let R be the TRS under consideration

f(_1,n__g(_1),_2) -> f(activate(_2),activate(_2),activate(_2)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 1 is a position in r0
we have r0|p0 = activate(_2)
activate(_3) -> _3 is in R
let l'0 be the left-hand side of this rule
theta0 = {_2/_3} is a mgu of r0|p0 and l'0

==> f(_1,n__g(_1),_2) -> f(activate(_2),_2,activate(_2)) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 2 is a position in r1
we have r1|p1 = activate(_2)
activate(_3) -> _3 is in R
let l'1 be the left-hand side of this rule
theta1 = {_2/_3} is a mgu of r1|p1 and l'1

==> f(_1,n__g(_1),_2) -> f(activate(_2),_2,_2) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0 is a position in r2
we have r2|p2 = activate(_2)
activate(n__g(_3)) -> g(_3) is in R
let l'2 be the left-hand side of this rule
theta2 = {_2/n__g(_3)} is a mgu of r2|p2 and l'2

==> f(_1,n__g(_1),n__g(_2)) -> f(g(_2),n__g(_2),n__g(_2)) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0 is a position in r3
we have r3|p3 = g(_2)
g(b) -> c is in R
let l'3 be the left-hand side of this rule
theta3 = {_2/b} is a mgu of r3|p3 and l'3

==> f(_1,n__g(_1),n__g(b)) -> f(c,n__g(b),n__g(b)) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 1.0 is a position in r4
we have r4|p4 = b
b -> c is in R
let l'4 be the left-hand side of this rule
theta4 = {} is a mgu of r4|p4 and l'4

==> f(_1,n__g(_1),n__g(b)) -> f(c,n__g(c),n__g(b)) is in EU_R^5
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {_1/c}
let theta' = {}
we have r|p = f(c,n__g(c),n__g(b)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(c,n__g(c),n__g(b)) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=5, depth k=2
191 rule(s) generated