YES

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

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

  g_A(x1,x2) = x1 + 1
  j_A(x1) = 1
  f1_A(x1) = 1
  f2_A(x1) = 0
  f3_A(x1) = 0
  f4_A(x1) = 1
  f5_A(x1) = 1
  f6_A(x1) = 0
  f7_A(x1) = 0
  f8_A(x1) = 0
  f9_A(x1) = 0
  f10_A(x1) = 1
  f1#_A(x1) = 0
  f2#_A(x1) = 0
  f4#_A(x1) = 0
  f5#_A(x1) = 0
  f7#_A(x1) = 0
  f8#_A(x1) = 0
  f10#_A(x1) = 0

weights

  w0 = 1
  w(g) = 1
  w(j) = 1
  w(f1) = 2
  w(f2) = 1
  w(f3) = 1
  w(f4) = 1
  w(f5) = 1
  w(f6) = 1
  w(f7) = 1
  w(f8) = 1
  w(f9) = 1
  w(f10) = 2

and precedence:

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