YES

Proof:
This system is quasi-decreasing.
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:
  split(x, nil) -> tp2(nil, nil)
  split(x, cons(y, ys)) -> tp2(split(x, ys), cons(y, split(x, ys)))
  split(x, cons(y, ys)) -> le(x, y)
  split(x, cons(y, ys)) -> split(x, ys)
  split(x, cons(y, ys)) -> tp2(cons(y, split(x, ys)), split(x, ys))
  le(0, y) -> true
  le(s(x), 0) -> false
  le(s(x), s(y)) -> le(x, y)
  s(x) -> x
  split(x, y) -> x
  split(x, y) -> y
  tp2(x, y) -> x
  tp2(x, y) -> y
  le(x, y) -> x
  le(x, y) -> y
  cons(x, y) -> x
  cons(x, y) -> y

 DP Processor:
  DPs:
   split#(x,nil()) -> tp2#(nil(),nil())
   split#(x,cons(y,ys)) -> cons#(y,split(x,ys))
   split#(x,cons(y,ys)) -> split#(x,ys)
   split#(x,cons(y,ys)) -> tp2#(split(x,ys),cons(y,split(x,ys)))
   split#(x,cons(y,ys)) -> le#(x,y)
   split#(x,cons(y,ys)) -> tp2#(cons(y,split(x,ys)),split(x,ys))
   le#(s(x),s(y)) -> le#(x,y)
  TRS:
   split(x,nil()) -> tp2(nil(),nil())
   split(x,cons(y,ys)) -> tp2(split(x,ys),cons(y,split(x,ys)))
   split(x,cons(y,ys)) -> le(x,y)
   split(x,cons(y,ys)) -> split(x,ys)
   split(x,cons(y,ys)) -> tp2(cons(y,split(x,ys)),split(x,ys))
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   s(x) -> x
   split(x,y) -> x
   split(x,y) -> y
   tp2(x,y) -> x
   tp2(x,y) -> y
   le(x,y) -> x
   le(x,y) -> y
   cons(x,y) -> x
   cons(x,y) -> y
  TDG Processor:
   DPs:
    split#(x,nil()) -> tp2#(nil(),nil())
    split#(x,cons(y,ys)) -> cons#(y,split(x,ys))
    split#(x,cons(y,ys)) -> split#(x,ys)
    split#(x,cons(y,ys)) -> tp2#(split(x,ys),cons(y,split(x,ys)))
    split#(x,cons(y,ys)) -> le#(x,y)
    split#(x,cons(y,ys)) -> tp2#(cons(y,split(x,ys)),split(x,ys))
    le#(s(x),s(y)) -> le#(x,y)
   TRS:
    split(x,nil()) -> tp2(nil(),nil())
    split(x,cons(y,ys)) -> tp2(split(x,ys),cons(y,split(x,ys)))
    split(x,cons(y,ys)) -> le(x,y)
    split(x,cons(y,ys)) -> split(x,ys)
    split(x,cons(y,ys)) -> tp2(cons(y,split(x,ys)),split(x,ys))
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    s(x) -> x
    split(x,y) -> x
    split(x,y) -> y
    tp2(x,y) -> x
    tp2(x,y) -> y
    le(x,y) -> x
    le(x,y) -> y
    cons(x,y) -> x
    cons(x,y) -> y
   graph:
    le#(s(x),s(y)) -> le#(x,y) -> le#(s(x),s(y)) -> le#(x,y)
    split#(x,cons(y,ys)) -> le#(x,y) ->
    le#(s(x),s(y)) -> le#(x,y)
    split#(x,cons(y,ys)) -> split#(x,ys) ->
    split#(x,cons(y,ys)) -> tp2#(cons(y,split(x,ys)),split(x,ys))
    split#(x,cons(y,ys)) -> split#(x,ys) ->
    split#(x,cons(y,ys)) -> le#(x,y)
    split#(x,cons(y,ys)) -> split#(x,ys) ->
    split#(x,cons(y,ys)) -> tp2#(split(x,ys),cons(y,split(x,ys)))
    split#(x,cons(y,ys)) -> split#(x,ys) ->
    split#(x,cons(y,ys)) -> split#(x,ys)
    split#(x,cons(y,ys)) -> split#(x,ys) ->
    split#(x,cons(y,ys)) -> cons#(y,split(x,ys))
    split#(x,cons(y,ys)) -> split#(x,ys) -> split#(x,nil()) -> tp2#(nil(),nil())
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 8/49
    DPs:
     split#(x,cons(y,ys)) -> split#(x,ys)
    TRS:
     split(x,nil()) -> tp2(nil(),nil())
     split(x,cons(y,ys)) -> tp2(split(x,ys),cons(y,split(x,ys)))
     split(x,cons(y,ys)) -> le(x,y)
     split(x,cons(y,ys)) -> split(x,ys)
     split(x,cons(y,ys)) -> tp2(cons(y,split(x,ys)),split(x,ys))
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     s(x) -> x
     split(x,y) -> x
     split(x,y) -> y
     tp2(x,y) -> x
     tp2(x,y) -> y
     le(x,y) -> x
     le(x,y) -> y
     cons(x,y) -> x
     cons(x,y) -> y
    Subterm Criterion Processor:
     simple projection:
      pi(split#) = 1
     problem:
      DPs:
       
