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))
  KBO Processor:
   argument filtering:
    pi(not) = [0]
    pi(implies) = [0,1]
    pi(or) = [0,1]
    pi(implies#) = [0,1]
   weight function:
    w0 = 1
    w(implies#) = w(or) = w(implies) = w(not) = 1
   precedence:
    implies > implies# ~ or ~ not
   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