Input TRS:
    1: a__U11(tt(),M,N) -> a__U12(tt(),M,N)
    2: a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
    3: a__plus(N,0()) -> mark(N)
    4: a__plus(N,s(M)) -> a__U11(tt(),M,N)
    5: mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
    6: mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
    7: mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    8: mark(tt()) -> tt()
    9: mark(s(X)) -> s(mark(X))
    10: mark(0()) -> 0()
    11: a__U11(X1,X2,X3) -> U11(X1,X2,X3)
    12: a__U12(X1,X2,X3) -> U12(X1,X2,X3)
    13: a__plus(X1,X2) -> plus(X1,X2)
Number of Rules: 13
Direct QWPOS(mPol) ... orients all.
	I(tt) = 2
	I(mark) = x1	sigma(mark) = [1]
	I(0) = 3
	I(plus) = x1 + x2	sigma(plus) = [1,2]
	I(s) = x1 + 3	sigma(s) = [1]
	I(U11) = x1 + x2 + x3 + 1	sigma(U11) = [1,2,3]
	I(U12) = x1 + x2 + x3 + 1	sigma(U12) = [1,3,2]
	I(a__U11) = x1 + x2 + x3 + 1	sigma(a__U11) = [1,2,3]
	I(a__U12) = x1 + x2 + x3 + 1	sigma(a__U12) = [1,3,2]
	I(a__plus) = x1 + x2	sigma(a__plus) = [1,2]
    PREC: mark > a__plus > 0 > tt = plus > a__U11 > a__U12 > s = U11 = U12
Number of Rules: 0