Termination w.r.t. Q proof of TRS/Cimeboolean

Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

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)

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

Q restricted rewrite system:
The TRS R consists of the following rules:

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)

Q is empty.

We use [23] with the following order to prove termination.

Recursive path order with status [2].
Precedence:

neg₁ > xor₂ > F
neg₁ > T
impl₂ > and₂ > xor₂ > F
impl₂ > T
or₂ > and₂ > xor₂ > F
equiv₂ > xor₂ > F
equiv₂ > T

Status:

neg₁: multiset
and₂: multiset
impl₂: multiset
equiv₂: multiset
or₂: multiset
T: multiset
F: multiset
xor₂: multiset