Logic Programming pair #487529349

details

property	value
status	complete
benchmark	NJ6.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	terminweb_new

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.82024502754 seconds
cpu usage	4.071453849
max memory	3.1299584E8

stage attributes

key	value
output-size	13471
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

f(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:

f(A, [], RES) :- g(A, [], RES).
f(.(A, As), .(B, Bs), RES) :- f(.(B, .(A, As)), Bs, RES).
g([], RES, RES).
g(.(C, Cs), D, RES) :- g(Cs, .(C, D), RES).


Query: f(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:

f_in_3: (b,b,f)

g_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:

   f_in_gga(A, [], RES) -> U1_gga(A, RES, g_in_gga(A, [], RES))
   g_in_gga([], RES, RES) -> g_out_gga([], RES, RES)
   g_in_gga(.(C, Cs), D, RES) -> U3_gga(C, Cs, D, RES, g_in_gga(Cs, .(C, D), RES))
   U3_gga(C, Cs, D, RES, g_out_gga(Cs, .(C, D), RES)) -> g_out_gga(.(C, Cs), D, RES)
   U1_gga(A, RES, g_out_gga(A, [], RES)) -> f_out_gga(A, [], RES)
   f_in_gga(.(A, As), .(B, Bs), RES) -> U2_gga(A, As, B, Bs, RES, f_in_gga(.(B, .(A, As)), Bs, RES))
   U2_gga(A, As, B, Bs, RES, f_out_gga(.(B, .(A, As)), Bs, RES)) -> f_out_gga(.(A, As), .(B, Bs), RES)

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

[]  =  []

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

g_in_gga(x1, x2, x3)  =  g_in_gga(x1, x2)

g_out_gga(x1, x2, x3)  =  g_out_gga(x1, x2, x3)

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

U3_gga(x1, x2, x3, x4, x5)  =  U3_gga(x1, x2, x3, x5)

f_out_gga(x1, x2, x3)  =  f_out_gga(x1, x2, x3)

U2_gga(x1, x2, x3, x4, x5, x6)  =  U2_gga(x1, x2, x3, x4, x6)





Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog

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