Input TRS:
    1: a__nats() -> a__adx(a__zeros())
    2: a__zeros() -> cons(0(),zeros())
    3: a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
    4: a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
    5: a__hd(cons(X,Y)) -> mark(X)
    6: a__tl(cons(X,Y)) -> mark(Y)
    7: mark(nats()) -> a__nats()
    8: mark(adx(X)) -> a__adx(mark(X))
    9: mark(zeros()) -> a__zeros()
    10: mark(incr(X)) -> a__incr(mark(X))
    11: mark(hd(X)) -> a__hd(mark(X))
    12: mark(tl(X)) -> a__tl(mark(X))
    13: mark(cons(X1,X2)) -> cons(X1,X2)
    14: mark(0()) -> 0()
    15: mark(s(X)) -> s(X)
    16: a__nats() -> nats()
    17: a__adx(X) -> adx(X)
    18: a__zeros() -> zeros()
    19: a__incr(X) -> incr(X)
    20: a__hd(X) -> hd(X)
    21: a__tl(X) -> tl(X)
Number of Rules: 21
Direct QWPOS(mSum) ... orients all.
	I(tl) = x1 + 4	sigma(tl) = [1]
	I(nats) = 2
	I(mark) = x1 + 3	sigma(mark) = [1]
	I(hd) = x1 + 4	sigma(hd) = [1]
	I(incr) = x1	sigma(incr) = [1]
	I(0) = 0
	I(s) = x1	sigma(s) = [1]
	I(a__zeros) = 2
	I(a__nats) = 4
	I(zeros) = 0
	I(cons) = x1 + x2 + 1	sigma(cons) = [2,1]
	I(adx) = x1 + 1	sigma(adx) = [1]
	I(a__incr) = x1	sigma(a__incr) = [1]
	I(a__adx) = x1 + 1	sigma(a__adx) = [1]
	I(a__tl) = x1 + 4	sigma(a__tl) = [1]
	I(a__hd) = x1 + 4	sigma(a__hd) = [1]
    PREC: nats > mark = a__nats = a__hd > a__adx = a__tl > a__zeros = a__incr > tl = hd = incr = 0 = zeros = cons = adx > s
Number of Rules: 0