YES

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())

linear polynomial interpretations on N:

  xor_A(x1,x2) = x1 + 1
  xor#_A(x1,x2) = 1
  F_A = 1
  F#_A = 0
  neg_A(x1) = x1 + 1
  neg#_A(x1) = 2
  and_A(x1,x2) = x1 + 1
  and#_A(x1,x2) = x2 + 2
  T_A = 1
  T#_A = 0
  impl_A(x1,x2) = x1 + 2
  impl#_A(x1,x2) = x1 + x2 + 3
  or_A(x1,x2) = x1 + x2 + 2
  or#_A(x1,x2) = x1 + x2 + 3
  equiv_A(x1,x2) = x1 + x2 + 1
  equiv#_A(x1,x2) = x1 + x2 + 2

precedence:

  neg = equiv > T > impl = or > and > xor > F