Logic Programming pair #487529391

details

property	value
status	complete
benchmark	permutation1.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	terminweb_old

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.25394105911 seconds
cpu usage	5.465844212
max memory	4.48630784E8

stage attributes

key	value
output-size	23024
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

perm(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, 9 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) MRRProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES


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

(0)
Obligation:
Clauses:

perm(Xs, .(X, Ys)) :- ','(app(X1s, .(X, X2s), Xs), ','(app(X1s, X2s, Zs), perm(Zs, Ys))).
perm([], []).
app(.(X, Xs), Ys, .(X, Zs)) :- app(Xs, Ys, Zs).
app([], Ys, Ys).


Query: perm(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:

perm_in_2: (b,f)

app_in_3: (f,f,b) (b,b,f)

Transforming Prolog into the following Term Rewriting System:

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

   perm_in_ga(Xs, .(X, Ys)) -> U1_ga(Xs, X, Ys, app_in_aag(X1s, .(X, X2s), Xs))
   app_in_aag(.(X, Xs), Ys, .(X, Zs)) -> U4_aag(X, Xs, Ys, Zs, app_in_aag(Xs, Ys, Zs))
   app_in_aag([], Ys, Ys) -> app_out_aag([], Ys, Ys)
   U4_aag(X, Xs, Ys, Zs, app_out_aag(Xs, Ys, Zs)) -> app_out_aag(.(X, Xs), Ys, .(X, Zs))
   U1_ga(Xs, X, Ys, app_out_aag(X1s, .(X, X2s), Xs)) -> U2_ga(Xs, X, Ys, app_in_gga(X1s, X2s, Zs))
   app_in_gga(.(X, Xs), Ys, .(X, Zs)) -> U4_gga(X, Xs, Ys, Zs, app_in_gga(Xs, Ys, Zs))
   app_in_gga([], Ys, Ys) -> app_out_gga([], Ys, Ys)
   U4_gga(X, Xs, Ys, Zs, app_out_gga(Xs, Ys, Zs)) -> app_out_gga(.(X, Xs), Ys, .(X, Zs))
   U2_ga(Xs, X, Ys, app_out_gga(X1s, X2s, Zs)) -> U3_ga(Xs, X, Ys, perm_in_ga(Zs, Ys))
   perm_in_ga([], []) -> perm_out_ga([], [])
   U3_ga(Xs, X, Ys, perm_out_ga(Zs, Ys)) -> perm_out_ga(Xs, .(X, Ys))

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

U1_ga(x1, x2, x3, x4)  =  U1_ga(x4)

app_in_aag(x1, x2, x3)  =  app_in_aag(x3)

.(x1, x2)  =  .(x2)

U4_aag(x1, x2, x3, x4, x5)  =  U4_aag(x5)

app_out_aag(x1, x2, x3)  =  app_out_aag(x1, x2)

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