(STRATEGY
    INNERMOST)

(VAR
    b l m n r x y)
(DATATYPES
    A = µX.< empty, true, node(X, X), false, 0, s(X) >)
(SIGNATURES
    isEmpty :: [A] -> A
    left :: [A] -> A
    right :: [A] -> A
    inc :: [A] -> A
    count :: [A x A] -> A
    if :: [A x A x A x A x A x A] -> A
    nrOfNodes :: [A] -> A)
(RULES
    isEmpty(empty()) -> true()
    isEmpty(node(l,r)) -> false()
    left(empty()) -> empty()
    left(node(l,r)) -> l
    right(empty()) -> empty()
    right(node(l,r)) -> r
    inc(0()) -> s(0())
    inc(s(x)) -> s(inc(x))
    count(n,x) -> if(isEmpty(n)
                    ,isEmpty(left(n))
                    ,right(n)
                    ,node(left(left(n))
                         ,node(right(left(n)),right(n)))
                    ,x
                    ,inc(x))
    if(true(),b,n,m,x,y) -> x
    if(false(),false(),n,m,x,y) ->
      count(m,x)
    if(false(),true(),n,m,x,y) ->
      count(n,y)
    nrOfNodes(n) -> count(n,0()))