(STRATEGY
    INNERMOST)

(VAR
    b c x y)
(DATATYPES
    A = µX.< 0, s(X), true, false >)
(SIGNATURES
    plus :: [A x A] -> A
    lt :: [A x A] -> A
    fib :: [A] -> A
    fibiter :: [A x A x A x A] -> A
    if :: [A x A x A x A x A] -> A)
(RULES
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    lt(0(),s(y)) -> true()
    lt(x,0()) -> false()
    lt(s(x),s(y)) -> lt(x,y)
    fib(x) -> fibiter(x
                     ,0()
                     ,0()
                     ,s(0()))
    fibiter(b,c,x,y) -> if(lt(c,b)
                          ,b
                          ,c
                          ,x
                          ,y)
    if(false(),b,c,x,y) -> x
    if(true(),b,c,x,y) -> fibiter(b
                                 ,s(c)
                                 ,y
                                 ,plus(x,y)))