Logic Programming pair #487529587

details

property	value
status	complete
benchmark	sublist.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n076.star.cs.uiowa.edu
space	talp_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.13601613045 seconds
cpu usage	4.047848305
max memory	3.14863616E8

stage attributes

key	value
output-size	15827
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

sublist(g,g)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 2 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:

append1([], Ys, Ys).
append1(.(X, Xs), Ys, .(X, Zs)) :- append1(Xs, Ys, Zs).
append2([], Ys, Ys).
append2(.(X, Xs), Ys, .(X, Zs)) :- append2(Xs, Ys, Zs).
sublist(X, Y) :- ','(append1(P, X1, Y), append2(X2, X, P)).


Query: sublist(g,g)
----------------------------------------

(1) PrologToPiTRSProof (SOUND)
We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:

sublist_in_2: (b,b)

append1_in_3: (f,f,b)

append2_in_3: (f,b,b)

Transforming Prolog into the following Term Rewriting System:

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

   sublist_in_gg(X, Y) -> U3_gg(X, Y, append1_in_aag(P, X1, Y))
   append1_in_aag([], Ys, Ys) -> append1_out_aag([], Ys, Ys)
   append1_in_aag(.(X, Xs), Ys, .(X, Zs)) -> U1_aag(X, Xs, Ys, Zs, append1_in_aag(Xs, Ys, Zs))
   U1_aag(X, Xs, Ys, Zs, append1_out_aag(Xs, Ys, Zs)) -> append1_out_aag(.(X, Xs), Ys, .(X, Zs))
   U3_gg(X, Y, append1_out_aag(P, X1, Y)) -> U4_gg(X, Y, append2_in_agg(X2, X, P))
   append2_in_agg([], Ys, Ys) -> append2_out_agg([], Ys, Ys)
   append2_in_agg(.(X, Xs), Ys, .(X, Zs)) -> U2_agg(X, Xs, Ys, Zs, append2_in_agg(Xs, Ys, Zs))
   U2_agg(X, Xs, Ys, Zs, append2_out_agg(Xs, Ys, Zs)) -> append2_out_agg(.(X, Xs), Ys, .(X, Zs))
   U4_gg(X, Y, append2_out_agg(X2, X, P)) -> sublist_out_gg(X, Y)

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

U3_gg(x1, x2, x3)  =  U3_gg(x1, x3)

append1_in_aag(x1, x2, x3)  =  append1_in_aag(x3)

append1_out_aag(x1, x2, x3)  =  append1_out_aag(x1, x2)

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

U1_aag(x1, x2, x3, x4, x5)  =  U1_aag(x1, x5)

U4_gg(x1, x2, x3)  =  U4_gg(x3)

append2_in_agg(x1, x2, x3)  =  append2_in_agg(x2, x3)

append2_out_agg(x1, x2, x3)  =  append2_out_agg(x1)

U2_agg(x1, x2, x3, x4, x5)  =  U2_agg(x1, x5)

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