Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    i(x) * x  → 1
2:    1 * y  → y
3:    x * 0  → 0
4:    (x * y) * z  → x * (y * z)
There are 2 dependency pairs:
5:    (x * y) *# z  → x *# (y * z)
6:    (x * y) *# z  → y *# z
Consider the SCC {5,6}. By taking the AF π with π(*#) = π(i) = 1 together with the lexicographic path order with precedence *1, the rules in {1-6} are strictly decreasing. Hence the TRS is terminating.
Tyrolean Termination Tool  (0.01 seconds)   ---  May 3, 2006