Input TRS:
    1: if(true(),x,y) -> x
    2: if(false(),x,y) -> y
    3: if(x,y,y) -> y
    4: if(if(x,y,z),u,v) -> if(x,if(y,u,v),if(z,u,v))
    5: if(x,if(x,y,z),z) -> if(x,y,z)
    6: if(x,y,if(x,y,z)) -> if(x,y,z)
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #if(if(x,y,z),u,v) -> #if(x,if(y,u,v),if(z,u,v))
   #2: #if(if(x,y,z),u,v) -> #if(y,u,v)
   #3: #if(if(x,y,z),u,v) -> #if(z,u,v)
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #1..3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
 false()	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: (/ 1 2) + x1 + x2 + x3
  #if(x1,x2,x3)	weight: x1
    Usable rules: { }
    Removed DPs: #1..3
Number of SCCs: 0, DPs: 0, edges: 0
YES