Logic Progr 19030 pair #381920013

details

property	value
status	complete
benchmark	div.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	talp_talp

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.28936505318 seconds
cpu usage	6.01554217
max memory	5.61860608E8

stage attributes

key	value
output-size	23453
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

div(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, 6 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 [EQUIVALENT, 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) QDPOrderProof [EQUIVALENT, 16 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE


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

(0)
Obligation:
Clauses:

div(X, s(Y), Z) :- div_s(X, Y, Z).
div_s(0, Y, 0).
div_s(s(X), Y, 0) :- lss(X, Y).
div_s(s(X), Y, s(Z)) :- ','(sub(X, Y, R), div_s(R, Y, Z)).
lss(s(X), s(Y)) :- lss(X, Y).
lss(0, s(Y)).
sub(s(X), s(Y), Z) :- sub(X, Y, Z).
sub(X, 0, X).


Query: div(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:

div_in_3: (b,b,f)

div_s_in_3: (b,b,f)

lss_in_2: (b,b)

sub_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:

   div_in_gga(X, s(Y), Z) -> U1_gga(X, Y, Z, div_s_in_gga(X, Y, Z))
   div_s_in_gga(0, Y, 0) -> div_s_out_gga(0, Y, 0)
   div_s_in_gga(s(X), Y, 0) -> U2_gga(X, Y, lss_in_gg(X, Y))
   lss_in_gg(s(X), s(Y)) -> U5_gg(X, Y, lss_in_gg(X, Y))
   lss_in_gg(0, s(Y)) -> lss_out_gg(0, s(Y))
   U5_gg(X, Y, lss_out_gg(X, Y)) -> lss_out_gg(s(X), s(Y))
   U2_gga(X, Y, lss_out_gg(X, Y)) -> div_s_out_gga(s(X), Y, 0)
   div_s_in_gga(s(X), Y, s(Z)) -> U3_gga(X, Y, Z, sub_in_gga(X, Y, R))
   sub_in_gga(s(X), s(Y), Z) -> U6_gga(X, Y, Z, sub_in_gga(X, Y, Z))
   sub_in_gga(X, 0, X) -> sub_out_gga(X, 0, X)
   U6_gga(X, Y, Z, sub_out_gga(X, Y, Z)) -> sub_out_gga(s(X), s(Y), Z)
   U3_gga(X, Y, Z, sub_out_gga(X, Y, R)) -> U4_gga(X, Y, Z, div_s_in_gga(R, Y, Z))
   U4_gga(X, Y, Z, div_s_out_gga(R, Y, Z)) -> div_s_out_gga(s(X), Y, s(Z))
   U1_gga(X, Y, Z, div_s_out_gga(X, Y, Z)) -> div_out_gga(X, s(Y), Z)

The argument filtering Pi contains the following mapping:

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