Logic Programming pair #487529573

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	n112.star.cs.uiowa.edu
space	talp_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.85959982872 seconds
cpu usage	4.050187196
max memory	3.13012224E8

stage attributes

key	value
output-size	15767
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

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)

[]  =  []

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