Termination Proof Script

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