1(2(0(x1))))))))))
   0(4(4(1(1(1(2(0(2(4(0(x1))))))))))) -> 2(5(4(2(5(0(4(0(3(0(x1))))))))))
   1(0(0(5(5(5(4(5(4(3(3(x1))))))))))) -> 4(2(5(5(1(0(1(2(1(3(x1))))))))))
   1(0(5(0(3(5(3(1(2(2(0(x1))))))))))) -> 1(5(1(0(4(1(0(5(2(2(x1))))))))))
   2(1(1(0(1(3(1(4(0(1(4(x1))))))))))) -> 3(4(0(5(5(3(0(3(0(5(x1))))))))))
   2(1(1(4(0(5(0(1(2(4(2(x1))))))))))) -> 0(1(3(3(0(1(0(2(3(2(x1))))))))))
   2(1(4(0(2(2(1(2(4(2(0(x1))))))))))) -> 4(3(2(2(1(0(2(3(2(1(x1))))))))))

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