Termination w.r.t. Q of the given QTRS could be proven:

(0) Obligation:

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

or(true, y) → true
or(x, true) → true
or(false, false) → false
mem(x, nil) → false
mem(x, set(y)) → =(x, y)
mem(x, union(y, z)) → or(mem(x, y), mem(x, z))

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Lexicographic Path Order [LPO].
Precedence:

mem₂ > or₂
mem₂ > false
mem₂ > =₂

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

or(true, y) → true
or(x, true) → true
or(false, false) → false
mem(x, nil) → false
mem(x, set(y)) → =(x, y)
mem(x, union(y, z)) → or(mem(x, y), mem(x, z))

(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