(STRATEGY
    INNERMOST)

(VAR
    x xs y)
(DATATYPES
    A = µX.< nil, 0, cons(X, X), true, false, s(X) >)
(SIGNATURES
    last :: [A] -> A
    del :: [A x A] -> A
    if :: [A x A x A x A] -> A
    eq :: [A x A] -> A
    reverse :: [A] -> A)
(RULES
    last(nil()) -> 0()
    last(cons(x,nil())) -> x
    last(cons(x,cons(y,xs))) ->
      last(cons(y,xs))
    del(x,nil()) -> nil()
    del(x,cons(y,xs)) -> if(eq(x,y)
                           ,x
                           ,y
                           ,xs)
    if(true(),x,y,xs) -> xs
    if(false(),x,y,xs) -> cons(y
                              ,del(x,xs))
    eq(0(),0()) -> true()
    eq(0(),s(y)) -> false()
    eq(s(x),0()) -> false()
    eq(s(x),s(y)) -> eq(x,y)
    reverse(nil()) -> nil()
    reverse(cons(x,xs)) ->
      cons(last(cons(x,xs))
          ,reverse(del(last(cons(x,xs))
                      ,cons(x,xs)))))