(STRATEGY
    INNERMOST)

(VAR
    x xs y)
(DATATYPES
    A = µX.< nil, 0, cons(X, X), true, false, s(X) >)
(SIGNATURES
    max :: [A] -> A
    if1 :: [A x A x A x A] -> A
    del :: [A x A] -> A
    if2 :: [A x A x A x A] -> A
    eq :: [A x A] -> A
    sort :: [A] -> A
    ge :: [A x A] -> A)
(RULES
    max(nil()) -> 0()
    max(cons(x,nil())) -> x
    max(cons(x,cons(y,xs))) ->
      if1(ge(x,y),x,y,xs)
    if1(true(),x,y,xs) -> max(cons(x
                                  ,xs))
    if1(false(),x,y,xs) ->
      max(cons(y,xs))
    del(x,nil()) -> nil()
    del(x,cons(y,xs)) -> if2(eq(x,y)
                            ,x
                            ,y
                            ,xs)
    if2(true(),x,y,xs) -> xs
    if2(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)
    sort(nil()) -> nil()
    sort(cons(x,xs)) ->
      cons(max(cons(x,xs))
          ,sort(del(max(cons(x,xs))
                   ,cons(x,xs))))
    ge(x,0()) -> true()
    ge(0(),s(x)) -> false()
    ge(s(x),s(y)) -> ge(x,y))