let R be the TRS under consideration

mergesort1(app(_1,_2)) -> merge(mergesort(_1),mergesort(_2)) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0 is a position in l0
we have l0|p0 = app(_1,_2)
split(nil) -> app(nil,nil) is in R
let r'0 be the right-hand side of this rule
theta0 = {_1/nil, _2/nil} is a mgu of l0|p0 and r'0

==> mergesort1(split(nil)) -> merge(mergesort(nil),mergesort(nil)) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = epsilon is a position in l1
we have l1|p1 = mergesort1(split(nil))
mergesort(_1) -> mergesort1(split(_1)) is in R
let r'1 be the right-hand side of this rule
theta1 = {_1/nil} is a mgu of l1|p1 and r'1

==> mergesort(nil) -> merge(mergesort(nil),mergesort(nil)) is in EU_R^2
let l be the left-hand side and r be the right-hand side of this rule
let p = 0
let theta = {}
let theta' = {}
we have r|p = mergesort(nil) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = mergesort(nil) is non-terminating w.r.t. R

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