Logic_Programming 2019-04-02 08.22 pair #434324513

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	n012.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.53886 seconds
cpu usage	10.5527
user time	9.99694
system time	0.555755
max virtual memory	3.9236832E7
max residence set size	1093668.0

stage attributes

key	value
starexec-result	YES

output

10.26/3.48	YES
10.26/3.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
10.26/3.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.26/3.50	
10.26/3.50	
10.26/3.50	Left Termination of the query pattern
10.26/3.50	
10.26/3.50	p(g)
10.26/3.50	
10.26/3.50	w.r.t. the given Prolog program could successfully be proven:
10.26/3.50	
10.26/3.50	(0) Prolog
10.26/3.50	(1) PrologToPiTRSProof [SOUND, 0 ms]
10.26/3.50	(2) PiTRS
10.26/3.50	(3) DependencyPairsProof [EQUIVALENT, 9 ms]
10.26/3.50	(4) PiDP
10.26/3.50	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
10.26/3.50	(6) AND
10.26/3.50	    (7) PiDP
10.26/3.50	        (8) UsableRulesProof [EQUIVALENT, 0 ms]
10.26/3.50	        (9) PiDP
10.26/3.50	        (10) PiDPToQDPProof [SOUND, 0 ms]
10.26/3.50	        (11) QDP
10.26/3.50	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.26/3.50	        (13) YES
10.26/3.50	    (14) PiDP
10.26/3.50	        (15) UsableRulesProof [EQUIVALENT, 0 ms]
10.26/3.50	        (16) PiDP
10.26/3.50	        (17) PiDPToQDPProof [SOUND, 0 ms]
10.26/3.50	        (18) QDP
10.26/3.50	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
10.26/3.50	        (20) YES
10.26/3.50	    (21) PiDP
10.26/3.50	        (22) PiDPToQDPProof [SOUND, 0 ms]
10.26/3.50	        (23) QDP
10.26/3.50	        (24) QDPQMonotonicMRRProof [EQUIVALENT, 41 ms]
10.26/3.50	        (25) QDP
10.26/3.50	        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
10.26/3.50	        (27) QDP
10.26/3.50	        (28) UsableRulesProof [EQUIVALENT, 0 ms]
10.26/3.50	        (29) QDP
10.26/3.50	        (30) QReductionProof [EQUIVALENT, 0 ms]
10.26/3.50	        (31) QDP
10.26/3.50	        (32) UsableRulesReductionPairsProof [EQUIVALENT, 3 ms]
10.26/3.50	        (33) QDP
10.26/3.50	        (34) PisEmptyProof [EQUIVALENT, 0 ms]
10.26/3.50	        (35) YES
10.26/3.50	
10.26/3.50	
10.26/3.50	----------------------------------------
10.26/3.50	
10.26/3.50	(0)
10.26/3.50	Obligation:
10.26/3.50	Clauses:
10.26/3.50	
10.26/3.50	p(cons(X, nil)).
10.26/3.50	p(cons(s(s(X)), cons(Y, Xs))) :- ','(p(cons(X, cons(Y, Xs))), ','(mult(X, Y, Z), p(cons(Z, Xs)))).
10.26/3.50	p(cons(0, Xs)) :- p(Xs).
10.26/3.50	sum(X, 0, X).
10.26/3.50	sum(X, s(Y), s(Z)) :- sum(X, Y, Z).
10.26/3.50	mult(X1, 0, 0).
10.26/3.50	mult(X, s(Y), Z) :- ','(mult(X, Y, W), sum(W, X, Z)).
10.26/3.50	
10.26/3.50	
10.26/3.50	Query: p(g)
10.26/3.50	----------------------------------------
10.26/3.50	
10.26/3.50	(1) PrologToPiTRSProof (SOUND)
10.26/3.50	We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:
10.26/3.50	
10.26/3.50	p_in_1: (b)
10.26/3.50	
10.26/3.50	mult_in_3: (b,b,f)
10.26/3.50	
10.26/3.50	sum_in_3: (b,b,f)
10.26/3.50	
10.26/3.50	Transforming Prolog into the following Term Rewriting System:
10.26/3.50	
10.26/3.50	Pi-finite rewrite system:
10.26/3.50	The TRS R consists of the following rules:
10.26/3.50	
10.26/3.50	   p_in_g(cons(X, nil)) -> p_out_g(cons(X, nil))
10.26/3.50	   p_in_g(cons(s(s(X)), cons(Y, Xs))) -> U1_g(X, Y, Xs, p_in_g(cons(X, cons(Y, Xs))))
10.26/3.50	   p_in_g(cons(0, Xs)) -> U4_g(Xs, p_in_g(Xs))
10.26/3.50	   U4_g(Xs, p_out_g(Xs)) -> p_out_g(cons(0, Xs))
10.26/3.50	   U1_g(X, Y, Xs, p_out_g(cons(X, cons(Y, Xs)))) -> U2_g(X, Y, Xs, mult_in_gga(X, Y, Z))
10.26/3.50	   mult_in_gga(X1, 0, 0) -> mult_out_gga(X1, 0, 0)
10.26/3.50	   mult_in_gga(X, s(Y), Z) -> U6_gga(X, Y, Z, mult_in_gga(X, Y, W))
10.26/3.50	   U6_gga(X, Y, Z, mult_out_gga(X, Y, W)) -> U7_gga(X, Y, Z, sum_in_gga(W, X, Z))
10.26/3.50	   sum_in_gga(X, 0, X) -> sum_out_gga(X, 0, X)
10.26/3.50	   sum_in_gga(X, s(Y), s(Z)) -> U5_gga(X, Y, Z, sum_in_gga(X, Y, Z))
10.26/3.50	   U5_gga(X, Y, Z, sum_out_gga(X, Y, Z)) -> sum_out_gga(X, s(Y), s(Z))
10.26/3.50	   U7_gga(X, Y, Z, sum_out_gga(W, X, Z)) -> mult_out_gga(X, s(Y), Z)
10.26/3.50	   U2_g(X, Y, Xs, mult_out_gga(X, Y, Z)) -> U3_g(X, Y, Xs, p_in_g(cons(Z, Xs)))
10.26/3.50	   U3_g(X, Y, Xs, p_out_g(cons(Z, Xs))) -> p_out_g(cons(s(s(X)), cons(Y, Xs)))
10.26/3.50	
10.26/3.50	The argument filtering Pi contains the following mapping:
10.26/3.50	p_in_g(x1)  =  p_in_g(x1)
10.26/3.50	
10.26/3.50	cons(x1, x2)  =  cons(x1, x2)

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