The grounded program is still cyclic after executing "problog ground --break-cycles"

[werifu]

Example 4 in the tutorial:
https://dtai.cs.kuleuven.be/problog/tutorial/various/08_bayesian_dataflow.html

% toss both coins for the first time
0.5::c1(0).
0.5::c2(0).

% keep tossing if none was heads
0.5::c1(T) :- T > 0, TT is T-1, \+ or_c1_c2(TT).
0.5::c2(T) :- T > 0, TT is T-1, \+ or_c1_c2(TT).
or_c1_c2(T) :- c1(T).
or_c1_c2(T) :- c2(T).

% return
return(T,1,1) :- or_c1_c2(T), c1(T), c2(T).
return(T,1,0) :- or_c1_c2(T), c1(T), \+ c2(T).
return(T,0,1) :- or_c1_c2(T), \+ c1(T), c2(T).
return(T,0,0) :- or_c1_c2(T),\+c1(T),\+c2(T).

query(return(T,_,_)) :- between(0,2,T).

In the original example, the last line is query(return(T,_,_)) :- between(0,5,T)., but query(return(T,_,_)) :- between(0,2,T). is a smaller case to reproduce this.
After grounded, the output code is as below:

0.5::c1(1) :- \+aux_0.
0.5::c2(1) :- \+aux_0.
0.5::c1(2) :- \+aux_0.
0.5::c2(2) :- \+aux_0.
0.5::c1(0).
0.5::c2(0).
or_c1_c2(0) :- c1(0).
or_c1_c2(0) :- c2(0).
return(0,1,1) :- or_c1_c2(0), c1(0), c2(0).
aux_1 :- c2(0).
return(0,1,0) :- or_c1_c2(0), c1(0), \+aux_1.
return(0,0,1) :- or_c1_c2(0), \+c1(0), c2(0).
aux_-1 :- c2(0).
return(0,0,0) :- or_c1_c2(0), \+c1(0), \+aux_-1.
aux_0 :- or_c1_c2(0).
aux_0 :- or_c1_c2(0).
or_c1_c2(1) :- c1(1).
or_c1_c2(1) :- c2(1).
return(1,1,1) :- or_c1_c2(1), c1(1), c2(1).
aux_17 :- c2(1).
return(1,1,0) :- or_c1_c2(1), c1(1), \+aux_17.
return(1,0,1) :- or_c1_c2(1), \+c1(1), c2(1).
aux_-17 :- c2(1).
return(1,0,0) :- or_c1_c2(1), \+c1(1), \+aux_-17.
aux_0 :- or_c1_c2(1).
aux_0 :- or_c1_c2(1).
or_c1_c2(2) :- c1(2).
or_c1_c2(2) :- c2(2).
return(2,1,1) :- or_c1_c2(2), c1(2), c2(2).
aux_36 :- c2(2).
return(2,1,0) :- or_c1_c2(2), c1(2), \+aux_36.
return(2,0,1) :- or_c1_c2(2), \+c1(2), c2(2).
aux_-36 :- c2(2).
return(2,0,0) :- or_c1_c2(2), \+c1(2), \+aux_-36.
query(return(0,1,1)).
query(return(0,1,0)).
query(return(0,0,1)).
query(return(0,0,0)).
query(return(1,1,1)).
query(return(1,1,0)).
query(return(1,0,1)).
query(return(1,0,0)).
query(return(2,1,1)).
query(return(2,1,0)).
query(return(2,0,1)).
query(return(2,0,0)).

There are cycles in this grounded file.
e.g.

0.5::c1(1) :- \+aux_0.
...
aux_0 :- or_c1_c2(1).
...
or_c1_c2(1) :- c1(1).
...

c1(1) <- aux_0 <- or_c1_c2(1) <- c1(1)

[rmanhaeve]

I have a feeling this is a bug in getting names for the auxiliary variables. By also specifying the --compact option I get:

0.5::c1(1) :- \+or_c1_c2(0).
0.5::c2(1) :- \+or_c1_c2(0).
0.5::c1(2) :- \+or_c1_c2(1).
0.5::c2(2) :- \+or_c1_c2(1).
0.5::c1(0).
0.5::c2(0).
or_c1_c2(0) :- c1(0).
or_c1_c2(0) :- c2(0).
return(0,1,1) :- or_c1_c2(0), c1(0), c2(0).
return(0,1,0) :- or_c1_c2(0), c1(0), \+c2(0).
return(0,0,1) :- or_c1_c2(0), \+c1(0), c2(0).
return(0,0,0) :- or_c1_c2(0), \+c1(0), \+c2(0).
or_c1_c2(1) :- c1(1).
or_c1_c2(1) :- c2(1).
return(1,1,1) :- or_c1_c2(1), c1(1), c2(1).
return(1,1,0) :- or_c1_c2(1), c1(1), \+c2(1).
return(1,0,1) :- or_c1_c2(1), \+c1(1), c2(1).
return(1,0,0) :- or_c1_c2(1), \+c1(1), \+c2(1).
or_c1_c2(2) :- c1(2).
or_c1_c2(2) :- c2(2).
return(2,1,1) :- or_c1_c2(2), c1(2), c2(2).
return(2,1,0) :- or_c1_c2(2), c1(2), \+c2(2).
return(2,0,1) :- or_c1_c2(2), \+c1(2), c2(2).
return(2,0,0) :- or_c1_c2(2), \+c1(2), \+c2(2).
query(return(0,1,1)).
query(return(0,1,0)).
query(return(0,0,1)).
query(return(0,0,0)).
query(return(1,1,1)).
query(return(1,1,0)).
query(return(1,0,1)).
query(return(1,0,0)).
query(return(2,1,1)).
query(return(2,1,0)).
query(return(2,0,1)).
query(return(2,0,0)).

Which seems better.