Logic Programming pair #487529121

details

property	value
status	complete
benchmark	overlap.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	talp_apt

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.95829200745 seconds
cpu usage	4.441765525
max memory	3.58141952E8

stage attributes

key	value
output-size	14450
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

overlap(g,g)

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

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 6 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 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


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

(0)
Obligation:
Clauses:

overlap(Xs, Ys) :- ','(member2(X, Xs), member1(X, Ys)).
has_a_or_b(Xs) :- overlap(Xs, .(a, .(b, []))).
member1(X, .(Y, Xs)) :- member1(X, Xs).
member1(X, .(X, Xs)).
member2(X, .(Y, Xs)) :- member2(X, Xs).
member2(X, .(X, Xs)).


Query: overlap(g,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:

overlap_in_2: (b,b)

member2_in_2: (f,b)

member1_in_2: (b,b)

Transforming Prolog into the following Term Rewriting System:

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

   overlap_in_gg(Xs, Ys) -> U1_gg(Xs, Ys, member2_in_ag(X, Xs))
   member2_in_ag(X, .(Y, Xs)) -> U5_ag(X, Y, Xs, member2_in_ag(X, Xs))
   member2_in_ag(X, .(X, Xs)) -> member2_out_ag(X, .(X, Xs))
   U5_ag(X, Y, Xs, member2_out_ag(X, Xs)) -> member2_out_ag(X, .(Y, Xs))
   U1_gg(Xs, Ys, member2_out_ag(X, Xs)) -> U2_gg(Xs, Ys, member1_in_gg(X, Ys))
   member1_in_gg(X, .(Y, Xs)) -> U4_gg(X, Y, Xs, member1_in_gg(X, Xs))
   member1_in_gg(X, .(X, Xs)) -> member1_out_gg(X, .(X, Xs))
   U4_gg(X, Y, Xs, member1_out_gg(X, Xs)) -> member1_out_gg(X, .(Y, Xs))
   U2_gg(Xs, Ys, member1_out_gg(X, Ys)) -> overlap_out_gg(Xs, Ys)

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

U1_gg(x1, x2, x3)  =  U1_gg(x2, x3)

member2_in_ag(x1, x2)  =  member2_in_ag(x2)

.(x1, x2)  =  .(x1, x2)

U5_ag(x1, x2, x3, x4)  =  U5_ag(x4)

member2_out_ag(x1, x2)  =  member2_out_ag(x1)

U2_gg(x1, x2, x3)  =  U2_gg(x3)

member1_in_gg(x1, x2)  =  member1_in_gg(x1, x2)

U4_gg(x1, x2, x3, x4)  =  U4_gg(x4)

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Logic Programming