Logic Progr 19030 pair #381919839

details

property	value
status	complete
benchmark	reach.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	terminweb_old

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.96328091621 seconds
cpu usage	8.339649313
max memory	5.05663488E8

stage attributes

key	value
output-size	39306
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 20 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, 2 ms]
        (32) QDP
        (33) QDPQMonotonicMRRProof [EQUIVALENT, 33 ms]
        (34) QDP
        (35) DependencyGraphProof [EQUIVALENT, 0 ms]
        (36) TRUE


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

(0)
Obligation:
Clauses:

reach(X, Y, Edges, Not_Visited) :- member(.(X, .(Y, [])), Edges).
reach(X, Z, Edges, Not_Visited) :- ','(member(.(X, .(Y, [])), Edges), ','(member(Y, Not_Visited), ','(delete(Y, Not_Visited, V1), reach(Y, Z, Edges, V1)))).
member(H, .(H, L)).
member(X, .(H, L)) :- member(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) (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, Edges, Not_Visited) -> U1_gggg(X, Y, Edges, Not_Visited, member_in_gg(.(X, .(Y, [])), Edges))
   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, Edges, Not_Visited, member_out_gg(.(X, .(Y, [])), Edges)) -> reach_out_gggg(X, Y, Edges, Not_Visited)
   reach_in_gggg(X, Z, Edges, Not_Visited) -> U2_gggg(X, Z, Edges, Not_Visited, member_in_ag(.(X, .(Y, [])), Edges))
   member_in_ag(H, .(H, L)) -> member_out_ag(H, .(H, L))
   member_in_ag(X, .(H, L)) -> U6_ag(X, H, L, member_in_ag(X, L))
   U6_ag(X, H, L, member_out_ag(X, L)) -> member_out_ag(X, .(H, L))
   U2_gggg(X, Z, Edges, Not_Visited, member_out_ag(.(X, .(Y, [])), Edges)) -> U3_gggg(X, Z, Edges, Not_Visited, Y, member_in_gg(Y, Not_Visited))
   U3_gggg(X, Z, Edges, Not_Visited, Y, member_out_gg(Y, Not_Visited)) -> U4_gggg(X, Z, Edges, Not_Visited, Y, delete_in_gga(Y, Not_Visited, V1))
   delete_in_gga(X, .(X, Y), Y) -> delete_out_gga(X, .(X, Y), Y)
   delete_in_gga(X, .(H, T1), .(H, T2)) -> U7_gga(X, H, T1, T2, delete_in_gga(X, T1, T2))

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