Derivational Complexity: TRS Innermost pair #487106944

details

property	value
status	complete
benchmark	27034.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.886 seconds
cpu usage	871.071
user time	862.039
system time	9.03145
max virtual memory	1.8779768E7
max residence set size	1.5235768E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 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), 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), 28 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 18 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1921 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 249 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 164 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 15 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 18 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2862 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 385 ms]
    (38) CdtProblem
    (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 14 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6790 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2910 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2862 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2875 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2817 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2863 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(2(x1)))))) -> 0(1(2(0(3(2(x1))))))
   3(1(4(4(0(2(0(3(x1)))))))) -> 3(1(4(0(4(2(0(3(x1))))))))
   4(5(4(3(4(5(2(1(x1)))))))) -> 4(5(4(4(3(5(2(1(x1))))))))
   0(3(2(4(3(0(5(3(0(x1))))))))) -> 0(3(2(4(0(3(5(3(0(x1)))))))))
   2(1(0(5(3(2(3(1(0(x1))))))))) -> 2(0(1(2(3(5(1(3(0(x1)))))))))
   5(1(5(4(2(1(3(2(5(x1))))))))) -> 5(1(3(2(4(5(1(2(5(x1)))))))))
   4(4(0(4(3(4(5(0(1(0(x1)))))))))) -> 4(4(0(4(3(5(4(0(1(0(x1))))))))))
   0(0(5(4(3(4(0(4(0(2(4(x1))))))))))) -> 2(2(5(4(5(2(2(4(2(2(x1))))))))))
   0(0(5(5(3(3(5(1(1(3(4(x1))))))))))) -> 1(1(2(2(5(0(4(2(4(4(x1))))))))))
   0(1(4(1(0(3(3(1(3(1(1(x1))))))))))) -> 1(4(4(2(3(5(0(4(0(0(x1))))))))))
   0(1(5(5(5(2(3(0(1(4(5(x1))))))))))) -> 1(3(0(5(0(5(0(4(2(4(x1))))))))))
   0(2(3(2(3(1(0(0(4(2(2(x1))))))))))) -> 5(3(3(1(0(4(4(4(2(3(x1))))))))))
   0(3(0(0(1(0(2(5(1(5(5(x1))))))))))) -> 0(0(5(2(0(1(3(4(0(2(x1))))))))))
   0(3(3(3(1(4(3(4(3(0(4(x1))))))))))) -> 5(5(1(2(1(2(4(1(2(3(x1))))))))))
   0(3(4(0(3(3(1(5(3(0(3(x1))))))))))) -> 0(5(3(0(5(3(1(4(2(3(x1))))))))))
   0(3(5(3(5(4(3(5(4(1(3(x1))))))))))) -> 2(4(5(1(0(4(4(3(0(2(x1))))))))))
   0(4(5(1(2(4(0(4(3(3(3(x1))))))))))) -> 0(4(1(4(3(2(4(5(4(3(x1))))))))))
   0(5(0(5(3(3(5(5(4(3(2(x1))))))))))) -> 1(1(3(3(3(0(5(4(2(3(x1))))))))))
   0(5(2(3(4(2(5(4(5(3(0(x1))))))))))) -> 4(3(2(1(2(5(4(1(4(2(x1))))))))))
   0(5(3(3(2(5(1(4(1(1(0(x1))))))))))) -> 4(5(2(4(3(0(0(2(1(5(x1))))))))))
   1(0(2(0(5(3(1(4(4(0(1(x1))))))))))) -> 0(3(2(5(1(5(5(3(3(4(x1))))))))))
   1(3(3(1(0(0(3(0(5(4(4(x1))))))))))) -> 4(3(3(2(0(5(4(1(0(0(x1))))))))))
   1(4(1(0(5(0(2(2(2(5(5(x1))))))))))) -> 1(4(1(5(0(0(2(2(2(5(5(x1)))))))))))
   1(4(5(3(1(3(4(1(3(4(0(x1))))))))))) -> 2(5(4(4(1(1(3(0(2(0(x1))))))))))
   1(5(5(4(2(5(1(2(0(0(3(x1))))))))))) -> 3(1(5(3(0(5(4(4(4(2(x1))))))))))
   2(1(3(1(0(4(5(5(1(4(1(x1))))))))))) -> 3(0(4(5(4(2(2(1(4(0(x1))))))))))
   2(2(4(2(5(2(2(3(3(0(3(x1))))))))))) -> 5(2(1(4(1(1(2(0(5(5(x1))))))))))

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