Termination w.r.t. Q proof of TRS/SK902.30.trs

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:

not(x) → xor(x, true)
implies(x, y) → xor(and(x, y), xor(x, true))
or(x, y) → xor(and(x, y), xor(x, y))
=(x, y) → xor(x, xor(y, true))

Q is empty.

↳ QTRS

  ↳ DirectTerminationProof

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

not(x) → xor(x, true)
implies(x, y) → xor(and(x, y), xor(x, true))
or(x, y) → xor(and(x, y), xor(x, y))
=(x, y) → xor(x, xor(y, true))

Q is empty.

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

Lexicographic path order with status [19].
Quasi-Precedence:

not₁ > true > xor₂
implies₂ > true > xor₂
implies₂ > and₂ > xor₂
or₂ > and₂ > xor₂
=₂ > true > xor₂

Status:

true: multiset
and₂: [1,2]
or₂: [1,2]
implies₂: [2,1]
=₂: [2,1]
xor₂: [1,2]
not₁: [1]