YES

Proof:
This system is confluent.
By \cite{ALS94}, Theorem 4.1.
This system is of type 3 or smaller.
This system is strongly deterministic.
All 4 critical pairs are joinable.
cons(x', cons(y', z')) = cons(y', insert(z', x')) <= lte(x', y') = false, lte(x', y') = true:
This critical pair is unfeasible.
cons(x', insert(y', z')) = cons(z', cons(x', y')) <= lte(z', x') = true, lte(z', x') = false:
This critical pair is unfeasible.
ordered(cons(x', y')) = false <= lte(z', x') = false, lte(z', x') = true:
This critical pair is unfeasible.
false = ordered(cons(x', y')) <= lte(z', x') = true, lte(z', x') = false:
This critical pair is unfeasible.
By \cite{A14}, Theorem 11.5.9.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to V(R) + Emb.
Call external tool:
ttt2 - trs 30
Input:
  lte(0, n) -> true
  lte(s(m), 0) -> false
  lte(s(m), s(n)) -> lte(m, n)
  insert(nil, m) -> cons(m, nil)
  insert(cons(n, l), m) -> cons(m, cons(n, l))
  insert(cons(n, l), m) -> lte(m, n)
  insert(cons(n, l), m) -> cons(n, insert(l, m))
  ordered(nil) -> true
  ordered(cons(m, nil)) -> true
  ordered(cons(m, cons(n, l))) -> ordered(cons(n, l))
  ordered(cons(m, cons(n, l))) -> lte(m, n)
  ordered(cons(m, cons(n, l))) -> false
  s(x) -> x
  insert(x, y) -> x
  insert(x, y) -> y
  lte(x, y) -> x
  lte(x, y) -> y
  ordered(x) -> x
  cons(x, y) -> x
  cons(x, y) -> y

