Logic Programming pair #487096188

details

property	value
status	complete
benchmark	pl3.5.6.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	talp_plumer

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.3703 seconds
cpu usage	6.30953
user time	5.90042
system time	0.409109
max virtual memory	2.0007048E7
max residence set size	723452.0

stage attributes

key	value
starexec-result	MAYBE

output

MAYBE
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

p(a)

w.r.t. the given Prolog program could not be shown:

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
    (3) DependencyPairsProof [EQUIVALENT, 0 ms]
    (4) PiDP
    (5) DependencyGraphProof [EQUIVALENT, 0 ms]
    (6) PiDP
    (7) UsableRulesProof [EQUIVALENT, 0 ms]
    (8) PiDP
    (9) PiDPToQDPProof [SOUND, 0 ms]
    (10) QDP
(11) PrologToPiTRSProof [SOUND, 0 ms]
(12) PiTRS
    (13) DependencyPairsProof [EQUIVALENT, 0 ms]
    (14) PiDP
    (15) DependencyGraphProof [EQUIVALENT, 0 ms]
    (16) PiDP
    (17) UsableRulesProof [EQUIVALENT, 0 ms]
    (18) PiDP
    (19) PiDPToQDPProof [SOUND, 0 ms]
    (20) QDP
(21) PrologToTRSTransformerProof [SOUND, 0 ms]
(22) QTRS
    (23) QTRSRRRProof [EQUIVALENT, 43 ms]
    (24) QTRS
    (25) QTRSRRRProof [EQUIVALENT, 0 ms]
    (26) QTRS
    (27) QTRSRRRProof [EQUIVALENT, 11 ms]
    (28) QTRS
    (29) QTRSRRRProof [EQUIVALENT, 10 ms]
    (30) QTRS
    (31) QTRSRRRProof [EQUIVALENT, 0 ms]
    (32) QTRS
(33) PrologToDTProblemTransformerProof [SOUND, 0 ms]
(34) TRIPLES
    (35) TriplesToPiDPProof [SOUND, 0 ms]
    (36) PiDP
    (37) DependencyGraphProof [EQUIVALENT, 0 ms]
    (38) PiDP
    (39) PiDPToQDPProof [SOUND, 0 ms]
    (40) QDP
(41) PrologToIRSwTTransformerProof [SOUND, 0 ms]
(42) IRSwT
    (43) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
    (44) IRSwT
    (45) IntTRSCompressionProof [EQUIVALENT, 17 ms]
    (46) IRSwT
    (47) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
    (48) IRSwT
    (49) IRSwTTerminationDigraphProof [EQUIVALENT, 6 ms]
    (50) IRSwT
    (51) FilterProof [EQUIVALENT, 0 ms]
    (52) IntTRS
    (53) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
    (54) NO


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

(0)
Obligation:
Clauses:

p(X) :- ','(l(X), q(X)).
q(.(A, [])).
r(1).
l([]).
l(.(H, T)) :- ','(r(H), l(T)).


Query: p(a)
----------------------------------------

(1) PrologToPiTRSProof (SOUND)
We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:

p_in_1: (f)

l_in_1: (f)

Transforming Prolog into the following Term Rewriting System:

Pi-finite rewrite system:
The TRS R consists of the following rules:

   p_in_a(X) -> U1_a(X, l_in_a(X))
   l_in_a([]) -> l_out_a([])
   l_in_a(.(H, T)) -> U3_a(H, T, r_in_a(H))
   r_in_a(1) -> r_out_a(1)

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