(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(X) → g(n__h(n__f(X)))
h(X) → n__h(X)
f(X) → n__f(X)
activate(n__h(X)) → h(activate(X))
activate(n__f(X)) → f(activate(X))
activate(X) → X
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Lexicographic path order with status [LPO].
Precedence:
activate1 > f1 > g1 > nh1
activate1 > f1 > nf1 > nh1
activate1 > h1 > nh1
Status:
f1: [1]
g1: [1]
nh1: [1]
nf1: [1]
h1: [1]
activate1: [1]
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
f(X) → g(n__h(n__f(X)))
h(X) → n__h(X)
f(X) → n__f(X)
activate(n__h(X)) → h(activate(X))
activate(n__f(X)) → f(activate(X))
activate(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