YES

Problem:
 xor(x,F()) -> x
 xor(x,neg(x)) -> F()
 and(x,T()) -> x
 and(x,F()) -> F()
 and(x,x) -> x
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))
 xor(x,x) -> F()
 impl(x,y) -> xor(and(x,y),xor(x,T()))
 or(x,y) -> xor(and(x,y),xor(x,y))
 equiv(x,y) -> xor(x,xor(y,T()))
 neg(x) -> xor(x,T())

Proof:
 DP Processor:
  DPs:
   and#(xor(x,y),z) -> and#(y,z)
   and#(xor(x,y),z) -> and#(x,z)
   and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
   impl#(x,y) -> xor#(x,T())
   impl#(x,y) -> and#(x,y)
   impl#(x,y) -> xor#(and(x,y),xor(x,T()))
   or#(x,y) -> xor#(x,y)
   or#(x,y) -> and#(x,y)
   or#(x,y) -> xor#(and(x,y),xor(x,y))
   equiv#(x,y) -> xor#(y,T())
   equiv#(x,y) -> xor#(x,xor(y,T()))
   neg#(x) -> xor#(x,T())
  TRS:
   xor(x,F()) -> x
   xor(x,neg(x)) -> F()
   and(x,T()) -> x
   and(x,F()) -> F()
   and(x,x) -> x
   and(xor(x,y),z) -> xor(and(x,z),and(y,z))
   xor(x,x) -> F()
   impl(x,y) -> xor(and(x,y),xor(x,T()))
   or(x,y) -> xor(and(x,y),xor(x,y))
   equiv(x,y) -> xor(x,xor(y,T()))
   neg(x) -> xor(x,T())
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [neg#](x0) = 5/2x0 + 2,
    
    [equiv#](x0, x1) = 2x0 + 2x1 + 2,
    
    [or#](x0, x1) = 2x0 + 1/2x1 + 2,
    
    [impl#](x0, x1) = 2x0 + 2x1 + 7/2,
    
    [and#](x0, x1) = 2x0 + 1/2x1,
    
    [xor#](x0, x1) = 2x0 + 1,
    
    [equiv](x0, x1) = 3/2x0 + 3/2x1 + 5/2,
    
    [or](x0, x1) = 5/2x0 + 2x1 + 2,
    
    [impl](x0, x1) = 5/2x0 + 1/2x1 + 3,
    
    [and](x0, x1) = x0,
    
    [T] = 0,
    
    [neg](x0) = x0 + 1,
    
    [xor](x0, x1) = x0 + x1 + 1,
    
    [F] = 0
   orientation:
    and#(xor(x,y),z) = 2x + 2y + 1/2z + 2 >= 2y + 1/2z = and#(y,z)
    
    and#(xor(x,y),z) = 2x + 2y + 1/2z + 2 >= 2x + 1/2z = and#(x,z)
    
    and#(xor(x,y),z) = 2x + 2y + 1/2z + 2 >= 2x + 1 = xor#(and(x,z),and(y,z))
    
    impl#(x,y) = 2x + 2y + 7/2 >= 2x + 1 = xor#(x,T())
    
    impl#(x,y) = 2x + 2y + 7/2 >= 2x + 1/2y = and#(x,y)
    
    impl#(x,y) = 2x + 2y + 7/2 >= 2x + 1 = xor#(and(x,y),xor(x,T()))
    
    or#(x,y) = 2x + 1/2y + 2 >= 2x + 1 = xor#(x,y)
    
    or#(x,y) = 2x + 1/2y + 2 >= 2x + 1/2y = and#(x,y)
    
    or#(x,y) = 2x + 1/2y + 2 >= 2x + 1 = xor#(and(x,y),xor(x,y))
    
    equiv#(x,y) = 2x + 2y + 2 >= 2y + 1 = xor#(y,T())
    
    equiv#(x,y) = 2x + 2y + 2 >= 2x + 1 = xor#(x,xor(y,T()))
    
    neg#(x) = 5/2x + 2 >= 2x + 1 = xor#(x,T())
    
    xor(x,F()) = x + 1 >= x = x
    
    xor(x,neg(x)) = 2x + 2 >= 0 = F()
    
    and(x,T()) = x >= x = x
    
    and(x,F()) = x >= 0 = F()
    
    and(x,x) = x >= x = x
    
    and(xor(x,y),z) = x + y + 1 >= x + y + 1 = xor(and(x,z),and(y,z))
    
    xor(x,x) = 2x + 1 >= 0 = F()
    
    impl(x,y) = 5/2x + 1/2y + 3 >= 2x + 2 = xor(and(x,y),xor(x,T()))
    
    or(x,y) = 5/2x + 2y + 2 >= 2x + y + 2 = xor(and(x,y),xor(x,y))
    
    equiv(x,y) = 3/2x + 3/2y + 5/2 >= x + y + 2 = xor(x,xor(y,T()))
    
    neg(x) = x + 1 >= x + 1 = xor(x,T())
   problem:
    DPs:
     
    TRS:
     xor(x,F()) -> x
     xor(x,neg(x)) -> F()
     and(x,T()) -> x
     and(x,F()) -> F()
     and(x,x) -> x
     and(xor(x,y),z) -> xor(and(x,z),and(y,z))
     xor(x,x) -> F()
     impl(x,y) -> xor(and(x,y),xor(x,T()))
     or(x,y) -> xor(and(x,y),xor(x,y))
     equiv(x,y) -> xor(x,xor(y,T()))
     neg(x) -> xor(x,T())
   Qed