(0) Obligation:

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

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

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Precedence:
and2 > or2
true > or2
false > or2

Status:
true: multiset
or2: multiset
false: multiset
and2: [2,1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

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


(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) TRUE