YES
Time: 0.006825
TRS:
 {          if(x, y, y) -> y,
  if(x, y, if(x, y, z)) -> if(x, y, z),
  if(x, if(x, y, z), z) -> if(x, y, z),
  if(if(x, y, z), u, v) -> if(x, if(y, u, v), if(z, u, v)),
       if(true(), x, y) -> x,
      if(false(), x, y) -> y}
 DP:
  DP:
   {if#(if(x, y, z), u, v) -> if#(x, if(y, 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#(z, u, v)}
  TRS:
  {          if(x, y, y) -> y,
   if(x, y, if(x, y, z)) -> if(x, y, z),
   if(x, if(x, y, z), z) -> if(x, y, z),
   if(if(x, y, z), u, v) -> if(x, if(y, u, v), if(z, u, v)),
        if(true(), x, y) -> x,
       if(false(), x, y) -> y}
  UR:
   {          if(x, y, y) -> y,
    if(x, y, if(x, y, z)) -> if(x, y, z),
    if(x, if(x, y, z), z) -> if(x, y, z),
    if(if(x, y, z), u, v) -> if(x, if(y, u, v), if(z, u, v)),
         if(true(), x, y) -> x,
        if(false(), x, y) -> y,
                  a(w, t) -> w,
                  a(w, t) -> t}
   EDG:
    {(if#(if(x, y, z), u, v) -> if#(z, u, v), if#(if(x, y, z), u, v) -> if#(z, u, v))
     (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#(z, u, v), if#(if(x, y, z), u, v) -> if#(x, if(y, u, v), if(z, u, v)))
     (if#(if(x, y, z), u, v) -> if#(x, if(y, u, v), if(z, u, v)), if#(if(x, y, z), u, v) -> if#(x, if(y, u, v), if(z, u, v)))
     (if#(if(x, y, z), u, v) -> if#(x, if(y, 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)), 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)))
     (if#(if(x, y, z), u, v) -> if#(y, u, v), if#(if(x, y, z), u, v) -> if#(y, u, v))
     (if#(if(x, y, z), u, v) -> if#(y, u, v), if#(if(x, y, z), u, v) -> if#(z, u, v))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {if#(if(x, y, z), u, v) -> if#(x, if(y, 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#(z, u, v)}
      
      SCC (3):
       Strict:
        {if#(if(x, y, z), u, v) -> if#(x, if(y, 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#(z, u, v)}
       Weak:
       {          if(x, y, y) -> y,
        if(x, y, if(x, y, z)) -> if(x, y, z),
        if(x, if(x, y, z), z) -> if(x, y, z),
        if(if(x, y, z), u, v) -> if(x, if(y, u, v), if(z, u, v)),
             if(true(), x, y) -> x,
            if(false(), x, y) -> y}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [if](x0, x1, x2) = x0 + x1 + x2 + 1,
         
         [true] = 1,
         
         [false] = 0,
         
         [if#](x0, x1, x2) = x0
        Strict:
         if#(if(x, y, z), u, v) -> if#(z, u, v)
         1 + 1x + 1y + 0u + 0v + 1z >= 0 + 0u + 0v + 1z
         if#(if(x, y, z), u, v) -> if#(y, u, v)
         1 + 1x + 1y + 0u + 0v + 1z >= 0 + 1y + 0u + 0v
         if#(if(x, y, z), u, v) -> if#(x, if(y, u, v), if(z, u, v))
         1 + 1x + 1y + 0u + 0v + 1z >= 0 + 1x + 0y + 0u + 0v + 0z
        Weak:
         if(false(), x, y) -> y
         1 + 1x + 1y >= 1y
         if(true(), x, y) -> x
         2 + 1x + 1y >= 1x
         if(if(x, y, z), u, v) -> if(x, if(y, u, v), if(z, u, v))
         2 + 1x + 1y + 1u + 1v + 1z >= 3 + 1x + 1y + 2u + 2v + 1z
         if(x, if(x, y, z), z) -> if(x, y, z)
         2 + 2x + 1y + 2z >= 1 + 1x + 1y + 1z
         if(x, y, if(x, y, z)) -> if(x, y, z)
         2 + 2x + 2y + 1z >= 1 + 1x + 1y + 1z
         if(x, y, y) -> y
         1 + 1x + 2y >= 1y
       Qed