(STRATEGY
    INNERMOST)

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