(STRATEGY
    INNERMOST)

(VAR
    L X X1 X2 Y)
(DATATYPES
    A = µX.< 0, true, s(X), false, cons(X, X), inf(X), nil, take(X, X), length(X), eq(X, X) >)
(SIGNATURES
    a__eq :: [A x A] -> A
    a__inf :: [A] -> A
    a__take :: [A x A] -> A
    a__length :: [A] -> A
    mark :: [A] -> A)
(RULES
    a__eq(0(),0()) -> true()
    a__eq(s(X),s(Y)) -> a__eq(X,Y)
    a__eq(X,Y) -> false()
    a__inf(X) -> cons(X,inf(s(X)))
    a__take(0(),X) -> nil()
    a__take(s(X),cons(Y,L)) ->
      cons(Y,take(X,L))
    a__length(nil()) -> 0()
    a__length(cons(X,L)) ->
      s(length(L))
    mark(eq(X1,X2)) -> a__eq(X1,X2)
    mark(inf(X)) -> a__inf(mark(X))
    mark(take(X1,X2)) ->
      a__take(mark(X1),mark(X2))
    mark(length(X)) ->
      a__length(mark(X))
    mark(0()) -> 0()
    mark(true()) -> true()
    mark(s(X)) -> s(X)
    mark(false()) -> false()
    mark(cons(X1,X2)) -> cons(X1,X2)
    mark(nil()) -> nil()
    a__eq(X1,X2) -> eq(X1,X2)
    a__inf(X) -> inf(X)
    a__take(X1,X2) -> take(X1,X2)
    a__length(X) -> length(X))