TRS Innermost pair #487093167

details

property	value
status	complete
benchmark	OvConsOS_nosorts_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.01979 seconds
cpu usage	12.4111
user time	11.9977
system time	0.413395
max virtual memory	3.6446892E7
max residence set size	613436.0

stage attributes

key	value
starexec-result	NO

output

NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination w.r.t. Q of the given QTRS could be disproven:

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 51 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 4 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 33 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) QDP
(9) MRRProof [EQUIVALENT, 0 ms]
(10) QDP
(11) MRRProof [EQUIVALENT, 16 ms]
(12) QDP
(13) DependencyGraphProof [EQUIVALENT, 0 ms]
(14) AND
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QReductionProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) TransformationProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) DependencyGraphProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) TransformationProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) DependencyGraphProof [EQUIVALENT, 0 ms]
        (30) AND
            (31) QDP
                (32) UsableRulesProof [EQUIVALENT, 0 ms]
                (33) QDP
                (34) QReductionProof [EQUIVALENT, 0 ms]
                (35) QDP
                (36) TransformationProof [EQUIVALENT, 0 ms]
                (37) QDP
                (38) NonTerminationLoopProof [COMPLETE, 0 ms]
                (39) NO
            (40) QDP
                (41) MRRProof [EQUIVALENT, 0 ms]
                (42) QDP


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

(0)
Obligation:
Q restricted rewrite system:
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)))
   a__take(0, IL) -> nil
   a__take(s(M), cons(N, IL)) -> cons(mark(N), take(M, IL))
   mark(zeros) -> a__zeros
   mark(and(X1, X2)) -> a__and(mark(X1), X2)
   mark(length(X)) -> a__length(mark(X))
   mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
   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)
   a__take(X1, X2) -> take(X1, X2)

The set Q consists of the following terms:

   a__zeros
   mark(zeros)
   mark(and(x0, x1))
   mark(length(x0))
   mark(take(x0, x1))
   mark(cons(x0, x1))
   mark(0)
   mark(tt)
   mark(nil)
   mark(s(x0))
   a__and(x0, x1)
   a__length(x0)
   a__take(x0, x1)


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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:

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