YES

(VAR x1 x z y x0)
(RULES
  f1(x1) -> f7(x1)
  f7(f7(f7(f7(x)))) -> f7(x)
  f7(j(z)) -> f7(f7(z))
  f2(x1) -> f7(x1)
  f3(x1) -> f7(x1)
  f6(x1) -> f7(x1)
  f8(x1) -> f7(x1)
  f9(x1) -> f7(x1)
  f10(x1) -> f7(x1)
  f11(x1) -> f7(x1)
  f4(y) -> f7(y)
  f5(y) -> f7(y)
  f12(y) -> f7(y)
  g(x0,x1) -> f7(x1)
)

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

  g_A(x1,x2) = x2 + 1
  j_A(x1) = x1 + 6
  f1_A(x1) = x1 + 3
  f2_A(x1) = x1 + 4
  f3_A(x1) = x1 + 5
  f4_A(x1) = 1
  f5_A(x1) = 0
  f6_A(x1) = x1 + 2
  f7_A(x1) = 0
  f8_A(x1) = x1 + 2
  f9_A(x1) = x1 + 1
  f10_A(x1) = x1 + 1
  f11_A(x1) = x1 + 4
  f12_A(x1) = 0
  g#_A(x1,x2) = x1
  f1#_A(x1) = 0
  f2#_A(x1) = 0
  f6#_A(x1) = x1
  f7#_A(x1) = 0
  f9#_A(x1) = 0
  f11#_A(x1) = 0
  f12#_A(x1) = 0

weights

  w0 = 6
  w(g) = 0
  w(j) = 5
  w(f1) = 3
  w(f2) = 2
  w(f3) = 4
  w(f4) = 5
  w(f5) = 1
  w(f6) = 1
  w(f7) = 1
  w(f8) = 2
  w(f9) = 1
  w(f10) = 1
  w(f11) = 1
  w(f12) = 1

and precedence:

g > f12 > f11 > f5 > f6 > f10 > f8 > f9 > f2 > f3 > f1 > f4 > j > f7
)