Logic Progr 19030 pair #381919965

details

property	value
status	complete
benchmark	pl7.6.2c.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	talp_plumer

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.99765014648 seconds
cpu usage	8.274202478
max memory	5.0907136E8

stage attributes

key	value
output-size	36247
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

reach(g,g,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, 27 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 [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) PiDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) PiDP
        (31) PiDPToQDPProof [SOUND, 3 ms]
        (32) QDP
        (33) QDPQMonotonicMRRProof [EQUIVALENT, 26 ms]
        (34) QDP
        (35) DependencyGraphProof [EQUIVALENT, 0 ms]
        (36) TRUE


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

(0)
Obligation:
Clauses:

reach(X, Y, E, L) :- member(.(X, .(Y, [])), E).
reach(X, Z, E, L) :- ','(member1(.(X, .(Y, [])), E), ','(member(Y, L), ','(delete(Y, L, V1), reach(Y, Z, E, V1)))).
member(H, .(H, L)).
member(X, .(H, L)) :- member(X, L).
member1(H, .(H, L)).
member1(X, .(H, L)) :- member1(X, L).
delete(X, .(X, Y), Y).
delete(X, .(H, T1), .(H, T2)) :- delete(X, T1, T2).


Query: reach(g,g,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:

reach_in_4: (b,b,b,b)

member_in_2: (b,b)

member1_in_2: (f,b)

delete_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:

   reach_in_gggg(X, Y, E, L) -> U1_gggg(X, Y, E, L, member_in_gg(.(X, .(Y, [])), E))
   member_in_gg(H, .(H, L)) -> member_out_gg(H, .(H, L))
   member_in_gg(X, .(H, L)) -> U6_gg(X, H, L, member_in_gg(X, L))
   U6_gg(X, H, L, member_out_gg(X, L)) -> member_out_gg(X, .(H, L))
   U1_gggg(X, Y, E, L, member_out_gg(.(X, .(Y, [])), E)) -> reach_out_gggg(X, Y, E, L)
   reach_in_gggg(X, Z, E, L) -> U2_gggg(X, Z, E, L, member1_in_ag(.(X, .(Y, [])), E))
   member1_in_ag(H, .(H, L)) -> member1_out_ag(H, .(H, L))
   member1_in_ag(X, .(H, L)) -> U7_ag(X, H, L, member1_in_ag(X, L))
   U7_ag(X, H, L, member1_out_ag(X, L)) -> member1_out_ag(X, .(H, L))

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