YES

(VAR z y x x0 x1)
(RULES
  f10(j(z)) -> f10(f10(z))
  f2(y) -> f10(y)
  f3(y) -> f10(y)
  f4(y) -> f10(y)
  f5(y) -> f10(y)
  f6(y) -> f10(y)
  f7(y) -> f10(y)
  f8(y) -> f10(y)
  f9(y) -> f10(y)
  f10(f10(f10(f10(x)))) -> f10(x)
  f12(y) -> f10(y)
  f11(y) -> f10(y)
  f13(y) -> f10(y)
  f1(y) -> f10(y)
  f14(y) -> f10(y)
  g(x0,x1) -> f10(x1)
)

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

  g_A(x1,x2) = 1
  j_A(x1) = 2
  f1_A(x1) = 0
  f2_A(x1) = 0
  f3_A(x1) = 1
  f4_A(x1) = 0
  f5_A(x1) = 0
  f6_A(x1) = 0
  f7_A(x1) = 0
  f8_A(x1) = 0
  f9_A(x1) = 0
  f10_A(x1) = 0
  f11_A(x1) = 0
  f12_A(x1) = 0
  f13_A(x1) = 0
  f14_A(x1) = 0
  f8#_A(x1) = x1

weights

  w0 = 2
  w(g) = 0
  w(j) = 3
  w(f1) = 1
  w(f2) = 1
  w(f3) = 1
  w(f4) = 1
  w(f5) = 2
  w(f6) = 1
  w(f7) = 1
  w(f8) = 1
  w(f9) = 1
  w(f10) = 1
  w(f11) = 1
  w(f12) = 1
  w(f13) = 1
  w(f14) = 2

and precedence:

f1 > j > f2 > f6 > f9 > f8 > f11 > f13 > f12 > f3 > f4 > f7 > f10 > g > f5 > f14
)