Logic Programming pair #487096596

details

property	value
status	complete
benchmark	rotate.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	talp_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.71848 seconds
cpu usage	3.99992
user time	3.81994
system time	0.179979
max virtual memory	1.9343016E7
max residence set size	292636.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

rotate(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:

rotate(X, Y) :- ','(append2(A, B, X), append1(B, A, Y)).
append1(.(X, Xs), Ys, .(X, Zs)) :- append1(Xs, Ys, Zs).
append1([], Ys, Ys).
append2(.(X, Xs), Ys, .(X, Zs)) :- append2(Xs, Ys, Zs).
append2([], Ys, Ys).


Query: rotate(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:

rotate_in_2: (b,f)

append2_in_3: (f,f,b)

append1_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:

   rotate_in_ga(X, Y) -> U1_ga(X, Y, append2_in_aag(A, B, X))
   append2_in_aag(.(X, Xs), Ys, .(X, Zs)) -> U4_aag(X, Xs, Ys, Zs, append2_in_aag(Xs, Ys, Zs))
   append2_in_aag([], Ys, Ys) -> append2_out_aag([], Ys, Ys)
   U4_aag(X, Xs, Ys, Zs, append2_out_aag(Xs, Ys, Zs)) -> append2_out_aag(.(X, Xs), Ys, .(X, Zs))
   U1_ga(X, Y, append2_out_aag(A, B, X)) -> U2_ga(X, Y, append1_in_gga(B, A, Y))
   append1_in_gga(.(X, Xs), Ys, .(X, Zs)) -> U3_gga(X, Xs, Ys, Zs, append1_in_gga(Xs, Ys, Zs))
   append1_in_gga([], Ys, Ys) -> append1_out_gga([], Ys, Ys)
   U3_gga(X, Xs, Ys, Zs, append1_out_gga(Xs, Ys, Zs)) -> append1_out_gga(.(X, Xs), Ys, .(X, Zs))
   U2_ga(X, Y, append1_out_gga(B, A, Y)) -> rotate_out_ga(X, Y)

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

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

append2_in_aag(x1, x2, x3)  =  append2_in_aag(x3)

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

U4_aag(x1, x2, x3, x4, x5)  =  U4_aag(x1, x5)

append2_out_aag(x1, x2, x3)  =  append2_out_aag(x1, x2)

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

append1_in_gga(x1, x2, x3)  =  append1_in_gga(x1, x2)

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

[]  =  []

append1_out_gga(x1, x2, x3)  =  append1_out_gga(x3)

rotate_out_ga(x1, x2)  =  rotate_out_ga(x2)

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