TRS Outer 67415 pair #381918027

details

property	value
status	complete
benchmark	LengthOfFiniteLists_nosorts_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n047.star.cs.uiowa.edu
space	Strategy_outermost_added_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	20.579200983 seconds
cpu usage	73.31095839
max memory	5.6899584E9

stage attributes

key	value
output-size	56665
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be proven:

(0) OTRS
(1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 100 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 65 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 35 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 30 ms]
(10) QTRS
(11) QTRSRRRProof [EQUIVALENT, 13 ms]
(12) QTRS
(13) QTRSRRRProof [EQUIVALENT, 0 ms]
(14) QTRS
(15) QTRSRRRProof [EQUIVALENT, 27 ms]
(16) QTRS
(17) DependencyPairsProof [EQUIVALENT, 5 ms]
(18) QDP
(19) DependencyGraphProof [EQUIVALENT, 0 ms]
(20) AND
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (25) YES
    (26) QDP
        (27) UsableRulesProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QDP
        (32) UsableRulesProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) TransformationProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) DependencyGraphProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPOrderProof [EQUIVALENT, 28 ms]
        (39) QDP
        (40) DependencyGraphProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) QDPOrderProof [EQUIVALENT, 20 ms]
        (43) QDP
        (44) QDPOrderProof [EQUIVALENT, 12 ms]
        (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 2018 ms]
        (47) QDP
        (48) PisEmptyProof [EQUIVALENT, 0 ms]
        (49) YES


----------------------------------------

(0)
Obligation:
Term rewrite system R:
The TRS R consists of the following rules:

   a__zeros -> cons(0, zeros)
   a__and(tt, X) -> mark(X)
   a__length(nil) -> 0
   a__length(cons(N, L)) -> s(a__length(mark(L)))
   mark(zeros) -> a__zeros
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(length(X)) -> a__length(mark(X))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(0) -> 0
   mark(tt) -> tt
   mark(nil) -> nil
   mark(s(X)) -> s(mark(X))
   a__zeros -> zeros
   a__and(X1, X2) -> and(X1, X2)
   a__length(X) -> length(X)



Outermost Strategy.

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(1) Raffelsieper-Zantema-Transformation (SOUND)
We applied the Raffelsieper-Zantema transformation  to transform the outermost TRS to a standard TRS.
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(2)
Obligation:

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job log

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actions all output return to TRS Outer 67415