YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 quot(0(),s(y)) -> 0()
 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 minus(minus(x,y),z) -> minus(x,plus(y,z))
 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)))))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   plus#(s(x),y) -> plus#(x,y)
   minus#(minus(x,y),z) -> plus#(y,z)
   minus#(minus(x,y),z) -> minus#(x,plus(y,z))
   app#(cons(x,l),k) -> app#(l,k)
   sum#(cons(x,cons(y,l))) -> plus#(x,y)
   sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
   sum#(app(l,cons(x,cons(y,k)))) -> 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#(app(l,sum(cons(x,cons(y,k)))))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   minus(minus(x,y),z) -> minus(x,plus(y,z))
   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)))))
  TDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    plus#(s(x),y) -> plus#(x,y)
    minus#(minus(x,y),z) -> plus#(y,z)
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    app#(cons(x,l),k) -> app#(l,k)
    sum#(cons(x,cons(y,l))) -> plus#(x,y)
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
    sum#(app(l,cons(x,cons(y,k)))) -> 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#(app(l,sum(cons(x,cons(y,k)))))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    minus(minus(x,y),z) -> minus(x,plus(y,z))
    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)))))
   graph:
    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)))))
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l)) ->
    sum#(app(l,cons(x,cons(y,k)))) -> app#(l,sum(cons(x,cons(y,k))))
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l)) ->
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l)) ->
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l)) ->
    sum#(cons(x,cons(y,l))) -> plus#(x,y)
    sum#(cons(x,cons(y,l))) -> plus#(x,y) ->
    plus#(s(x),y) -> plus#(x,y)
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k))) ->
    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)))) -> 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))) ->
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k))) ->
    sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k))) ->
    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)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
    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#(app(l,sum(cons(x,cons(y,k))))) ->
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k))))) ->
    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))))) ->
    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)))) ->
    app#(cons(x,l),k) -> app#(l,k)
    app#(cons(x,l),k) -> app#(l,k) -> app#(cons(x,l),k) -> app#(l,k)
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(s(x),y) -> plus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> plus#(y,z)
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    minus#(s(x),s(y)) -> minus#(x,y) ->
    minus#(minus(x,y),z) -> plus#(y,z)
    minus#(s(x),s(y)) -> minus#(x,y) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(minus(x,y),z) -> plus#(y,z) ->
    plus#(s(x),y) -> plus#(x,y)
    minus#(minus(x,y),z) -> minus#(x,plus(y,z)) ->
    minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    minus#(minus(x,y),z) -> minus#(x,plus(y,z)) ->
    minus#(minus(x,y),z) -> plus#(y,z)
    minus#(minus(x,y),z) -> minus#(x,plus(y,z)) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 8
    #arcs: 31/144
    DPs:
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
     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)))))
    Usable Rule Processor:
     DPs:
      quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      minus(minus(x,y),z) -> minus(x,plus(y,z))
      plus(0(),y) -> y
      plus(s(x),y) -> s(plus(x,y))
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       minus(minus(x,y),z) -> minus(x,plus(y,z))
      interpretation:
       [quot#](x0, x1) = x0,
       
       [plus](x0, x1) = 3x0 + 3x1 + 6,
       
       [s](x0) = 1x0 + 0,
       
       [minus](x0, x1) = x0,
       
       [0] = 2
      orientation:
       quot#(s(x),s(y)) = 1x + 0 >= x = quot#(minus(x,y),s(y))
       
       minus(x,0()) = x >= x = x
       
       minus(s(x),s(y)) = 1x + 0 >= x = minus(x,y)
       
       minus(minus(x,y),z) = x >= x = minus(x,plus(y,z))
       
       plus(0(),y) = 3y + 6 >= y = y
       
       plus(s(x),y) = 4x + 3y + 6 >= 4x + 4y + 7 = s(plus(x,y))
      problem:
       DPs:
        
