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

(0) Obligation:

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

g(X) → h(activate(X))
c → d
h(n__d) → g(n__c)
d → n__d
c → n__c
activate(n__d) → d
activate(n__c) → c
activate(X) → X

Q is empty.

(1) QTRS Reverse (EQUIVALENT transformation)

We applied the QTRS Reverse Processor [REVERSE].

(2) Obligation:

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

g(x) → activate(h(x))
c'(x) → d'(x)
n__d'(h(x)) → n__c'(g(x))
d'(x) → n__d'(x)
c'(x) → n__c'(x)
n__d'(activate(x)) → d'(x)
n__c'(activate(x)) → c'(x)
activate(x) → x

Q is empty.

(3) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:

n__d' h → n__d' h

n__d' h → n__d' h
by OverlapClosure OC 3

n__d' h → d' h
by OverlapClosure OC 3

n__d' h → c' h
by OverlapClosure OC 3

n__d' h → n__c' activate h
by OverlapClosure OC 2

n__d' h → n__c' g
by original rule (OC 1)

g → activate h
by original rule (OC 1)

n__c' activate → c'
by original rule (OC 1)

c' → d'
by original rule (OC 1)

d' → n__d'
by original rule (OC 1)

(4) NO