Logic Programming pair #487529207

details

property	value
status	complete
benchmark	intlist.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.77417707443 seconds
cpu usage	4.102866595
max memory	2.78904832E8

stage attributes

key	value
output-size	15250
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

int(g,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, 0 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


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

(0)
Obligation:
Clauses:

intlist([], []).
intlist(.(X, XS), .(s(X), YS)) :- intlist(XS, YS).
int(0, 0, .(0, [])).
int(0, s(Y), .(0, XS)) :- int(s(0), s(Y), XS).
int(s(X), 0, []).
int(s(X), s(Y), XS) :- ','(int(X, Y, ZS), intlist(ZS, XS)).


Query: int(g,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:

int_in_3: (b,b,f)

intlist_in_2: (b,f)

Transforming Prolog into the following Term Rewriting System:

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

   int_in_gga(0, 0, .(0, [])) -> int_out_gga(0, 0, .(0, []))
   int_in_gga(0, s(Y), .(0, XS)) -> U2_gga(Y, XS, int_in_gga(s(0), s(Y), XS))
   int_in_gga(s(X), 0, []) -> int_out_gga(s(X), 0, [])
   int_in_gga(s(X), s(Y), XS) -> U3_gga(X, Y, XS, int_in_gga(X, Y, ZS))
   U3_gga(X, Y, XS, int_out_gga(X, Y, ZS)) -> U4_gga(X, Y, XS, intlist_in_ga(ZS, XS))
   intlist_in_ga([], []) -> intlist_out_ga([], [])
   intlist_in_ga(.(X, XS), .(s(X), YS)) -> U1_ga(X, XS, YS, intlist_in_ga(XS, YS))
   U1_ga(X, XS, YS, intlist_out_ga(XS, YS)) -> intlist_out_ga(.(X, XS), .(s(X), YS))
   U4_gga(X, Y, XS, intlist_out_ga(ZS, XS)) -> int_out_gga(s(X), s(Y), XS)
   U2_gga(Y, XS, int_out_gga(s(0), s(Y), XS)) -> int_out_gga(0, s(Y), .(0, XS))

The argument filtering Pi contains the following mapping:
int_in_gga(x1, x2, x3)  =  int_in_gga(x1, x2)

0  =  0

int_out_gga(x1, x2, x3)  =  int_out_gga(x3)

s(x1)  =  s(x1)

U2_gga(x1, x2, x3)  =  U2_gga(x3)

U3_gga(x1, x2, x3, x4)  =  U3_gga(x4)

U4_gga(x1, x2, x3, x4)  =  U4_gga(x4)

intlist_in_ga(x1, x2)  =  intlist_in_ga(x1)

[]  =  []

intlist_out_ga(x1, x2)  =  intlist_out_ga(x2)

popout

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

job log

popout

actions all output return to Logic Programming