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()))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 1 3 2
     v()	weight: 0
     u()	weight: 0
 false()	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: (/ 1 4) + 2 * x1 + x2 + x3
Number of strict rules: 1
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: 2, edges: 4
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     v()	weight: 0
     u()	weight: 0
 false()	weight: 0
  true()	weight: 0
    if(x1,x2,x3)	weight: (/ 1 2) + x2 + x3
  #if(x1,x2,x3)	weight: x1
    Usable rules: { }
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0, edges: 0
YES