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:

f(f(X)) → c
c → d
h(X) → c

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:

[f₁, c, d, h₁]

Status:

c: multiset
f₁: multiset
h₁: multiset
d: multiset

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

f(f(X)) → c
h(X) → c

(2) Obligation:

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

c → d

Q is empty.

(3) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Recursive path order with status [RPO].
Quasi-Precedence:

c > d

Status:

c: multiset
d: multiset

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

c → d

(4) Obligation:

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

(5) RisEmptyProof (EQUIVALENT transformation)

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

(6) TRUE