The following code is representing the finite state transducer above. I need help filling the prolog code's transitions where it asks to be filled.

% FILL IN THE FST SPECIFICATION WHERE

% INDICATED THROUGHOUT THE FILE.

?- % Transitions out of state 0

transition(0, '#', 0, '#').

transition(0, '^', 0, eps).

% S below can be anything, except for #, ^, z, s, x, eps

% Pay close attention to how to interpret J&M's use of

% "other" and "#" in transitions.

% "other" means anything not used in any transitions

% going out of this state, excluding "#".

transition(0, S, 0, S) :-

S \= '#',

S \= '^',

S \= z,

S \= s,

S \= x,

S \= eps.

% S below must be one of z, s, x

transition(0, S, 1, S) :-

S = z;

S = s;

S = x.

% Transitions out of state 1

transition(1, S, 0, S) :-

% FILL IN LINES HERE THAT RESTRICT WHAT S CAN BE

S \= eps.

transition(1, S, 1, S) :-

% FILL IN LINES HERE THAT ALLOW S TO BE OTHER SYMBOLS

S = x.

transition(1, ^, 2, eps).

% Transitions out of state 2

% ADD YOUR TRANSITIONS HERE

% transitions out of state 3

transition(3, s, 4, s).

% transitions out of state 4

transition(4, '#', 0, '#').

% transitions out of state 5

transition(5, S, 1, S) :-

S = z;

S = s;

S = x.

transition(5, S, 0, S) :-

S \= z,

S \= s,

S \= x,

S \= '^',

S \= '#',

S \= eps.

transition(5, '^', 2, eps).

initial(0).

final(0).

other A.E Z,S? other z.sx E:e A:E do q1 #othe Z, X #, other other A.E Z,S? other z.sx E:e A:E do q1 #othe Z, X #, other