Logic Progr 19030 pair #381920011

details

property	value
status	complete
benchmark	permutation.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	talp_apt

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.13098502159 seconds
cpu usage	5.394634497
max memory	4.73837568E8

stage attributes

key	value
output-size	23048
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 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
    (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:

app1(.(X0, X), Y, .(X0, Z)) :- app1(X, Y, Z).
app1([], Y, Y).
app2(.(X0, X), Y, .(X0, Z)) :- app2(X, Y, Z).
app2([], Y, Y).
perm(X, .(X0, Y)) :- ','(app1(X1, .(X0, X2), X), ','(app2(X1, X2, Z), perm(Z, Y))).
perm([], []).


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)

app1_in_3: (f,f,b)

app2_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:

   perm_in_ga(X, .(X0, Y)) -> U3_ga(X, X0, Y, app1_in_aag(X1, .(X0, X2), X))
   app1_in_aag(.(X0, X), Y, .(X0, Z)) -> U1_aag(X0, X, Y, Z, app1_in_aag(X, Y, Z))
   app1_in_aag([], Y, Y) -> app1_out_aag([], Y, Y)
   U1_aag(X0, X, Y, Z, app1_out_aag(X, Y, Z)) -> app1_out_aag(.(X0, X), Y, .(X0, Z))
   U3_ga(X, X0, Y, app1_out_aag(X1, .(X0, X2), X)) -> U4_ga(X, X0, Y, X1, X2, app2_in_gga(X1, X2, Z))
   app2_in_gga(.(X0, X), Y, .(X0, Z)) -> U2_gga(X0, X, Y, Z, app2_in_gga(X, Y, Z))
   app2_in_gga([], Y, Y) -> app2_out_gga([], Y, Y)
   U2_gga(X0, X, Y, Z, app2_out_gga(X, Y, Z)) -> app2_out_gga(.(X0, X), Y, .(X0, Z))
   U4_ga(X, X0, Y, X1, X2, app2_out_gga(X1, X2, Z)) -> U5_ga(X, X0, Y, perm_in_ga(Z, Y))
   perm_in_ga([], []) -> perm_out_ga([], [])
   U5_ga(X, X0, Y, perm_out_ga(Z, Y)) -> perm_out_ga(X, .(X0, Y))

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

U3_ga(x1, x2, x3, x4)  =  U3_ga(x4)

app1_in_aag(x1, x2, x3)  =  app1_in_aag(x3)

.(x1, x2)  =  .(x2)

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