TRS Standard pair #487071758

details

property	value
status	complete
benchmark	OvConsOS_nosorts_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.45568 seconds
cpu usage	5.79612
user time	5.49811
system time	0.298011
max virtual memory	1.8544088E7
max residence set size	399300.0

stage attributes

key	value
starexec-result	NO

output

NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 47 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 14 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 20 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 18 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) QDP
        (23) UsableRulesProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) MRRProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) MRRProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) MNOCProof [EQUIVALENT, 1 ms]
        (34) QDP
        (35) TransformationProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QReductionProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) TransformationProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) UsableRulesProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) QReductionProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) TransformationProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) NonTerminationLoopProof [COMPLETE, 0 ms]
        (50) NO


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

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

   zeros -> cons(0, n__zeros)
   and(tt, X) -> activate(X)
   length(nil) -> 0
   length(cons(N, L)) -> s(length(activate(L)))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, n__take(M, activate(IL)))
   zeros -> n__zeros
   take(X1, X2) -> n__take(X1, X2)
   activate(n__zeros) -> zeros
   activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
   activate(X) -> X

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(activate(x_1)) = x_1
   POL(and(x_1, x_2)) = 2 + 2*x_1 + x_2
   POL(cons(x_1, x_2)) = 2*x_1 + x_2
   POL(length(x_1)) = x_1
   POL(n__take(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(n__zeros) = 0
   POL(nil) = 0
   POL(s(x_1)) = x_1
   POL(take(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(tt) = 0
   POL(zeros) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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