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)
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [and#](x0, x1, x2) = x0 + x1 + 1,
    
    [band](x0, x1) = 0,
    
    [and](x0, x1, x2) = x0 + x1 + x2,
    
    [not](x0) = x0 + 1
   orientation:
    and#(not(not(x)),y,not(z)) = x + y + 3 >= y + 1 = and#(y,band(x,z),x)
    
    and(not(not(x)),y,not(z)) = x + y + z + 3 >= x + y = and(y,band(x,z),x)
   problem:
    DPs:
     
    TRS:
     and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
   Qed