YES

Problem:
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 if(x,y,y) -> y
 if(if(x,y,z),u,v) -> if(x,if(y,u,v),if(z,u,v))
 if(x,if(x,y,z),z) -> if(x,y,z)
 if(x,y,if(x,y,z)) -> if(x,y,z)

Proof:
 DP Processor:
  DPs:
   if#(if(x,y,z),u,v) -> if#(z,u,v)
   if#(if(x,y,z),u,v) -> if#(y,u,v)
   if#(if(x,y,z),u,v) -> if#(x,if(y,u,v),if(z,u,v))
  TRS:
   if(true(),x,y) -> x
   if(false(),x,y) -> y
   if(x,y,y) -> y
   if(if(x,y,z),u,v) -> if(x,if(y,u,v),if(z,u,v))
   if(x,if(x,y,z),z) -> if(x,y,z)
   if(x,y,if(x,y,z)) -> if(x,y,z)
  LPO Processor:
   argument filtering:
    pi(true) = []
    pi(if) = [0,1,2]
    pi(false) = []
    pi(if#) = 0
   precedence:
    if# ~ false ~ if ~ true
   problem:
    DPs:
     
    TRS:
     if(true(),x,y) -> x
     if(false(),x,y) -> y
     if(x,y,y) -> y
     if(if(x,y,z),u,v) -> if(x,if(y,u,v),if(z,u,v))
     if(x,if(x,y,z),z) -> if(x,y,z)
     if(x,y,if(x,y,z)) -> if(x,y,z)
   Qed