Logic Progr 19030 pair #381919746

details

property	value
status	complete
benchmark	permute2.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	prolog_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.05101895332 seconds
cpu usage	5.041084951
max memory	4.45054976E8

stage attributes

key	value
output-size	15287
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

permute(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) MRRProof [EQUIVALENT, 1 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
Clauses:

permute([], []).
permute(.(X, Y), .(U, V)) :- ','(delete(U, .(X, Y), W), permute(W, V)).
delete(X, .(X, Y), Y).
delete(U, .(X, Y), .(X, Z)) :- delete(U, Y, Z).


Query: permute(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:

permute_in_2: (b,f)

delete_in_3: (f,b,f)

Transforming Prolog into the following Term Rewriting System:

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

   permute_in_ga([], []) -> permute_out_ga([], [])
   permute_in_ga(.(X, Y), .(U, V)) -> U1_ga(X, Y, U, V, delete_in_aga(U, .(X, Y), W))
   delete_in_aga(X, .(X, Y), Y) -> delete_out_aga(X, .(X, Y), Y)
   delete_in_aga(U, .(X, Y), .(X, Z)) -> U3_aga(U, X, Y, Z, delete_in_aga(U, Y, Z))
   U3_aga(U, X, Y, Z, delete_out_aga(U, Y, Z)) -> delete_out_aga(U, .(X, Y), .(X, Z))
   U1_ga(X, Y, U, V, delete_out_aga(U, .(X, Y), W)) -> U2_ga(X, Y, U, V, permute_in_ga(W, V))
   U2_ga(X, Y, U, V, permute_out_ga(W, V)) -> permute_out_ga(.(X, Y), .(U, V))

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

[]  =  []

permute_out_ga(x1, x2)  =  permute_out_ga(x2)

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

U1_ga(x1, x2, x3, x4, x5)  =  U1_ga(x5)

delete_in_aga(x1, x2, x3)  =  delete_in_aga(x2)

delete_out_aga(x1, x2, x3)  =  delete_out_aga(x1, x3)

U3_aga(x1, x2, x3, x4, x5)  =  U3_aga(x2, x5)

U2_ga(x1, x2, x3, x4, x5)  =  U2_ga(x3, x5)

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