YES

TRS:

  app(nil(),k) -> k
  app(l,nil()) -> l
  app(cons(x,l),k) -> cons(x,app(l,k))
  sum(cons(x,nil())) -> cons(x,nil())
  sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l))
  a(h(),h(),x) -> s(x)
  a(x,s(y),h()) -> a(x,y,s(h()))
  a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z))
  a(s(x),h(),z) -> a(x,z,z)

linear polynomial interpretations on N:

  app_A(x1,x2) = x1 + x2 + 1
  app#_A(x1,x2) = x2 + 7
  nil_A = 3
  nil#_A = 8
  cons_A(x1,x2) = x1 + x2 + 4
  cons#_A(x1,x2) = 6
  sum_A(x1) = x1
  sum#_A(x1) = x1
  a_A(x1,x2,x3) = x3
  a#_A(x1,x2,x3) = x1 + 7
  h_A = 1
  h#_A = 5
  s_A(x1) = x1
  s#_A(x1) = 4

precedence:

  nil > sum > a > cons > app = h > s