YES

TRS:

  a(h(),h(),h(),x) -> s(x)
  a(l,x,s(y),h()) -> a(l,x,y,s(h()))
  a(l,x,s(y),s(z)) -> a(l,x,y,a(l,x,s(y),z))
  a(l,s(x),h(),z) -> a(l,x,z,z)
  a(s(l),h(),h(),z) -> a(l,z,h(),z)
  +(x,h()) -> x
  +(h(),x) -> x
  +(s(x),s(y)) -> s(s(+(x,y)))
  +(+(x,y),z) -> +(x,+(y,z))
  s(h()) -> 1()
  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(),h()),l))

linear polynomial interpretations on N:

  a_A(x1,x2,x3,x4) = x4
  a#_A(x1,x2,x3,x4) = x1 + 2
  h_A = 1
  h#_A = 3
  s_A(x1) = x1
  s#_A(x1) = 1
  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = x1 + x2 + 2
  1_A = 0
  1#_A = 0
  app_A(x1,x2) = x1 + x2 + 1
  app#_A(x1,x2) = 5
  nil_A = 1
  nil#_A = 0
  cons_A(x1,x2) = x1 + x2 + 2
  cons#_A(x1,x2) = 4
  sum_A(x1) = x1
  sum#_A(x1) = x1 + 2

precedence:

  app = sum > cons > a = nil > s = + > h > 1