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)
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [and#](x0, x1, x2) = -1x0 + x1 + x2 + -16,
    
    [band](x0, x1) = x1 + -8,
    
    [and](x0, x1, x2) = 3x0 + 3x1 + 2x2 + 2,
    
    [not](x0) = 1x0 + 0
   orientation:
    and#(not(not(x)),y,not(z)) = 1x + y + 1z + 0 >= x + -1y + z + -8 = and#(y,band(x,z),x)
    
    and(not(not(x)),y,not(z)) = 5x + 3y + 3z + 4 >= 2x + 3y + 3z + 2 = and(y,band(x,z),x)
   problem:
    DPs:
     
    TRS:
     and(not(not(x)),y,not(z)) -> and(y,band(x,z),x)
   Qed