SWISH -- SWI-Prolog for SHaring

:- use_module(library(clpfd)).

transition(even, term, X, _) :- X #= 0.
transition(even, odd, X, Y) :- X #\= 0, Y #= X - 1.

transition(odd, term, X, _) :- X #= 0.
transition(odd, even, X, Y) :- X #\= 0, Y #= X - 1.

transition(fac, term, X, _) :- X #= 0.
transition(fac, fac, X, Y) :- X #\= 0, Y #= X - 1.

transition(f, f, X, Y) :- Y #= X-1.

hasBaseCase(X) :- transition(X,Y,_,_), X\=Y.
noBaseCase(X) :- \+ (hasBaseCase(X)).

infCountdown(X, Y) :- transition(X, term, C1, _),
    				  transition(X, X, Z, 0), Z #> C1, Y #< C1,
    				  \+ (transition(X, term, Y, _)).

infCountdown(X, Y) :- transition(X, term, C1, _),
    				  transition(X, X, Z, 0), Z #< C1, Y #> C1,
					  \+ (transition(X, term, Y, _)).

nStepTransition(1, X, Y, Z, W) :- transition(X, Y, Z, W).
nStepTransition(N, X, Y, Z, W) :- N \= 1, M is N-1,
    							  nStepTransition(M, X, A, Z, B),
								  transition(A, Y, B, W).

infCountdown2(X, Y) :- transition(X, term, C1, _),
    				  	  nStepTransition(2, X, X, Z, 0), Z #> C1, Y #< C1,
    					  \+ (transition(X, term, Y, _)),
    					  \+ nStepTransition(2, X, term, Y, 0).

% ?- noBaseCase(f). % true
% ?- infCountdown(fac, X). % X in inf .. -1
% ?- infCountdown2(even, X). % X in inf .. -1