let R be the TRS under consideration

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

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(id(s(s(s(s(s(s(s(_1))))))))),_2,_2) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0.0 is a position in r1
we have r1|p1 = id(s(s(s(s(s(s(s(_1))))))))
id(s(_3)) -> s(id(_3)) is in R
let l'1 be the left-hand side of this rule
theta1 = {_3/s(s(s(s(s(s(_1))))))} is a mgu of r1|p1 and l'1

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(id(s(s(s(s(s(s(_1))))))))),_2,_2) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0.0.0 is a position in r2
we have r2|p2 = id(s(s(s(s(s(s(_1)))))))
id(s(_3)) -> s(id(_3)) is in R
let l'2 be the left-hand side of this rule
theta2 = {_3/s(s(s(s(s(_1)))))} is a mgu of r2|p2 and l'2

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(id(s(s(s(s(s(_1))))))))),_2,_2) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0.0.0.0 is a position in r3
we have r3|p3 = id(s(s(s(s(s(_1))))))
id(s(_3)) -> s(id(_3)) is in R
let l'3 be the left-hand side of this rule
theta3 = {_3/s(s(s(s(_1))))} is a mgu of r3|p3 and l'3

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(id(s(s(s(s(_1))))))))),_2,_2) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 0.0.0.0.0 is a position in r4
we have r4|p4 = id(s(s(s(s(_1)))))
id(s(_3)) -> s(id(_3)) is in R
let l'4 be the left-hand side of this rule
theta4 = {_3/s(s(s(_1)))} is a mgu of r4|p4 and l'4

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(id(s(s(s(_1))))))))),_2,_2) is in EU_R^5
let r5 be the right-hand side of this rule
p5 = 0.0.0.0.0.0 is a position in r5
we have r5|p5 = id(s(s(s(_1))))
id(s(_3)) -> s(id(_3)) is in R
let l'5 be the left-hand side of this rule
theta5 = {_3/s(s(_1))} is a mgu of r5|p5 and l'5

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(s(id(s(s(_1))))))))),_2,_2) is in EU_R^6
let r6 be the right-hand side of this rule
p6 = 0.0.0.0.0.0.0 is a position in r6
we have r6|p6 = id(s(s(_1)))
id(s(_3)) -> s(id(_3)) is in R
let l'6 be the left-hand side of this rule
theta6 = {_3/s(_1)} is a mgu of r6|p6 and l'6

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(s(s(id(s(_1))))))))),_2,_2) is in EU_R^7
let r7 be the right-hand side of this rule
p7 = 0.0.0.0.0.0.0.0 is a position in r7
we have r7|p7 = id(s(_1))
id(s(_3)) -> s(id(_3)) is in R
let l'7 be the left-hand side of this rule
theta7 = {_1/_3} is a mgu of r7|p7 and l'7

==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(s(s(s(id(_1))))))))),_2,_2) is in EU_R^8
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {_1/id(_1), _2/_2}
we have r|p = f(s(s(s(s(s(s(s(s(id(_1))))))))),_2,_2) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=8, depth k=10
17061 rule(s) generated