Derivational Complexity: TRS Innermost pair #487106602

details

property	value
status	complete
benchmark	26976.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.843 seconds
cpu usage	925.265
user time	917.408
system time	7.85639
max virtual memory	1.8781624E7
max residence set size	1.4831716E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 48 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), 22 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), 35 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 8 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 1932 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 214 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 196 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 5 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 35 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 2644 ms]
(36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 309 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), 5744 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2335 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2410 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2391 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2379 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2394 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2351 ms]
    (56) 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(1(3(2(3(1(x1)))))))
   0(3(3(2(0(2(2(x1))))))) -> 0(3(2(3(2(0(2(x1)))))))
   3(1(2(4(5(3(3(x1))))))) -> 3(1(5(4(2(3(3(x1)))))))
   4(3(4(1(2(4(4(x1))))))) -> 4(4(1(4(3(2(4(x1)))))))
   0(3(1(2(1(2(0(4(x1)))))))) -> 0(3(0(1(2(2(1(4(x1))))))))
   1(1(1(2(4(4(5(1(x1)))))))) -> 1(1(1(5(1(4(4(2(x1))))))))
   1(4(4(3(4(2(3(0(0(x1))))))))) -> 1(4(3(0(4(3(2(4(0(x1)))))))))
   1(0(0(2(2(2(5(2(3(3(x1)))))))))) -> 0(1(2(3(0(0(5(5(4(3(x1))))))))))
   1(2(2(5(1(1(2(4(2(0(x1)))))))))) -> 2(4(1(5(4(3(4(1(3(0(x1))))))))))
   3(5(2(1(2(0(5(4(2(4(x1)))))))))) -> 3(5(2(1(2(5(0(4(2(4(x1))))))))))
   4(2(2(2(2(4(4(4(1(3(x1)))))))))) -> 4(5(5(0(3(5(0(2(5(1(x1))))))))))
   5(0(1(5(1(2(2(1(4(1(x1)))))))))) -> 5(0(1(1(5(2(2(1(4(1(x1))))))))))
   0(0(0(4(5(5(2(4(5(1(3(x1))))))))))) -> 3(1(3(5(4(2(5(1(1(1(x1))))))))))
   0(0(5(1(0(0(5(4(3(4(1(x1))))))))))) -> 2(1(4(0(1(5(4(3(4(2(x1))))))))))
   0(1(5(2(0(5(3(3(0(2(2(x1))))))))))) -> 4(1(5(3(0(3(0(2(0(4(x1))))))))))
   0(3(1(3(4(4(4(1(2(5(2(x1))))))))))) -> 1(4(3(2(2(1(1(1(3(4(x1))))))))))
   0(3(1(4(0(1(2(0(3(5(0(x1))))))))))) -> 1(5(4(0(2(5(3(4(3(4(x1))))))))))
   0(4(5(2(5(5(4(3(5(1(0(x1))))))))))) -> 5(3(4(5(5(3(3(5(4(4(x1))))))))))
   1(0(0(2(2(3(5(0(2(0(4(x1))))))))))) -> 2(1(1(3(5(2(2(5(4(4(x1))))))))))
   1(0(2(3(2(3(3(0(3(2(0(x1))))))))))) -> 3(2(2(3(5(5(1(4(0(1(x1))))))))))
   1(1(2(5(1(4(2(5(5(2(4(x1))))))))))) -> 0(2(2(2(5(3(1(1(0(4(x1))))))))))
   1(2(4(5(5(3(2(4(1(1(5(x1))))))))))) -> 3(4(1(5(3(1(1(4(0(3(x1))))))))))
   1(3(0(1(5(5(3(3(5(3(3(x1))))))))))) -> 5(2(1(3(0(2(5(5(2(0(x1))))))))))
   1(3(0(2(0(5(0(0(1(1(4(x1))))))))))) -> 5(2(4(0(0(5(3(0(3(0(x1))))))))))
   1(3(4(2(0(5(2(0(4(4(4(x1))))))))))) -> 3(0(1(3(0(1(0(2(3(5(x1))))))))))

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actions all output return to Derivational Complexity: TRS Innermost