YES

We show the termination of R/S, where R is

  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)

and S is:

  cons(x,cons(y,l)) -> cons(y,cons(x,l))

Since R almost dominates S and S is non-duplicating,
it is enough to show finiteness of (P, Q).
Here P consists of the dependency pairs

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

and Q consists of the rules:

  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)
  cons(x,cons(y,l)) -> cons(y,cons(x,l))

The weakly monotone algebra (N, >) with

  app#_A(x1,x2) = x2
  cons_A(x1,x2) = 1
  sum#_A(x1) = x1
  plus_A(x1,x2) = x2 + 1
  plus#_A(x1,x2) = 0
  app_A(x1,x2) = x1 + x2 + 1
  sum_A(x1) = 1
  s_A(x1) = 1
  0_A = 1
  pred#_A(x1) = 0
  nil_A = 1
  pred_A(x1) = 1

strictly orients the following dependency pairs:

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

We remove them from the set of dependency pairs.

The weakly monotone algebra (N, >) with

  app#_A(x1,x2) = x1
  cons_A(x1,x2) = x2 + 1
  sum#_A(x1) = x1
  plus_A(x1,x2) = x1 + x2 + 1
  app_A(x1,x2) = x1 + x2 + 1
  sum_A(x1) = x1
  plus#_A(x1,x2) = 0
  s_A(x1) = 1
  nil_A = 1
  0_A = 1
  pred_A(x1) = 2

strictly orients the following dependency pairs:

  app#(cons(x,l),k) -> app#(l,k)
  sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))

We remove them from the set of dependency pairs.

The weakly monotone algebra (N, >) with

  sum#_A(x1) = x1
  app_A(x1,x2) = x1 + x2 + 1
  cons_A(x1,x2) = 1
  sum_A(x1) = 1
  plus#_A(x1,x2) = x1
  s_A(x1) = x1 + 1
  nil_A = 1
  plus_A(x1,x2) = x1 + x2
  0_A = 1
  pred_A(x1) = 1

strictly orients the following dependency pairs:

  plus#(s(x),y) -> plus#(x,y)

We remove them from the set of dependency pairs.

The weakly monotone algebra (N, >) with

  sum#_A(x1) = x1
  app_A(x1,x2) = x1 + x2 + 1
  cons_A(x1,x2) = x2 + 2
  sum_A(x1) = 3
  nil_A = 1
  plus_A(x1,x2) = x2 + 1
  0_A = 1
  s_A(x1) = 1
  pred_A(x1) = 3

strictly orients the following dependency pairs:

  sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))

We remove them from the set of dependency pairs.

No dependency pair remains.