YES
Time: 0.001867
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}
  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))}
   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}
     SPSC:
      Simple Projection:
       pi(if#) = 0
      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#(z, u, v)}
      EDG:
       {(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#(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#(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#(z, u, v), if#(if(x, y, z), u, v) -> if#(z, u, v))}
       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#(z, u, v)}
        SCC (2):
         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#(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}
         SPSC:
          Simple Projection:
           pi(if#) = 0
          Strict:
           {if#(if(x, y, z), u, v) -> if#(z, u, v)}
          EDG:
           {(if#(if(x, y, z), u, v) -> if#(z, u, v), if#(if(x, y, z), u, v) -> if#(z, u, v))}
           SCCS (1):
            Scc:
             {if#(if(x, y, z), u, v) -> if#(z, u, v)}
            SCC (1):
             Strict:
              {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}
             SPSC:
              Simple Projection:
               pi(if#) = 0
              Strict:
               {}
              Qed