YES

Problem:
 implies(not(x),y) -> or(x,y)
 implies(not(x),or(y,z)) -> implies(y,or(x,z))
 implies(x,or(y,z)) -> or(y,implies(x,z))

Proof:
 DP Processor:
  DPs:
   implies#(not(x),or(y,z)) -> implies#(y,or(x,z))
   implies#(x,or(y,z)) -> implies#(x,z)
  TRS:
   implies(not(x),y) -> or(x,y)
   implies(not(x),or(y,z)) -> implies(y,or(x,z))
   implies(x,or(y,z)) -> or(y,implies(x,z))
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [implies#](x0, x1) = x1,
    
    [or](x0, x1) = x1 + 1,
    
    [implies](x0, x1) = x1 + 1,
    
    [not](x0) = 0
   orientation:
    implies#(not(x),or(y,z)) = z + 1 >= z + 1 = implies#(y,or(x,z))
    
    implies#(x,or(y,z)) = z + 1 >= z = implies#(x,z)
    
    implies(not(x),y) = y + 1 >= y + 1 = or(x,y)
    
    implies(not(x),or(y,z)) = z + 2 >= z + 2 = implies(y,or(x,z))
    
    implies(x,or(y,z)) = z + 2 >= z + 2 = or(y,implies(x,z))
   problem:
    DPs:
     implies#(not(x),or(y,z)) -> implies#(y,or(x,z))
    TRS:
     implies(not(x),y) -> or(x,y)
     implies(not(x),or(y,z)) -> implies(y,or(x,z))
     implies(x,or(y,z)) -> or(y,implies(x,z))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [implies#](x0, x1) = x0 + x1,
     
     [or](x0, x1) = x0 + x1,
     
     [implies](x0, x1) = x0 + x1,
     
     [not](x0) = x0 + 1
    orientation:
     implies#(not(x),or(y,z)) = x + y + z + 1 >= x + y + z = implies#(y,or(x,z))
     
     implies(not(x),y) = x + y + 1 >= x + y = or(x,y)
     
     implies(not(x),or(y,z)) = x + y + z + 1 >= x + y + z = implies(y,or(x,z))
     
     implies(x,or(y,z)) = x + y + z >= x + y + z = or(y,implies(x,z))
    problem:
     DPs:
      
     TRS:
      implies(not(x),y) -> or(x,y)
      implies(not(x),or(y,z)) -> implies(y,or(x,z))
      implies(x,or(y,z)) -> or(y,implies(x,z))
    Qed