'$skip_max_list'/4 issue

[notoria]

?- [user].
:- use_module(library(between)).

sml(S, M, Xs0, Xs) :- '$skip_max_list'(S, M, Xs0, Xs).

query :-
   between(0, 9, M),
   Es = [0,1,2|Es],
   sml(S, M, Es, Fs),
   write_term(user_output, [S,M,Es,Fs], [variable_names(['Es'=Es,'Fs'=Fs])]), nl,
   false.

?- query.
% Warning: couldn't append history (existing file)
[0,0,[0,1,2|Es],[0,1,2|Es]]
[1,1,[0,1,2|Es],[1,2,0|Fs]]
[2,2,[0,1,2|Es],[2,0,1|Fs]]
[3,3,[0,1,2|Es],[0,1,2|Es]]
[4,4,[0,1,2|Es],[1,2,0|Fs]] % unexpected 4
[5,5,[0,1,2|Es],[2,0,1|Fs]] % unexpected 5
[3,6,[0,1,2|Es],[0,1,2|Es]]
[3,7,[0,1,2|Es],[0,1,2|Es]]
[3,8,[0,1,2|Es],[0,1,2|Es]]
[3,9,[0,1,2|Es],[0,1,2|Es]]
   false.
?-

[UWN]

First thing I do not understand: How can the variable name be written out that way? What do we see there?? The variable Es is instantiated to a non-variable term so how does it show now in the output?

[notoria]

I remember now why the skip can be bigger than lambda+mu, it's for efficiency reason.

But:

?- length(Es0, 6), Es = [0,1,2|Es], nth0(N, Es, E, Fs), append(Es0, _, Fs).
   Es0 = [1,2,0,1,2,0], Es = [0,1,2|Es], N = 0, E = 0, Fs = [1,2,0|Fs]
;  Es0 = [0,2,0,1,2,0], Es = [0,1,2|Es], N = 1, E = 1, Fs = [0,2,0,1|2]
;  Es0 = [0,1,0,1,2,0], Es = [0,1,2|Es], N = 2, E = 2, Fs = [0,1,0,1,2|Es]
;  Es0 = [0,1,2,1,2,0], Es = [0,1,2|Es], N = 3, E = 0, Fs = [0,1,2,1,2,0|1]
;  Es0 = [0,1,2,0,2,0], Es = [0,1,2|Es], N = 4, E = 1, Fs = [0,1,2,0,2,0,1|2]
;  Es0 = [0,1,2,0,1,0], Es = [0,1,2|Es], N = 5, E = 2, Fs = [0,1,2,0,1,0,1,2|Es]
;  Es0 = [0,1,2,0,1,2], Es = [0,1,2|Es], N = 6, E = 0, Fs = [0,1,2,0,1,2,1,2,0|1]

The predicate nth0/4 has an issue. The value of Es0 should rotate.

The option variable_names is a bit permissive:

?- Es = [0,1,2|Es], write_term(user_output, A=Es, [variable_names(['Es'=A,'B'=Es,'C'=0])]), nl.
Es=[0,1,2|B]
   Es = [0,1,2|Es].
?-

A new option cycle_names could be created for cyclic term.

[UWN]

..., [0,2,0,1|2]

A max_depth writing would really be preferable.