prolog Searching the Lists
predicate([a,c,b,d,e],[a,b,c,d]).

predicate([a,c,b,e,d],[a,b,c,d]).

has_prefix_perm(List1, List2) :-
    permutation(List2, Permutation),
    prefix(Permutation, List1),
    !.

has_prefix_perm(_, []) :- !.
has_prefix_perm([Head1|List1], List2) :-
    once(select(Head1, List2, Rest)),
    has_prefix_perm(List1, Rest).

has_prefix_perm(List1, List2) :-
    length(List2, L),
    length(LittleL1, L),
    append(LittleL1, _, List1),
    permutation(LittleL1, List2),
    !.

perm_prefix(Ls1, Ls2) :- phrase(perm(Ls2), Ls1, _).

perm([])  --> [].
perm(Ls0) --> [L], { select(L, Ls0, Ls1) }, perm(Ls1).

?- perm_prefix([a,c,b,d,e],[a,b,c,d]).
true

?- perm_prefix([a,c,b,e,d],[a,b,c,d]).
false.