let R be the TRS under consideration

a__h(_1) -> a__g(mark(_1),_1) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0.0 is a position in r0
we have r0|p0 = _1
a__a -> a is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/a__a} is a mgu of r0|p0 and l'0

==> a__h(a__a) -> a__g(mark(a),a__a) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0 is a position in r1
we have r1|p1 = mark(a)
mark(a) -> a__a is in R
let l'1 be the left-hand side of this rule
theta1 = {} is a mgu of r1|p1 and l'1

==> a__h(a__a) -> a__g(a__a,a__a) 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 = a__a
a__a -> a is in R
let l'2 be the left-hand side of this rule
theta2 = {} is a mgu of r2|p2 and l'2

==> a__h(a__a) -> a__g(a,a__a) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = epsilon is a position in r3
we have r3|p3 = a__g(a,a__a)
a__g(a,_1) -> a__f(b,_1) is in R
let l'3 be the left-hand side of this rule
theta3 = {_1/a__a} is a mgu of r3|p3 and l'3

==> a__h(a__a) -> a__f(b,a__a) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 1 is a position in r4
we have r4|p4 = a__a
a__a -> b is in R
let l'4 be the left-hand side of this rule
theta4 = {} is a mgu of r4|p4 and l'4

==> a__h(a__a) -> a__f(b,b) is in EU_R^5
let r5 be the right-hand side of this rule
p5 = epsilon is a position in r5
we have r5|p5 = a__f(b,b)
a__f(_1,_1) -> a__h(a__a) is in R
let l'5 be the left-hand side of this rule
theta5 = {_1/b} is a mgu of r5|p5 and l'5

==> a__h(a__a) -> a__h(a__a) is in EU_R^6
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {}
we have r|p = a__h(a__a) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = a__h(a__a) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=6, depth k=2
585 rule(s) generated