Logic Programming pair #487096648

details

property	value
status	complete
benchmark	nat.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	talp_talp

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.07552 seconds
cpu usage	4.91494
user time	4.67587
system time	0.239075
max virtual memory	1.8678168E7
max residence set size	402824.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

factorial(g,a)

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

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 8 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, 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


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

(0)
Obligation:
Clauses:

isNat(s(X)) :- isNat(X).
isNat(0).
notEq(s(X), s(Y)) :- notEq(X, Y).
notEq(s(X), 0).
notEq(0, s(X)).
lt(s(X), s(Y)) :- lt(X, Y).
lt(0, s(Y)).
gt(s(X), s(Y)) :- gt(X, Y).
gt(s(X), 0).
le(s(X), s(Y)) :- le(X, Y).
le(0, s(Y)).
le(0, 0).
even(s(X)) :- odd(X).
even(0).
odd(s(X)) :- even(X).
odd(s(0)).
add(s(X), Y, s(Z)) :- add(X, Y, Z).
add(0, X, X).
mult(s(X), Y, R) :- ','(mult(X, Y, Z), add(Y, Z, R)).
mult(0, Y, 0).
factorial(s(X), R) :- ','(factorial(X, Y), mult(s(X), Y, R)).
factorial(0, s(0)).


Query: factorial(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:

factorial_in_2: (b,f)

mult_in_3: (b,b,f)

add_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:

   factorial_in_ga(s(X), R) -> U11_ga(X, R, factorial_in_ga(X, Y))
   factorial_in_ga(0, s(0)) -> factorial_out_ga(0, s(0))
   U11_ga(X, R, factorial_out_ga(X, Y)) -> U12_ga(X, R, mult_in_gga(s(X), Y, R))
   mult_in_gga(s(X), Y, R) -> U9_gga(X, Y, R, mult_in_gga(X, Y, Z))
   mult_in_gga(0, Y, 0) -> mult_out_gga(0, Y, 0)
   U9_gga(X, Y, R, mult_out_gga(X, Y, Z)) -> U10_gga(X, Y, R, add_in_gga(Y, Z, R))
   add_in_gga(s(X), Y, s(Z)) -> U8_gga(X, Y, Z, add_in_gga(X, Y, Z))
   add_in_gga(0, X, X) -> add_out_gga(0, X, X)
   U8_gga(X, Y, Z, add_out_gga(X, Y, Z)) -> add_out_gga(s(X), Y, s(Z))
   U10_gga(X, Y, R, add_out_gga(Y, Z, R)) -> mult_out_gga(s(X), Y, R)
   U12_ga(X, R, mult_out_gga(s(X), Y, R)) -> factorial_out_ga(s(X), R)

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