YES
Time: 0.009504
TRS:
 {    implies(x, or(y, z)) -> or(y, implies(x, z)),
         implies(not x, y) -> or(x, y),
  implies(not x, or(y, z)) -> implies(y, or(x, z))}
 DP:
  DP:
   {    implies#(x, or(y, z)) -> implies#(x, z),
    implies#(not x, or(y, z)) -> implies#(y, or(x, z))}
  TRS:
  {    implies(x, or(y, z)) -> or(y, implies(x, z)),
          implies(not x, y) -> or(x, y),
   implies(not x, or(y, z)) -> implies(y, or(x, z))}
  UR:
   {}
   EDG:
    {(implies#(not x, or(y, z)) -> implies#(y, or(x, z)), implies#(not x, or(y, z)) -> implies#(y, or(x, z)))
     (implies#(not x, or(y, z)) -> implies#(y, or(x, z)), implies#(x, or(y, z)) -> implies#(x, z))
     (implies#(x, or(y, z)) -> implies#(x, z), implies#(x, or(y, z)) -> implies#(x, z))
     (implies#(x, or(y, z)) -> implies#(x, z), implies#(not x, or(y, z)) -> implies#(y, or(x, z)))}
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {    implies#(x, or(y, z)) -> implies#(x, z),
        implies#(not x, or(y, z)) -> implies#(y, or(x, z))}
      
      SCC (2):
       Strict:
        {    implies#(x, or(y, z)) -> implies#(x, z),
         implies#(not x, or(y, z)) -> implies#(y, or(x, z))}
       Weak:
       {    implies(x, or(y, z)) -> or(y, implies(x, z)),
               implies(not x, y) -> or(x, y),
        implies(not x, or(y, z)) -> implies(y, or(x, z))}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [or](x0, x1) = x0 + x1 + 1,
         
         [implies](x0, x1) = 0,
         
         [not](x0) = x0 + 1,
         
         [implies#](x0, x1) = x0 + x1
        Strict:
         implies#(not x, or(y, z)) -> implies#(y, or(x, z))
         2 + 1x + 1y + 1z >= 1 + 1x + 1y + 1z
         implies#(x, or(y, z)) -> implies#(x, z)
         1 + 1x + 1y + 1z >= 0 + 1x + 1z
        Weak:
         implies(not x, or(y, z)) -> implies(y, or(x, z))
         0 + 0x + 0y + 0z >= 0 + 0x + 0y + 0z
         implies(not x, y) -> or(x, y)
         0 + 0x + 0y >= 1 + 1x + 1y
         implies(x, or(y, z)) -> or(y, implies(x, z))
         0 + 0x + 0y + 0z >= 1 + 0x + 1y + 0z
       Qed