Logic Programming pair #487529663

details

property	value
status	complete
benchmark	log2a.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	lpexamples

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.25356292725 seconds
cpu usage	5.563295619
max memory	4.77855744E8

stage attributes

key	value
output-size	16626
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

log2(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, 4 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [SOUND, 14 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, 42 ms]
        (20) QDP
        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
        (22) TRUE


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

(0)
Obligation:
Clauses:

log2(X, Y) :- log2(X, 0, Y).
log2(0, I, I).
log2(s(0), I, I).
log2(s(s(X)), I, Y) :- ','(half(s(s(X)), X1), log2(X1, s(I), Y)).
half(0, 0).
half(s(0), 0).
half(s(s(X)), s(Y)) :- half(X, Y).


Query: log2(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:

log2_in_2: (b,f)

log2_in_3: (b,b,f)

half_in_2: (b,f)

Transforming Prolog into the following Term Rewriting System:

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

   log2_in_ga(X, Y) -> U1_ga(X, Y, log2_in_gga(X, 0, Y))
   log2_in_gga(0, I, I) -> log2_out_gga(0, I, I)
   log2_in_gga(s(0), I, I) -> log2_out_gga(s(0), I, I)
   log2_in_gga(s(s(X)), I, Y) -> U2_gga(X, I, Y, half_in_ga(s(s(X)), X1))
   half_in_ga(0, 0) -> half_out_ga(0, 0)
   half_in_ga(s(0), 0) -> half_out_ga(s(0), 0)
   half_in_ga(s(s(X)), s(Y)) -> U4_ga(X, Y, half_in_ga(X, Y))
   U4_ga(X, Y, half_out_ga(X, Y)) -> half_out_ga(s(s(X)), s(Y))
   U2_gga(X, I, Y, half_out_ga(s(s(X)), X1)) -> U3_gga(X, I, Y, log2_in_gga(X1, s(I), Y))
   U3_gga(X, I, Y, log2_out_gga(X1, s(I), Y)) -> log2_out_gga(s(s(X)), I, Y)
   U1_ga(X, Y, log2_out_gga(X, 0, Y)) -> log2_out_ga(X, Y)

The argument filtering Pi contains the following mapping:
log2_in_ga(x1, x2)  =  log2_in_ga(x1)

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

log2_in_gga(x1, x2, x3)  =  log2_in_gga(x1, x2)

0  =  0

log2_out_gga(x1, x2, x3)  =  log2_out_gga(x3)

s(x1)  =  s(x1)

U2_gga(x1, x2, x3, x4)  =  U2_gga(x2, x4)

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