Logic Programming pair #487529303

details

property	value
status	complete
benchmark	p_nonlin.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n184.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.17876911163 seconds
cpu usage	9.001849124
max memory	8.70416384E8

stage attributes

key	value
output-size	30335
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

p(g)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 14 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [SOUND, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 2 ms]
        (13) YES
    (14) PiDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) PiDP
        (17) PiDPToQDPProof [SOUND, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) PiDP
        (22) PiDPToQDPProof [SOUND, 0 ms]
        (23) QDP
        (24) QDPQMonotonicMRRProof [EQUIVALENT, 96 ms]
        (25) QDP
        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) UsableRulesProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QReductionProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) PisEmptyProof [EQUIVALENT, 0 ms]
        (35) YES


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

(0)
Obligation:
Clauses:

p(cons(X, nil)).
p(cons(s(s(X)), cons(Y, Xs))) :- ','(p(cons(X, cons(Y, Xs))), ','(mult(X, Y, Z), p(cons(Z, Xs)))).
p(cons(0, Xs)) :- p(Xs).
sum(X, 0, X).
sum(X, s(Y), s(Z)) :- sum(X, Y, Z).
mult(X1, 0, 0).
mult(X, s(Y), Z) :- ','(mult(X, Y, W), sum(W, X, Z)).


Query: p(g)
----------------------------------------

(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: (b)

mult_in_3: (b,b,f)

sum_in_3: (b,b,f)

Transforming Prolog into the following Term Rewriting System:

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

   p_in_g(cons(X, nil)) -> p_out_g(cons(X, nil))
   p_in_g(cons(s(s(X)), cons(Y, Xs))) -> U1_g(X, Y, Xs, p_in_g(cons(X, cons(Y, Xs))))
   p_in_g(cons(0, Xs)) -> U4_g(Xs, p_in_g(Xs))
   U4_g(Xs, p_out_g(Xs)) -> p_out_g(cons(0, Xs))
   U1_g(X, Y, Xs, p_out_g(cons(X, cons(Y, Xs)))) -> U2_g(X, Y, Xs, mult_in_gga(X, Y, Z))
   mult_in_gga(X1, 0, 0) -> mult_out_gga(X1, 0, 0)
   mult_in_gga(X, s(Y), Z) -> U6_gga(X, Y, Z, mult_in_gga(X, Y, W))
   U6_gga(X, Y, Z, mult_out_gga(X, Y, W)) -> U7_gga(X, Y, Z, sum_in_gga(W, X, Z))
   sum_in_gga(X, 0, X) -> sum_out_gga(X, 0, X)
   sum_in_gga(X, s(Y), s(Z)) -> U5_gga(X, Y, Z, sum_in_gga(X, Y, Z))
   U5_gga(X, Y, Z, sum_out_gga(X, Y, Z)) -> sum_out_gga(X, s(Y), s(Z))
   U7_gga(X, Y, Z, sum_out_gga(W, X, Z)) -> mult_out_gga(X, s(Y), Z)
   U2_g(X, Y, Xs, mult_out_gga(X, Y, Z)) -> U3_g(X, Y, Xs, p_in_g(cons(Z, Xs)))

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