0.00/0.50	NO
0.00/0.50	
0.00/0.50	Problem:
0.00/0.50	ihalf(0()) -> tp1(0())
0.00/0.50	ihalf(s(y)) -> tp1(s(s(x))) <= ihalf(y) = tp(x)
0.00/0.50	ihalf(half(x)) -> tp1(x)
0.00/0.50	iadd(y) -> tp2(0(), y)
0.00/0.50	iadd(s(z)) -> tp2(s(x), y) <= iadd(z) = tp2(x, y)
0.00/0.50	iadd(add(x, y)) -> tp2(x, y)
0.00/0.50	imul(0()) -> tp2(0(), y)
0.00/0.50	imul(0()) -> tp2(x, 0())
0.00/0.50	imul(s(z)) -> tp2(s(x), s(y)) <= iadd(z) = tp2(w, y), imul(w) = tp2(x, s(y))
0.00/0.50	imul(mul(x, y)) -> tp2(x, y)
0.00/0.50	imh(y) -> tp1(x) <= imul(y) = tp2(x, z), ihalf(z) = tp1(s(x))
0.00/0.50	imh(mh(x)) -> tp1(x)
0.00/0.50	
0.00/0.50	Proof:
0.00/0.50	This system is not confluent.
0.00/0.50	This system is oriented.
0.00/0.50	For the unconditional rule imul(0()) -> tp2(x, 0()) the variables of the right-hand side are not a subset of the variables of the left-hand side but the right-hand side is a normal form wrt R_u.
0.00/0.50	
0.00/0.51	EOF