YES

Problem:
 and(x,or(y,z)) -> or(and(x,y),and(x,z))
 and(x,and(y,y)) -> and(x,y)
 or(or(x,y),and(y,z)) -> or(x,y)
 or(x,and(x,y)) -> x
 or(true(),y) -> true()
 or(x,false()) -> x
 or(x,x) -> x
 or(x,or(y,y)) -> or(x,y)
 and(x,true()) -> x
 and(false(),y) -> false()
 and(x,x) -> x

Proof:
 DP Processor:
  DPs:
   and#(x,or(y,z)) -> and#(x,z)
   and#(x,or(y,z)) -> and#(x,y)
   and#(x,or(y,z)) -> or#(and(x,y),and(x,z))
   and#(x,and(y,y)) -> and#(x,y)
   or#(x,or(y,y)) -> or#(x,y)
  TRS:
   and(x,or(y,z)) -> or(and(x,y),and(x,z))
   and(x,and(y,y)) -> and(x,y)
   or(or(x,y),and(y,z)) -> or(x,y)
   or(x,and(x,y)) -> x
   or(true(),y) -> true()
   or(x,false()) -> x
   or(x,x) -> x
   or(x,or(y,y)) -> or(x,y)
   and(x,true()) -> x
   and(false(),y) -> false()
   and(x,x) -> x
  TDG Processor:
   DPs:
    and#(x,or(y,z)) -> and#(x,z)
    and#(x,or(y,z)) -> and#(x,y)
    and#(x,or(y,z)) -> or#(and(x,y),and(x,z))
    and#(x,and(y,y)) -> and#(x,y)
    or#(x,or(y,y)) -> or#(x,y)
   TRS:
    and(x,or(y,z)) -> or(and(x,y),and(x,z))
    and(x,and(y,y)) -> and(x,y)
    or(or(x,y),and(y,z)) -> or(x,y)
    or(x,and(x,y)) -> x
    or(true(),y) -> true()
    or(x,false()) -> x
    or(x,x) -> x
    or(x,or(y,y)) -> or(x,y)
    and(x,true()) -> x
    and(false(),y) -> false()
    and(x,x) -> x
   graph:
    or#(x,or(y,y)) -> or#(x,y) -> or#(x,or(y,y)) -> or#(x,y)
    and#(x,and(y,y)) -> and#(x,y) -> and#(x,and(y,y)) -> and#(x,y)
    and#(x,and(y,y)) -> and#(x,y) ->
    and#(x,or(y,z)) -> or#(and(x,y),and(x,z))
    and#(x,and(y,y)) -> and#(x,y) -> and#(x,or(y,z)) -> and#(x,y)
    and#(x,and(y,y)) -> and#(x,y) ->
    and#(x,or(y,z)) -> and#(x,z)
    and#(x,or(y,z)) -> or#(and(x,y),and(x,z)) ->
    or#(x,or(y,y)) -> or#(x,y)
    and#(x,or(y,z)) -> and#(x,z) -> and#(x,and(y,y)) -> and#(x,y)
    and#(x,or(y,z)) -> and#(x,z) ->
    and#(x,or(y,z)) -> or#(and(x,y),and(x,z))
    and#(x,or(y,z)) -> and#(x,z) -> and#(x,or(y,z)) -> and#(x,y)
    and#(x,or(y,z)) -> and#(x,z) -> and#(x,or(y,z)) -> and#(x,z)
    and#(x,or(y,z)) -> and#(x,y) -> and#(x,and(y,y)) -> and#(x,y)
    and#(x,or(y,z)) -> and#(x,y) ->
    and#(x,or(y,z)) -> or#(and(x,y),and(x,z))
    and#(x,or(y,z)) -> and#(x,y) -> and#(x,or(y,z)) -> and#(x,y)
    and#(x,or(y,z)) -> and#(x,y) -> and#(x,or(y,z)) -> and#(x,z)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 14/25
    DPs:
     and#(x,and(y,y)) -> and#(x,y)
     and#(x,or(y,z)) -> and#(x,z)
     and#(x,or(y,z)) -> and#(x,y)
    TRS:
     and(x,or(y,z)) -> or(and(x,y),and(x,z))
     and(x,and(y,y)) -> and(x,y)
     or(or(x,y),and(y,z)) -> or(x,y)
     or(x,and(x,y)) -> x
     or(true(),y) -> true()
     or(x,false()) -> x
     or(x,x) -> x
     or(x,or(y,y)) -> or(x,y)
     and(x,true()) -> x
     and(false(),y) -> false()
     and(x,x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(and#) = 1
     problem:
      DPs:
       
      TRS:
       and(x,or(y,z)) -> or(and(x,y),and(x,z))
       and(x,and(y,y)) -> and(x,y)
       or(or(x,y),and(y,z)) -> or(x,y)
       or(x,and(x,y)) -> x
       or(true(),y) -> true()
       or(x,false()) -> x
       or(x,x) -> x
       or(x,or(y,y)) -> or(x,y)
       and(x,true()) -> x
       and(false(),y) -> false()
       and(x,x) -> x
     Qed
    
    DPs:
     or#(x,or(y,y)) -> or#(x,y)
    TRS:
     and(x,or(y,z)) -> or(and(x,y),and(x,z))
     and(x,and(y,y)) -> and(x,y)
     or(or(x,y),and(y,z)) -> or(x,y)
     or(x,and(x,y)) -> x
     or(true(),y) -> true()
     or(x,false()) -> x
     or(x,x) -> x
     or(x,or(y,y)) -> or(x,y)
     and(x,true()) -> x
     and(false(),y) -> false()
     and(x,x) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(or#) = 1
     problem:
      DPs:
       
      TRS:
       and(x,or(y,z)) -> or(and(x,y),and(x,z))
       and(x,and(y,y)) -> and(x,y)
       or(or(x,y),and(y,z)) -> or(x,y)
       or(x,and(x,y)) -> x
       or(true(),y) -> true()
       or(x,false()) -> x
       or(x,x) -> x
       or(x,or(y,y)) -> or(x,y)
       and(x,true()) -> x
       and(false(),y) -> false()
       and(x,x) -> x
     Qed