YES

(VAR y x1 x z x0)
(RULES
  f10(y) -> f4(y)
  f1(y) -> f4(y)
  f9(y) -> f4(y)
  f3(x1) -> f4(x1)
  f5(x1) -> f4(x1)
  f4(f4(f4(f4(x)))) -> f4(x)
  f7(x1) -> f4(x1)
  f4(j(z)) -> f4(f4(z))
  f2(y) -> f4(y)
  f6(y) -> f4(y)
  f8(y) -> f4(y)
  g(x0,x1) -> f4(x1)
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  g_A(x1,x2) = 2
  j_A(x1) = 1
  f1_A(x1) = 3
  f2_A(x1) = 1
  f3_A(x1) = 4
  f4_A(x1) = 1
  f5_A(x1) = 6
  f6_A(x1) = 1
  f7_A(x1) = 2
  f8_A(x1) = 1
  f9_A(x1) = 5
  f10_A(x1) = 4
  f2#_A(x1) = 0
  f4#_A(x1) = 0
  f5#_A(x1) = 0
  f6#_A(x1) = 0
  f7#_A(x1) = x1
  f8#_A(x1) = 0
  f9#_A(x1) = 0
  f10#_A(x1) = x1

weights

  w0 = 6
  w(g) = 0
  w(j) = 5
  w(f1) = 4
  w(f2) = 3
  w(f3) = 1
  w(f4) = 1
  w(f5) = 1
  w(f6) = 3
  w(f7) = 2
  w(f8) = 3
  w(f9) = 4
  w(f10) = 4

and precedence:

f9 > f10 > j > f7 > f1 > f8 > f6 > g > f2 > f5 > f3 > f4
)