Derivational Complexity: TRS Innermost pair #487106414

details

property	value
status	complete
benchmark	165904.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)	295.577 seconds
cpu usage	891.183
user time	884.386
system time	6.79709
max virtual memory	3.7112228E7
max residence set size	1.528768E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 71 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 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), 0 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), 19 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 5760 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 15 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 23 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 12.7 s]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 330 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 9816 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1096 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1082 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1080 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2249 ms]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 64 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2250 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2306 ms]
    (62) CdtProblem
    (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 142 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2625 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 337 ms]
    (68) 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(x1))) -> 2(1(2(2(x1))))
   0(2(0(2(1(x1))))) -> 0(1(2(1(2(2(1(2(2(1(x1))))))))))
   0(2(2(0(0(x1))))) -> 1(0(1(2(1(0(x1))))))
   1(0(1(2(2(x1))))) -> 1(1(1(1(2(1(2(2(2(2(2(1(x1))))))))))))
   0(1(2(0(2(2(1(x1))))))) -> 1(2(2(1(2(1(1(2(2(2(2(2(1(1(x1))))))))))))))
   0(2(2(0(0(2(2(x1))))))) -> 0(2(2(2(1(0(1(2(2(2(2(2(x1))))))))))))
   1(2(2(0(2(0(0(2(x1)))))))) -> 2(2(2(0(2(0(1(2(2(x1)))))))))
   1(1(2(0(1(2(2(0(2(x1))))))))) -> 1(1(1(1(2(2(0(2(2(1(x1))))))))))
   1(1(2(1(0(2(0(0(2(x1))))))))) -> 1(2(2(2(2(1(2(2(2(0(2(2(2(2(x1))))))))))))))
   2(1(1(0(1(0(2(1(0(x1))))))))) -> 1(2(1(1(1(1(1(2(2(0(0(0(2(0(x1))))))))))))))
   0(0(2(0(0(2(0(0(0(2(x1)))))))))) -> 0(0(1(0(2(1(0(2(2(2(1(x1)))))))))))
   0(1(1(0(0(1(1(2(0(2(x1)))))))))) -> 1(2(0(2(2(2(1(2(2(2(1(x1)))))))))))
   0(2(1(1(2(1(1(2(0(0(x1)))))))))) -> 1(2(2(2(2(2(2(0(0(1(2(1(1(2(0(x1)))))))))))))))

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