Input TRS:
    1: a__incr(nil()) -> nil()
    2: a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L))
    3: a__adx(nil()) -> nil()
    4: a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L)))
    5: a__nats() -> a__adx(a__zeros())
    6: a__zeros() -> cons(0(),zeros())
    7: a__head(cons(X,L)) -> mark(X)
    8: a__tail(cons(X,L)) -> mark(L)
    9: mark(incr(X)) -> a__incr(mark(X))
    10: mark(adx(X)) -> a__adx(mark(X))
    11: mark(nats()) -> a__nats()
    12: mark(zeros()) -> a__zeros()
    13: mark(head(X)) -> a__head(mark(X))
    14: mark(tail(X)) -> a__tail(mark(X))
    15: mark(nil()) -> nil()
    16: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    17: mark(s(X)) -> s(mark(X))
    18: mark(0()) -> 0()
    19: a__incr(X) -> incr(X)
    20: a__adx(X) -> adx(X)
    21: a__nats() -> nats()
    22: a__zeros() -> zeros()
    23: a__head(X) -> head(X)
    24: a__tail(X) -> tail(X)
Number of Rules: 24
Direct QWPOS(max) ... orients all.
	I(a__head) = x1 + 1	sigma(a__head) = [1]
	I(nats) = 4
	I(mark) = x1	sigma(mark) = [1]
	I(incr) = x1	sigma(incr) = [1]
	I(0) = 0
	I(nil) = 0
	I(s) = x1	sigma(s) = [1]
	I(head) = x1 + 1	sigma(head) = [1]
	I(a__tail) = x1 + 1	sigma(a__tail) = [1]
	I(a__zeros) = 2
	I(a__nats) = 4
	I(zeros) = 2
	I(cons) = max(x1 + 1, x2)	sigma(cons) = [1,2]
	I(adx) = x1	sigma(adx) = [1]
	I(a__incr) = x1	sigma(a__incr) = [1]
	I(a__adx) = x1	sigma(a__adx) = [1]
	I(tail) = x1 + 1	sigma(tail) = [1]
    PREC: a__head = mark > a__tail = a__adx > nil = head = a__nats = tail > nats = a__zeros = a__incr > 0 = zeros = cons > incr = s = adx
Number of Rules: 0