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{145, 178 + x1}
  active#_A(x1) = max{145, 178 + x1}
  f_A(x1) = max{10, 11 + x1}
  f#_A(x1) = max{10, 11 + x1}
  mark_A(x1) = max{179, 160 + x1}
  mark#_A(x1) = max{179, 160 + x1}
  chk_A(x1) = max{161, 33 + x1}
  chk#_A(x1) = max{161, 33 + x1}
  no_A(x1) = max{129, 145 + x1}
  no#_A(x1) = max{129, 145 + x1}
  mat_A(x1,x2) = max{145, 10 + x1, 126 + x2}
  mat#_A(x1,x2) = max{145, 10 + x1, 126 + x2}
  X_A = 1
  X#_A = 1
  y_A = 19
  y#_A = 19
  c_A = 0
  c#_A = 0
  tp_A(x1) = max{0, 127 + x1}
  tp#_A(x1) = max{0, 127 + x1}

precedence:

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