YES

Problem:
 and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)

Proof:
 DP Processor:
  DPs:
   and#(not(not(x)),y,not(z)) -> and#(y,band(x,z),x)
  TRS:
   and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
  Usable Rule Processor:
   DPs:
    and#(not(not(x)),y,not(z)) -> and#(y,band(x,z),x)
   TRS:
    
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     
    interpretation:
     [and#](x0, x1, x2) = -7x0 + x1 + -2x2,
     
     [band](x0, x1) = x1,
     
     [not](x0) = 3x0
    orientation:
     and#(not(not(x)),y,not(z)) = -1x + y + 1z >= -2x + -7y + z = and#(y,band(x,z),x)
    problem:
     DPs:
      
     TRS:
      
    Qed