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))
  CDG 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))
   graph:
    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)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 2/4
    DPs:
     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))
    Subterm Criterion Processor:
     simple projection:
      pi(implies#) = 1
     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