MAYBE

Problem:
 g(A()) -> A()
 g(B()) -> A()
 g(B()) -> B()
 g(C()) -> A()
 g(C()) -> B()
 g(C()) -> C()
 foldB(t,0()) -> t
 foldB(t,s(n)) -> f(foldB(t,n),B())
 foldC(t,0()) -> t
 foldC(t,s(n)) -> f(foldC(t,n),C())
 f(t,x) -> f'(t,g(x))
 f'(triple(a,b,c),C()) -> triple(a,b,s(c))
 f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
 f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
 f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)

Proof:
 Open