(STRATEGY
    INNERMOST)

(VAR
    x y z)
(DATATYPES
    A = µX.< true, 0, false, s(X) >)
(SIGNATURES
    cond1 :: [A x A x A x A] -> A
    cond2 :: [A x A x A x A] -> A
    cond3 :: [A x A x A x A] -> A
    gr :: [A x A] -> A
    or :: [A x A] -> A
    p :: [A] -> A)
(RULES
    cond1(true(),x,y,z) ->
      cond2(gr(x,0()),x,y,z)
    cond2(true(),x,y,z) ->
      cond1(or(gr(x,z),gr(y,z))
           ,p(x)
           ,y
           ,z)
    cond2(false(),x,y,z) ->
      cond3(gr(y,0()),x,y,z)
    cond3(true(),x,y,z) ->
      cond1(or(gr(x,z),gr(y,z))
           ,x
           ,p(y)
           ,z)
    cond3(false(),x,y,z) ->
      cond1(or(gr(x,z),gr(y,z)),x,y,z)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
    or(false(),false()) -> false()
    or(true(),x) -> true()
    or(x,true()) -> true()
    p(0()) -> 0()
    p(s(x)) -> x)