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)
or(x, y) → xor(and(x, y), xor(x, y))
implies(x, y) → xor(and(x, y), xor(x, true))
and(x, true) → x
and(x, false) → false
and(x, x) → x
xor(x, false) → x
xor(x, x) → false
and(xor(x, y), z) → xor(and(x, z), and(y, z))

Q is empty.


QTRS
  ↳ DirectTerminationProof

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

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

Q is empty.

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

Lexicographic path order with status [19].
Quasi-Precedence:
not1 > xor2 > false
not1 > true
or2 > and2 > xor2 > false
implies2 > true
implies2 > and2 > xor2 > false

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