Derivational Complexity: TRS Innermost pair #487106782

details

property	value
status	complete
benchmark	26949.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	293.18 seconds
cpu usage	822.409
user time	814.159
system time	8.24975
max virtual memory	1.9044288E7
max residence set size	1.5040856E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 64 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 4 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms]
(12) TRS for Loop Detection
(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), 32 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), 2165 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 157 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 134 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 3073 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 347 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), 5432 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2453 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2443 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2345 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2389 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2375 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(2(0(2(2(x1)))))) -> 0(2(1(0(2(2(x1))))))
   0(3(1(2(2(4(2(x1))))))) -> 0(3(2(1(2(4(2(x1)))))))
   1(0(0(1(1(1(2(4(x1)))))))) -> 1(0(1(1(1(0(2(4(x1))))))))
   3(4(0(3(3(1(3(5(x1)))))))) -> 3(4(0(3(3(3(1(5(x1))))))))
   3(0(0(1(0(1(1(0(2(x1))))))))) -> 3(0(0(0(1(1(1(0(2(x1)))))))))
   0(0(3(5(0(3(5(4(5(5(2(x1))))))))))) -> 5(1(5(1(3(3(1(4(0(4(x1))))))))))
   0(1(2(1(5(2(0(5(4(4(4(x1))))))))))) -> 5(1(3(2(5(0(0(0(0(0(x1))))))))))
   0(1(3(1(0(1(4(3(0(5(5(x1))))))))))) -> 1(4(0(2(3(0(5(5(4(5(x1))))))))))
   0(3(1(0(5(3(0(1(2(1(2(x1))))))))))) -> 2(0(3(2(0(4(1(0(1(0(x1))))))))))
   0(3(4(1(0(5(3(0(1(5(2(x1))))))))))) -> 1(0(0(2(3(0(0(3(3(2(x1))))))))))
   0(3(4(3(3(3(0(3(1(0(0(x1))))))))))) -> 1(4(3(1(5(5(2(4(1(5(x1))))))))))
   0(4(5(5(4(4(0(2(4(3(3(x1))))))))))) -> 3(5(3(4(1(4(3(4(4(5(x1))))))))))
   0(5(0(3(3(2(4(0(4(0(0(x1))))))))))) -> 5(0(5(2(4(5(1(2(0(5(x1))))))))))
   0(5(2(5(1(0(4(2(3(2(3(x1))))))))))) -> 3(1(5(0(5(3(3(3(3(4(x1))))))))))
   0(5(3(5(3(2(1(1(4(3(3(x1))))))))))) -> 2(1(0(2(3(3(0(4(4(1(x1))))))))))
   1(0(0(4(0(4(0(0(4(4(4(x1))))))))))) -> 2(5(2(0(5(1(3(5(1(4(x1))))))))))
   1(0(0(5(5(2(2(1(0(3(1(x1))))))))))) -> 1(2(2(2(4(4(1(1(2(0(x1))))))))))
   1(1(3(1(2(5(3(0(2(1(0(x1))))))))))) -> 4(4(5(0(4(2(2(3(0(3(x1))))))))))
   1(2(4(1(4(2(4(0(4(2(5(x1))))))))))) -> 2(1(0(4(0(1(4(0(1(3(x1))))))))))
   1(2(5(1(3(2(3(3(0(5(4(x1))))))))))) -> 4(3(2(2(3(0(3(1(0(4(x1))))))))))
   1(2(5(3(5(2(3(5(5(2(2(x1))))))))))) -> 4(4(5(5(1(2(4(4(3(0(x1))))))))))
   1(3(0(3(2(4(3(3(4(5(2(x1))))))))))) -> 1(1(4(5(3(2(4(0(5(2(x1))))))))))
   1(3(2(4(0(4(4(2(2(4(3(x1))))))))))) -> 1(1(5(5(3(1(5(1(1(4(x1))))))))))
   1(3(5(2(1(0(5(3(0(3(4(x1))))))))))) -> 3(4(2(5(0(5(0(1(3(4(x1))))))))))
   1(4(1(3(1(5(4(0(1(2(0(x1))))))))))) -> 1(3(2(1(3(2(4(5(2(4(x1))))))))))
   1(5(3(0(1(2(0(0(4(5(5(x1))))))))))) -> 2(4(3(4(1(2(1(2(0(4(x1))))))))))
   2(0(1(4(0(0(5(4(2(3(2(x1))))))))))) -> 5(5(5(0(3(2(4(3(1(0(x1))))))))))

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