YES

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()))

max/plus interpretations on N:

  if_A(x1,x2,x3) = max{6, 4 + x1, 4 + x2, 3 + x3}
  if#_A(x1,x2,x3) = max{0, 2, 1, 5}
  true_A = 0
  true#_A = 0
  false_A = 0
  false#_A = 0
  u_A = 2
  u#_A = 3
  v_A = 3
  v#_A = 4

precedence:

  if > true = false = v > u