(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< true, false, 0, s(X) >)
(SIGNATURES
    cond1 :: [A x A x A x A] -> A
    cond2 :: [A x A x A x A] -> A
    gr :: [A x A] -> A
    p :: [A] -> A
    eq :: [A x A] -> A
    and :: [A x A] -> A)
(RULES
    cond1(true(),x,y,z) ->
      cond2(gr(y,z),x,y,z)
    cond2(true(),x,y,z) ->
      cond2(gr(y,z),p(x),p(y),z)
    cond2(false(),x,y,z) ->
      cond1(and(eq(x,y),gr(x,z))
           ,x
           ,y
           ,z)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
    p(0()) -> 0()
    p(s(x)) -> x
    eq(0(),0()) -> true()
    eq(s(x),0()) -> false()
    eq(0(),s(x)) -> false()
    eq(s(x),s(y)) -> eq(x,y)
    and(true(),true()) -> true()
    and(false(),x) -> false()
    and(x,false()) -> false())