 DP Processor:
  DPs:
   lte#(s(m),s(n)) -> lte#(m,n)
   insert#(nil(),m) -> cons#(m,nil())
   insert#(cons(n,l),m) -> cons#(m,cons(n,l))
   insert#(cons(n,l),m) -> lte#(m,n)
   insert#(cons(n,l),m) -> insert#(l,m)
   insert#(cons(n,l),m) -> cons#(n,insert(l,m))
   ordered#(cons(m,cons(n,l))) -> ordered#(cons(n,l))
   ordered#(cons(m,cons(n,l))) -> lte#(m,n)
  TRS:
   lte(0(),n) -> true()
   lte(s(m),0()) -> false()
   lte(s(m),s(n)) -> lte(m,n)
   insert(nil(),m) -> cons(m,nil())
   insert(cons(n,l),m) -> cons(m,cons(n,l))
   insert(cons(n,l),m) -> lte(m,n)
   insert(cons(n,l),m) -> cons(n,insert(l,m))
   ordered(nil()) -> true()
   ordered(cons(m,nil())) -> true()
   ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
   ordered(cons(m,cons(n,l))) -> lte(m,n)
   ordered(cons(m,cons(n,l))) -> false()
   s(x) -> x
   insert(x,y) -> x
   insert(x,y) -> y
   lte(x,y) -> x
   lte(x,y) -> y
   ordered(x) -> x
   cons(x,y) -> x
   cons(x,y) -> y
  TDG Processor:
   DPs:
    lte#(s(m),s(n)) -> lte#(m,n)
    insert#(nil(),m) -> cons#(m,nil())
    insert#(cons(n,l),m) -> cons#(m,cons(n,l))
    insert#(cons(n,l),m) -> lte#(m,n)
    insert#(cons(n,l),m) -> insert#(l,m)
    insert#(cons(n,l),m) -> cons#(n,insert(l,m))
    ordered#(cons(m,cons(n,l))) -> ordered#(cons(n,l))
    ordered#(cons(m,cons(n,l))) -> lte#(m,n)
   TRS:
    lte(0(),n) -> true()
    lte(s(m),0()) -> false()
    lte(s(m),s(n)) -> lte(m,n)
    insert(nil(),m) -> cons(m,nil())
    insert(cons(n,l),m) -> cons(m,cons(n,l))
    insert(cons(n,l),m) -> lte(m,n)
    insert(cons(n,l),m) -> cons(n,insert(l,m))
    ordered(nil()) -> true()
    ordered(cons(m,nil())) -> true()
    ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
    ordered(cons(m,cons(n,l))) -> lte(m,n)
    ordered(cons(m,cons(n,l))) -> false()
    s(x) -> x
    insert(x,y) -> x
    insert(x,y) -> y
    lte(x,y) -> x
    lte(x,y) -> y
    ordered(x) -> x
    cons(x,y) -> x
    cons(x,y) -> y
   graph:
    ordered#(cons(m,cons(n,l))) -> ordered#(cons(n,l)) ->
    ordered#(cons(m,cons(n,l))) -> lte#(m,n)
    ordered#(cons(m,cons(n,l))) -> ordered#(cons(n,l)) ->
    ordered#(cons(m,cons(n,l))) -> ordered#(cons(n,l))
    ordered#(cons(m,cons(n,l))) -> lte#(m,n) ->
    lte#(s(m),s(n)) -> lte#(m,n)
    insert#(cons(n,l),m) -> insert#(l,m) ->
    insert#(cons(n,l),m) -> cons#(n,insert(l,m))
    insert#(cons(n,l),m) -> insert#(l,m) ->
    insert#(cons(n,l),m) -> insert#(l,m)
    insert#(cons(n,l),m) -> insert#(l,m) ->
    insert#(cons(n,l),m) -> lte#(m,n)
    insert#(cons(n,l),m) -> insert#(l,m) ->
    insert#(cons(n,l),m) -> cons#(m,cons(n,l))
    insert#(cons(n,l),m) -> insert#(l,m) ->
    insert#(nil(),m) -> cons#(m,nil())
    insert#(cons(n,l),m) -> lte#(m,n) -> lte#(s(m),s(n)) -> lte#(m,n)
    lte#(s(m),s(n)) -> lte#(m,n) -> lte#(s(m),s(n)) -> lte#(m,n)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 10/64
    DPs:
     insert#(cons(n,l),m) -> insert#(l,m)
    TRS:
     lte(0(),n) -> true()
     lte(s(m),0()) -> false()
     lte(s(m),s(n)) -> lte(m,n)
     insert(nil(),m) -> cons(m,nil())
     insert(cons(n,l),m) -> cons(m,cons(n,l))
     insert(cons(n,l),m) -> lte(m,n)
     insert(cons(n,l),m) -> cons(n,insert(l,m))
     ordered(nil()) -> true()
     ordered(cons(m,nil())) -> true()
     ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
     ordered(cons(m,cons(n,l))) -> lte(m,n)
     ordered(cons(m,cons(n,l))) -> false()
     s(x) -> x
     insert(x,y) -> x
     insert(x,y) -> y
     lte(x,y) -> x
     lte(x,y) -> y
     ordered(x) -> x
     cons(x,y) -> x
     cons(x,y) -> y
    Subterm Criterion Processor:
     simple projection:
      pi(insert#) = 0
     problem:
      DPs:
       
      TRS:
       lte(0(),n) -> true()
       lte(s(m),0()) -> false()
       lte(s(m),s(n)) -> lte(m,n)
       insert(nil(),m) -> cons(m,nil())
       insert(cons(n,l),m) -> cons(m,cons(n,l))
       insert(cons(n,l),m) -> lte(m,n)
       insert(cons(n,l),m) -> cons(n,insert(l,m))
       ordered(nil()) -> true()
       ordered(cons(m,nil())) -> true()
       ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
       ordered(cons(m,cons(n,l))) -> lte(m,n)
       ordered(cons(m,cons(n,l))) -> false()
       s(x) -> x
       insert(x,y) -> x
       insert(x,y) -> y
       lte(x,y) -> x
       lte(x,y) -> y
       ordered(x) -> x
       cons(x,y) -> x
       cons(x,y) -> y
     Qed
    
