Logic Programming pair #487096342

details

property	value
status	complete
benchmark	prime.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.30867 seconds
cpu usage	9.75949
user time	9.26527
system time	0.494223
max virtual memory	1.887626E7
max residence set size	1513264.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

prime(g)

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

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 24 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 0 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
    (21) PiDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) PiDP
        (24) PiDPToQDPProof [SOUND, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) PiDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) PiDP
        (31) PiDPToQDPProof [SOUND, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) PiDP
        (36) UsableRulesProof [EQUIVALENT, 0 ms]
        (37) PiDP
        (38) PiDPToQDPProof [SOUND, 0 ms]
        (39) QDP
        (40) QDPOrderProof [EQUIVALENT, 101 ms]
        (41) QDP
        (42) DependencyGraphProof [EQUIVALENT, 0 ms]
        (43) TRUE


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

(0)
Obligation:
Clauses:

div(X, Y, Z) :- quot(X, Y, Y, Z).
quot(0, s(Y), s(Z), 0).
quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U).
quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U).
prime(s(s(X))) :- pr(s(s(X)), s(X)).
pr(X, s(0)).
pr(X, s(s(Y))) :- ','(not_divides(s(s(Y)), X), pr(X, s(Y))).
not_divides(Y, X) :- ','(div(X, Y, U), ','(times(U, Y, Z), neq(X, Z))).
neq(s(X), 0).
neq(0, s(X)).
neq(s(X), s(Y)) :- neq(X, Y).
times(0, Y, 0).
times(s(X), Y, Z) :- ','(times(X, Y, U), add(U, Y, Z)).
add(X, 0, X).
add(0, X, X).
add(s(X), Y, s(Z)) :- add(X, Y, Z).


Query: prime(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:

prime_in_1: (b)

pr_in_2: (b,b)

not_divides_in_2: (b,b)

div_in_3: (b,b,f)

quot_in_4: (b,b,b,f)

times_in_3: (b,b,f)

add_in_3: (b,b,f)

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