Logic Programming pair #487096514

details

property	value
status	complete
benchmark	insert-fbf.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	BCGGV05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.23866 seconds
cpu usage	5.67731
user time	5.38666
system time	0.290648
max virtual memory	1.8944652E7
max residence set size	528312.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

insert(a,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, 3 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 4 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [SOUND, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 3 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) PiDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) PiDP
        (31) PiDPToQDPProof [SOUND, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) PiDP
        (36) UsableRulesProof [EQUIVALENT, 0 ms]
        (37) PiDP
        (38) PiDPToQDPProof [SOUND, 0 ms]
        (39) QDP
        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (41) YES


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

(0)
Obligation:
Clauses:

insert(X, void, tree(X, void, void)).
insert(X, tree(X, Left, Right), tree(X, Left, Right)).
insert(X, tree(Y, Left, Right), tree(Y, Left1, Right)) :- ','(less(X, Y), insert(X, Left, Left1)).
insert(X, tree(Y, Left, Right), tree(Y, Left, Right1)) :- ','(less(Y, X), insert(X, Right, Right1)).
less(0, s(X1)).
less(s(X), s(Y)) :- less(X, Y).


Query: insert(a,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:

insert_in_3: (f,b,f) (b,b,f)

less_in_2: (f,b) (b,b) (b,f)

Transforming Prolog into the following Term Rewriting System:

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

   insert_in_aga(X, void, tree(X, void, void)) -> insert_out_aga(X, void, tree(X, void, void))
   insert_in_aga(X, tree(X, Left, Right), tree(X, Left, Right)) -> insert_out_aga(X, tree(X, Left, Right), tree(X, Left, Right))
   insert_in_aga(X, tree(Y, Left, Right), tree(Y, Left1, Right)) -> U1_aga(X, Y, Left, Right, Left1, less_in_ag(X, Y))
   less_in_ag(0, s(X1)) -> less_out_ag(0, s(X1))
   less_in_ag(s(X), s(Y)) -> U5_ag(X, Y, less_in_ag(X, Y))
   U5_ag(X, Y, less_out_ag(X, Y)) -> less_out_ag(s(X), s(Y))
   U1_aga(X, Y, Left, Right, Left1, less_out_ag(X, Y)) -> U2_aga(X, Y, Left, Right, Left1, insert_in_gga(X, Left, Left1))
   insert_in_gga(X, void, tree(X, void, void)) -> insert_out_gga(X, void, tree(X, void, void))
   insert_in_gga(X, tree(X, Left, Right), tree(X, Left, Right)) -> insert_out_gga(X, tree(X, Left, Right), tree(X, Left, Right))
   insert_in_gga(X, tree(Y, Left, Right), tree(Y, Left1, Right)) -> U1_gga(X, Y, Left, Right, Left1, less_in_gg(X, Y))
   less_in_gg(0, s(X1)) -> less_out_gg(0, s(X1))
   less_in_gg(s(X), s(Y)) -> U5_gg(X, Y, less_in_gg(X, Y))
   U5_gg(X, Y, less_out_gg(X, Y)) -> less_out_gg(s(X), s(Y))
   U1_gga(X, Y, Left, Right, Left1, less_out_gg(X, Y)) -> U2_gga(X, Y, Left, Right, Left1, insert_in_gga(X, Left, Left1))
   insert_in_gga(X, tree(Y, Left, Right), tree(Y, Left, Right1)) -> U3_gga(X, Y, Left, Right, Right1, less_in_gg(Y, X))
   U3_gga(X, Y, Left, Right, Right1, less_out_gg(Y, X)) -> U4_gga(X, Y, Left, Right, Right1, insert_in_gga(X, Right, Right1))

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