(STRATEGY
    INNERMOST)

(VAR
    L X X1 X2 XS Y YS)
(DATATYPES
    A = µX.< nil, mark(X), ok(X) >)
(SIGNATURES
    active :: [A] -> A
    app :: [A x A] -> A
    cons :: [A x A] -> A
    from :: [A] -> A
    s :: [A] -> A
    zWadr :: [A x A] -> A
    prefix :: [A] -> A
    proper :: [A] -> A
    top :: [A] -> A)
(RULES
    active(app(nil(),YS)) ->
      mark(YS)
    active(app(cons(X,XS),YS)) ->
      mark(cons(X,app(XS,YS)))
    active(from(X)) -> mark(cons(X
                                ,from(s(X))))
    active(zWadr(nil(),YS)) ->
      mark(nil())
    active(zWadr(XS,nil())) ->
      mark(nil())
    active(zWadr(cons(X,XS)
                ,cons(Y,YS))) -> mark(cons(app(Y
                                              ,cons(X,nil()))
                                          ,zWadr(XS,YS)))
    active(prefix(L)) ->
      mark(cons(nil()
               ,zWadr(L,prefix(L))))
    active(app(X1,X2)) ->
      app(active(X1),X2)
    active(app(X1,X2)) -> app(X1
                             ,active(X2))
    active(cons(X1,X2)) ->
      cons(active(X1),X2)
    active(from(X)) ->
      from(active(X))
    active(s(X)) -> s(active(X))
    active(zWadr(X1,X2)) ->
      zWadr(active(X1),X2)
    active(zWadr(X1,X2)) -> zWadr(X1
                                 ,active(X2))
    active(prefix(X)) ->
      prefix(active(X))
    app(mark(X1),X2) -> mark(app(X1
                                ,X2))
    app(X1,mark(X2)) -> mark(app(X1
                                ,X2))
    cons(mark(X1),X2) ->
      mark(cons(X1,X2))
    from(mark(X)) -> mark(from(X))
    s(mark(X)) -> mark(s(X))
    zWadr(mark(X1),X2) ->
      mark(zWadr(X1,X2))
    zWadr(X1,mark(X2)) ->
      mark(zWadr(X1,X2))
    prefix(mark(X)) ->
      mark(prefix(X))
    proper(app(X1,X2)) ->
      app(proper(X1),proper(X2))
    proper(nil()) -> ok(nil())
    proper(cons(X1,X2)) ->
      cons(proper(X1),proper(X2))
    proper(from(X)) ->
      from(proper(X))
    proper(s(X)) -> s(proper(X))
    proper(zWadr(X1,X2)) ->
      zWadr(proper(X1),proper(X2))
    proper(prefix(X)) ->
      prefix(proper(X))
    app(ok(X1),ok(X2)) -> ok(app(X1
                                ,X2))
    cons(ok(X1),ok(X2)) ->
      ok(cons(X1,X2))
    from(ok(X)) -> ok(from(X))
    s(ok(X)) -> ok(s(X))
    zWadr(ok(X1),ok(X2)) ->
      ok(zWadr(X1,X2))
    prefix(ok(X)) -> ok(prefix(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X)))