Left Termination of the query pattern prime_fact_in_2(g, a) w.r.t. the given Prolog program could not be shown:

(0) Obligation:

Clauses:

prime_fact(0, L) :- ','(!, eq(L, [])).
prime_fact(s(0), L) :- ','(!, eq(L, [])).
prime_fact(X, .(F, Fs)) :- ','(prime_number(P), ','(div(X, P, Q, 0), ','(!, ','(eq(F, P), prime_fact(Q, Fs))))).
prime_number(X) :- prime_number(s(s(0)), [], X).
prime_number(C, Ps, C) :- no_divisor_in_list(C, Ps).
prime_number(C, Ps, P) :- ','(no_divisor_in_list(C, Ps), ','(!, prime_number(s(C), .(C, Ps), P))).
prime_number(C, Ps, P) :- prime_number(s(C), Ps, P).
no_divisor_in_list(X1, []).
no_divisor_in_list(V, .(D, Ds)) :- ','(not_div(V, D), no_divisor_in_list(V, Ds)).
not_div(V, D) :- ','(div(V, D, X2, 0), ','(!, failure(a))).
not_div(X3, X4).
failure(b).
div(X5, 0, X6, X7) :- ','(!, failure(a)).
div(0, X8, Z, R) :- ','(!, ','(eq(Z, 0), eq(R, 0))).
div(X, Y, s(Z), R) :- ','(minus(X, Y, U), ','(!, div(U, Y, Z, R))).
div(X, X9, X10, X).
minus(X, 0, X).
minus(s(X), s(Y), Z) :- minus(X, Y, Z).
eq(X, X).

Queries:

prime_fact(g,a).