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(plus(x,y),l))
  sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
  plus(0(),y) -> y
  plus(s(x),y) -> s(plus(x,y))
  sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
  pred(cons(s(x),nil())) -> cons(x,nil())

linear polynomial interpretations on N:

  app_A(x1,x2) = x1 + x2 + 3
  app#_A(x1,x2) = 7
  nil_A = 1
  nil#_A = 1
  cons_A(x1,x2) = x2 + 3
  cons#_A(x1,x2) = 5
  sum_A(x1) = 5
  sum#_A(x1) = x1
  plus_A(x1,x2) = x2 + 4
  plus#_A(x1,x2) = 3
  0_A = 1
  0#_A = 0
  s_A(x1) = 1
  s#_A(x1) = 2
  pred_A(x1) = 4
  pred#_A(x1) = 4

precedence:

  app > sum > cons = 0 > plus > s = pred > nil