    DPs:
     ordered#(cons(m,cons(n,l))) -> ordered#(cons(n,l))
    TRS:
     lte(0(),n) -> true()
     lte(s(m),0()) -> false()
     lte(s(m),s(n)) -> lte(m,n)
     insert(nil(),m) -> cons(m,nil())
     insert(cons(n,l),m) -> cons(m,cons(n,l))
     insert(cons(n,l),m) -> lte(m,n)
     insert(cons(n,l),m) -> cons(n,insert(l,m))
     ordered(nil()) -> true()
     ordered(cons(m,nil())) -> true()
     ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
     ordered(cons(m,cons(n,l))) -> lte(m,n)
     ordered(cons(m,cons(n,l))) -> false()
     s(x) -> x
     insert(x,y) -> x
     insert(x,y) -> y
     lte(x,y) -> x
     lte(x,y) -> y
     ordered(x) -> x
     cons(x,y) -> x
     cons(x,y) -> y
    Subterm Criterion Processor:
     simple projection:
      pi(ordered#) = 0
     problem:
      DPs:
       
      TRS:
       lte(0(),n) -> true()
       lte(s(m),0()) -> false()
       lte(s(m),s(n)) -> lte(m,n)
       insert(nil(),m) -> cons(m,nil())
       insert(cons(n,l),m) -> cons(m,cons(n,l))
       insert(cons(n,l),m) -> lte(m,n)
       insert(cons(n,l),m) -> cons(n,insert(l,m))
       ordered(nil()) -> true()
       ordered(cons(m,nil())) -> true()
       ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
       ordered(cons(m,cons(n,l))) -> lte(m,n)
       ordered(cons(m,cons(n,l))) -> false()
       s(x) -> x
       insert(x,y) -> x
       insert(x,y) -> y
       lte(x,y) -> x
       lte(x,y) -> y
       ordered(x) -> x
       cons(x,y) -> x
       cons(x,y) -> y
     Qed
    
    DPs:
     lte#(s(m),s(n)) -> lte#(m,n)
    TRS:
     lte(0(),n) -> true()
     lte(s(m),0()) -> false()
     lte(s(m),s(n)) -> lte(m,n)
     insert(nil(),m) -> cons(m,nil())
     insert(cons(n,l),m) -> cons(m,cons(n,l))
     insert(cons(n,l),m) -> lte(m,n)
     insert(cons(n,l),m) -> cons(n,insert(l,m))
     ordered(nil()) -> true()
     ordered(cons(m,nil())) -> true()
     ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
     ordered(cons(m,cons(n,l))) -> lte(m,n)
     ordered(cons(m,cons(n,l))) -> false()
     s(x) -> x
     insert(x,y) -> x
     insert(x,y) -> y
     lte(x,y) -> x
     lte(x,y) -> y
     ordered(x) -> x
     cons(x,y) -> x
     cons(x,y) -> y
    Subterm Criterion Processor:
     simple projection:
      pi(lte#) = 0
     problem:
      DPs:
       
      TRS:
       lte(0(),n) -> true()
       lte(s(m),0()) -> false()
       lte(s(m),s(n)) -> lte(m,n)
       insert(nil(),m) -> cons(m,nil())
       insert(cons(n,l),m) -> cons(m,cons(n,l))
       insert(cons(n,l),m) -> lte(m,n)
       insert(cons(n,l),m) -> cons(n,insert(l,m))
       ordered(nil()) -> true()
       ordered(cons(m,nil())) -> true()
       ordered(cons(m,cons(n,l))) -> ordered(cons(n,l))
       ordered(cons(m,cons(n,l))) -> lte(m,n)
       ordered(cons(m,cons(n,l))) -> false()
       s(x) -> x
       insert(x,y) -> x
       insert(x,y) -> y
       lte(x,y) -> x
       lte(x,y) -> y
       ordered(x) -> x
       cons(x,y) -> x
       cons(x,y) -> y
     Qed