YES

TRS:

  active(f(x)) -> mark(f(f(x)))
  chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
  mat(f(x),f(y())) -> f(mat(x,y()))
  chk(no(c())) -> active(c())
  mat(f(x),c()) -> no(c())
  f(active(x)) -> active(f(x))
  f(no(x)) -> no(f(x))
  f(mark(x)) -> mark(f(x))
  tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))

max/plus interpretations on N:

  active_A(x1) = max{238, 254 + x1}
  active#_A(x1) = max{272, 247 + x1}
  f_A(x1) = max{9, 24 + x1}
  f#_A(x1) = max{33, 35 + x1}
  mark_A(x1) = max{255, 230 + x1}
  mark#_A(x1) = max{270, 3 + x1}
  chk_A(x1) = max{240, 2 + x1}
  chk#_A(x1) = max{4, 17 + x1}
  no_A(x1) = max{236, 252 + x1}
  no#_A(x1) = max{276, 1}
  mat_A(x1,x2) = max{252, 239, -48 + x2}
  mat#_A(x1,x2) = max{275, 2, 277 + x2}
  X_A = 1
  X#_A = 34
  y_A = 300
  y#_A = 276
  c_A = 0
  c#_A = 0
  tp_A(x1) = max{0, 47 + x1}
  tp#_A(x1) = max{1, 48 + x1}

precedence:

  chk > tp > mat > no > active > mark > f > X = y = c