      TRS:
       split(x,nil()) -> tp2(nil(),nil())
       split(x,cons(y,ys)) -> tp2(split(x,ys),cons(y,split(x,ys)))
       split(x,cons(y,ys)) -> le(x,y)
       split(x,cons(y,ys)) -> split(x,ys)
       split(x,cons(y,ys)) -> tp2(cons(y,split(x,ys)),split(x,ys))
       le(0(),y) -> true()
       le(s(x),0()) -> false()
       le(s(x),s(y)) -> le(x,y)
       s(x) -> x
       split(x,y) -> x
       split(x,y) -> y
       tp2(x,y) -> x
       tp2(x,y) -> y
       le(x,y) -> x
       le(x,y) -> y
       cons(x,y) -> x
       cons(x,y) -> y
     Qed
    
    DPs:
     le#(s(x),s(y)) -> le#(x,y)
    TRS:
     split(x,nil()) -> tp2(nil(),nil())
     split(x,cons(y,ys)) -> tp2(split(x,ys),cons(y,split(x,ys)))
     split(x,cons(y,ys)) -> le(x,y)
     split(x,cons(y,ys)) -> split(x,ys)
     split(x,cons(y,ys)) -> tp2(cons(y,split(x,ys)),split(x,ys))
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     s(x) -> x
     split(x,y) -> x
     split(x,y) -> y
     tp2(x,y) -> x
     tp2(x,y) -> y
     le(x,y) -> x
     le(x,y) -> y
     cons(x,y) -> x
     cons(x,y) -> y
    Subterm Criterion Processor:
     simple projection:
      pi(le#) = 0
     problem:
      DPs:
       
      TRS:
       split(x,nil()) -> tp2(nil(),nil())
       split(x,cons(y,ys)) -> tp2(split(x,ys),cons(y,split(x,ys)))
       split(x,cons(y,ys)) -> le(x,y)
       split(x,cons(y,ys)) -> split(x,ys)
       split(x,cons(y,ys)) -> tp2(cons(y,split(x,ys)),split(x,ys))
       le(0(),y) -> true()
       le(s(x),0()) -> false()
       le(s(x),s(y)) -> le(x,y)
       s(x) -> x
       split(x,y) -> x
       split(x,y) -> y
       tp2(x,y) -> x
       tp2(x,y) -> y
       le(x,y) -> x
       le(x,y) -> y
       cons(x,y) -> x
       cons(x,y) -> y
     Qed