Logic Programming pair #487529127

details

property	value
status	complete
benchmark	naive_rev.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	talp_apt

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.8727581501 seconds
cpu usage	4.008719233
max memory	3.02985216E8

stage attributes

key	value
output-size	13096
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

reverse(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


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

(0)
Obligation:
Clauses:

app(.(X, Xs), Ys, .(X, Zs)) :- app(Xs, Ys, Zs).
app([], Ys, Ys).
reverse(.(X, Xs), Ys) :- ','(reverse(Xs, Zs), app(Zs, .(X, []), Ys)).
reverse([], []).


Query: reverse(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:

reverse_in_2: (b,f)

app_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:

   reverse_in_ga(.(X, Xs), Ys) -> U2_ga(X, Xs, Ys, reverse_in_ga(Xs, Zs))
   reverse_in_ga([], []) -> reverse_out_ga([], [])
   U2_ga(X, Xs, Ys, reverse_out_ga(Xs, Zs)) -> U3_ga(X, Xs, Ys, app_in_gga(Zs, .(X, []), Ys))
   app_in_gga(.(X, Xs), Ys, .(X, Zs)) -> U1_gga(X, Xs, Ys, Zs, app_in_gga(Xs, Ys, Zs))
   app_in_gga([], Ys, Ys) -> app_out_gga([], Ys, Ys)
   U1_gga(X, Xs, Ys, Zs, app_out_gga(Xs, Ys, Zs)) -> app_out_gga(.(X, Xs), Ys, .(X, Zs))
   U3_ga(X, Xs, Ys, app_out_gga(Zs, .(X, []), Ys)) -> reverse_out_ga(.(X, Xs), Ys)

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

.(x1, x2)  =  .(x1, x2)

U2_ga(x1, x2, x3, x4)  =  U2_ga(x1, x4)

[]  =  []

reverse_out_ga(x1, x2)  =  reverse_out_ga(x2)

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

app_in_gga(x1, x2, x3)  =  app_in_gga(x1, x2)

U1_gga(x1, x2, x3, x4, x5)  =  U1_gga(x1, x5)

app_out_gga(x1, x2, x3)  =  app_out_gga(x3)





Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

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