Logic Progr 19030 pair #381920144

details

property	value
status	complete
benchmark	convert.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.11076998711 seconds
cpu usage	5.524837329
max memory	4.46636032E8

stage attributes

key	value
output-size	23846
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

convert(g,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
    (21) PiDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) PiDP
        (24) PiDPToQDPProof [SOUND, 0 ms]
        (25) QDP
        (26) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES


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

(0)
Obligation:
Clauses:

convert([], B, 0).
convert(.(0, XS), B, X) :- ','(convert(XS, B, Y), times(Y, B, X)).
convert(.(s(Y), XS), B, s(X)) :- convert(.(Y, XS), B, X).
plus(0, Y, Y).
plus(s(X), Y, s(Z)) :- plus(X, Y, Z).
times(0, Y, 0).
times(s(X), Y, Z) :- ','(times(X, Y, U), plus(Y, U, Z)).


Query: convert(g,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:

convert_in_3: (b,b,f)

times_in_3: (b,b,f)

plus_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:

   convert_in_gga([], B, 0) -> convert_out_gga([], B, 0)
   convert_in_gga(.(0, XS), B, X) -> U1_gga(XS, B, X, convert_in_gga(XS, B, Y))
   convert_in_gga(.(s(Y), XS), B, s(X)) -> U3_gga(Y, XS, B, X, convert_in_gga(.(Y, XS), B, X))
   U3_gga(Y, XS, B, X, convert_out_gga(.(Y, XS), B, X)) -> convert_out_gga(.(s(Y), XS), B, s(X))
   U1_gga(XS, B, X, convert_out_gga(XS, B, Y)) -> U2_gga(XS, B, X, times_in_gga(Y, B, X))
   times_in_gga(0, Y, 0) -> times_out_gga(0, Y, 0)
   times_in_gga(s(X), Y, Z) -> U5_gga(X, Y, Z, times_in_gga(X, Y, U))
   U5_gga(X, Y, Z, times_out_gga(X, Y, U)) -> U6_gga(X, Y, Z, plus_in_gga(Y, U, Z))
   plus_in_gga(0, Y, Y) -> plus_out_gga(0, Y, Y)
   plus_in_gga(s(X), Y, s(Z)) -> U4_gga(X, Y, Z, plus_in_gga(X, Y, Z))
   U4_gga(X, Y, Z, plus_out_gga(X, Y, Z)) -> plus_out_gga(s(X), Y, s(Z))
   U6_gga(X, Y, Z, plus_out_gga(Y, U, Z)) -> times_out_gga(s(X), Y, Z)
   U2_gga(XS, B, X, times_out_gga(Y, B, X)) -> convert_out_gga(.(0, XS), B, X)

The argument filtering Pi contains the following mapping:
convert_in_gga(x1, x2, x3)  =  convert_in_gga(x1, x2)

[]  =  []

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