Logic Programming pair #487096484

details

property	value
status	complete
benchmark	tree_member-bf.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	BCGGV05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.57868 seconds
cpu usage	6.38797
user time	6.01686
system time	0.371111
max virtual memory	1.9144344E7
max residence set size	762000.0

stage attributes

key	value
starexec-result	MAYBE

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

tree_member(g,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) DependencyPairsProof [EQUIVALENT, 0 ms]
    (24) QDP
    (25) DependencyGraphProof [EQUIVALENT, 0 ms]
    (26) QDP
    (27) MNOCProof [EQUIVALENT, 0 ms]
    (28) QDP
    (29) UsableRulesProof [EQUIVALENT, 0 ms]
    (30) QDP
    (31) QReductionProof [EQUIVALENT, 0 ms]
    (32) QDP
(33) PrologToIRSwTTransformerProof [SOUND, 0 ms]
(34) IRSwT
    (35) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
    (36) IRSwT
    (37) IntTRSCompressionProof [EQUIVALENT, 27 ms]
    (38) IRSwT
    (39) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
    (40) IRSwT
    (41) IRSwTTerminationDigraphProof [EQUIVALENT, 2 ms]
    (42) IRSwT
    (43) FilterProof [EQUIVALENT, 1 ms]
    (44) IntTRS
    (45) IntTRSPeriodicNontermProof [COMPLETE, 5 ms]
    (46) NO
(47) PrologToDTProblemTransformerProof [SOUND, 48 ms]
(48) TRIPLES
    (49) TriplesToPiDPProof [SOUND, 0 ms]
    (50) PiDP
    (51) DependencyGraphProof [EQUIVALENT, 0 ms]
    (52) PiDP
    (53) PiDPToQDPProof [SOUND, 0 ms]
    (54) QDP


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

(0)
Obligation:
Clauses:

tree_member(X, tree(X, X1, X2)).
tree_member(X, tree(X3, Left, X4)) :- tree_member(X, Left).
tree_member(X, tree(X5, X6, Right)) :- tree_member(X, Right).


Query: tree_member(g,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:

tree_member_in_2: (b,f)

Transforming Prolog into the following Term Rewriting System:

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

   tree_member_in_ga(X, tree(X, X1, X2)) -> tree_member_out_ga(X, tree(X, X1, X2))
   tree_member_in_ga(X, tree(X3, Left, X4)) -> U1_ga(X, X3, Left, X4, tree_member_in_ga(X, Left))
   tree_member_in_ga(X, tree(X5, X6, Right)) -> U2_ga(X, X5, X6, Right, tree_member_in_ga(X, Right))
   U2_ga(X, X5, X6, Right, tree_member_out_ga(X, Right)) -> tree_member_out_ga(X, tree(X5, X6, Right))
   U1_ga(X, X3, Left, X4, tree_member_out_ga(X, Left)) -> tree_member_out_ga(X, tree(X3, Left, X4))

The argument filtering Pi contains the following mapping:
tree_member_in_ga(x1, x2)  =  tree_member_in_ga(x1)

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