YES

The TRS could be proven terminating. The proof took 21 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (11ms).

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

f#(n__f(n__a)) → f#(n__a)activate#(n__a) → a#
activate#(n__f(X)) → f#(X)activate#(n__g(X)) → g#(X)
f#(n__f(n__a)) → f#(n__g(f(n__a)))

Rewrite Rules

f(n__f(n__a)) → f(n__g(f(n__a)))f(X) → n__f(X)
a → n__ag(X) → n__g(X)
activate(n__f(X)) → f(X)activate(n__a) → a
activate(n__g(X)) → g(X)activate(X) → X

Original Signature

Termination of terms over the following signature is verified: f, activate, g, n__a, a, n__f, n__g

Strategy

There are no SCCs!