       TRS:
        minus(x,0()) -> x
        minus(s(x),s(y)) -> minus(x,y)
        minus(minus(x,y),z) -> minus(x,plus(y,z))
        plus(0(),y) -> y
        plus(s(x),y) -> s(plus(x,y))
      Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
     minus#(minus(x,y),z) -> minus#(x,plus(y,z))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
     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)))))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
       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)))))
     Qed
    
    DPs:
     sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
     sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
     sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
     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)))))
    EDG Processor:
     DPs:
      sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
      sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
      sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      quot(0(),s(y)) -> 0()
      quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      plus(0(),y) -> y
      plus(s(x),y) -> s(plus(x,y))
      minus(minus(x,y),z) -> minus(x,plus(y,z))
      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)))))
     graph:
      sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l)) ->
      sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
      sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k))) ->
      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))))) ->
      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))))) ->
      sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
      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)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 5/9
      DPs:
       sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
       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)))))
      Usable Rule Processor:
       DPs:
        sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
       TRS:
        sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
        sum(cons(x,nil())) -> cons(x,nil())
        plus(0(),y) -> y
        plus(s(x),y) -> s(plus(x,y))
        app(nil(),k) -> k
        app(l,nil()) -> l
        app(cons(x,l),k) -> cons(x,app(l,k))
       Semantic Labeling Processor:
        dimension: 1
        usable rules:
         
        interpretation:
         [sum](x0) = 1,
         
         [cons](x0, x1) = x1 + 1,
         
         [app](x0, x1) = x0 + x1 + 1,
         
         [nil] = 0,
         
         [plus](x0, x1) = x0 + x1,
         
         [s](x0) = 0,
         
         [0] = 1
         labeled:
          sum#
          plus
         usable (for model):
          sum#
          app
          cons
          sum
          plus
          nil
          0
          s
         argument filtering:
          pi(0) = []
          pi(s) = []
          pi(plus) = []
          pi(nil) = []
          pi(app) = 1
          pi(cons) = 1
          pi(sum) = 0
          pi(sum#) = []
        precedence:
         sum# ~ sum ~ cons ~ app ~ nil ~ plus ~ s ~ 0
        problem:
         DPs:
          
         TRS:
          sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
          sum(cons(x,nil())) -> cons(x,nil())
          plus(0(),y) -> y
          plus(s(x),y) -> s(plus(x,y))
          app(nil(),k) -> k
          app(l,nil()) -> l
          app(cons(x,l),k) -> cons(x,app(l,k))
        Qed
      
      DPs:
       sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
       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)))))
      Usable Rule Processor:
       DPs:
        sum#(cons(x,cons(y,l))) -> sum#(cons(plus(x,y),l))
       TRS:
        plus(0(),y) -> y
        plus(s(x),y) -> s(plus(x,y))
       Semantic Labeling Processor:
        dimension: 1
        usable rules:
         
        interpretation:
         [cons](x0, x1) = x0 + x1 + 1,
         
         [plus](x0, x1) = x0 + x1,
         
         [s](x0) = x0 + 1,
         
         [0] = 0
         labeled:
          sum#
          cons
          plus
          s
         usable (for model):
          sum#
          cons
          plus
          0
          s
         argument filtering:
          pi(0) = []
          pi(s) = []
          pi(plus) = 1
          pi(cons) = 1
          pi(sum#) = []
        precedence:
         sum# ~ cons ~ plus ~ s ~ 0
        problem:
         DPs:
          
         TRS:
          plus(0(),y) -> y
          plus(s(x),y) -> s(plus(x,y))
        Qed
    
    DPs:
     app#(cons(x,l),k) -> app#(l,k)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
     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)))))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
       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)))))
     Qed
    
    DPs:
     plus#(s(x),y) -> plus#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     minus(minus(x,y),z) -> minus(x,plus(y,z))
     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)))))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       minus(minus(x,y),z) -> minus(x,plus(y,z))
       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)))))
     Qed