/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) ->
 app(app(minus(),app(p(),app(s(),x))),app(p(),app(s(),y)))
 app(p(),app(s(),x)) -> x
 app(app(div(),0()),app(s(),y)) -> 0()
 app(app(div(),app(s(),x)),app(s(),y)) ->
 app(s(),app(app(div(),app(app(minus(),x),app(id(),y))),app(s(),y)))
 app(id(),x) -> x
 app(id(),x) -> app(s(),app(s(),app(s(),x)))
 app(id(),app(p(),x)) -> app(id(),app(s(),app(id(),x)))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   id ==> id0/0 id1/1
   div ==> div0/0 div1/1 div2/2
   p ==> p0/0 p1/1
   s ==> s0/0 s1/1
   0 ==> 00/0
   minus ==> minus0/0 minus1/1 minus2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   
  uncurry-rules:
   app(map1(x4),x5) -> map2(x4,x5)
   app(map0(),x4) -> map1(x4)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(minus1(x11),x12) -> minus2(x11,x12)
   app(minus0(),x11) -> minus1(x11)
   app(s0(),x15) -> s1(x15)
   app(p0(),x17) -> p1(x17)
   app(div1(x19),x20) -> div2(x19,x20)
   app(div0(),x19) -> div1(x19)
   app(id0(),x22) -> id1(x22)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   minus2(x,00()) -> x
   minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
   p1(s1(x)) -> x
   div2(00(),s1(y)) -> 00()
   div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
   id1(x) -> x
   id1(x) -> s1(s1(s1(x)))
   id1(p1(x)) -> id1(s1(id1(x)))
   app(map1(x4),x5) -> map2(x4,x5)
   app(map0(),x4) -> map1(x4)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(minus1(x11),x12) -> minus2(x11,x12)
   app(minus0(),x11) -> minus1(x11)
   app(s0(),x15) -> s1(x15)
   app(p0(),x17) -> p1(x17)
   app(div1(x19),x20) -> div2(x19,x20)
   app(div0(),x19) -> div1(x19)
   app(id0(),x22) -> id1(x22)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(y))
    minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
    minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
    div{2,#}(s1(x),s1(y)) -> id{1,#}(y)
    div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y))
    div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y))
    id{1,#}(p1(x)) -> id{1,#}(x)
    id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
    app#(minus1(x11),x12) -> minus{2,#}(x11,x12)
    app#(p0(),x17) -> p{1,#}(x17)
    app#(div1(x19),x20) -> div{2,#}(x19,x20)
    app#(id0(),x22) -> id{1,#}(x22)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    minus2(x,00()) -> x
    minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
    p1(s1(x)) -> x
    div2(00(),s1(y)) -> 00()
    div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
    id1(x) -> x
    id1(x) -> s1(s1(s1(x)))
    id1(p1(x)) -> id1(s1(id1(x)))
    app(map1(x4),x5) -> map2(x4,x5)
    app(map0(),x4) -> map1(x4)
    app(cons1(x8),x9) -> cons2(x8,x9)
    app(cons0(),x8) -> cons1(x8)
    app(minus1(x11),x12) -> minus2(x11,x12)
    app(minus0(),x11) -> minus1(x11)
    app(s0(),x15) -> s1(x15)
    app(p0(),x17) -> p1(x17)
    app(div1(x19),x20) -> div2(x19,x20)
    app(div0(),x19) -> div1(x19)
    app(id0(),x22) -> id1(x22)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(y))
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
     div{2,#}(s1(x),s1(y)) -> id{1,#}(y)
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y))
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y))
     id{1,#}(p1(x)) -> id{1,#}(x)
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(minus1(x11),x12) -> minus{2,#}(x11,x12)
     app#(p0(),x17) -> p{1,#}(x17)
     app#(div1(x19),x20) -> div{2,#}(x19,x20)
     app#(id0(),x22) -> id{1,#}(x22)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     minus2(x,00()) -> x
     minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
     p1(s1(x)) -> x
     div2(00(),s1(y)) -> 00()
     div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
     id1(x) -> x
     id1(x) -> s1(s1(s1(x)))
     id1(p1(x)) -> id1(s1(id1(x)))
     app(map1(x4),x5) -> map2(x4,x5)
     app(map0(),x4) -> map1(x4)
     app(cons1(x8),x9) -> cons2(x8,x9)
     app(cons0(),x8) -> cons1(x8)
     app(minus1(x11),x12) -> minus2(x11,x12)
     app(minus0(),x11) -> minus1(x11)
     app(s0(),x15) -> s1(x15)
     app(p0(),x17) -> p1(x17)
     app(div1(x19),x20) -> div2(x19,x20)
     app(div0(),x19) -> div1(x19)
     app(id0(),x22) -> id1(x22)
    graph:
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x))) ->
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x))) ->
     id{1,#}(p1(x)) -> id{1,#}(x)
     id{1,#}(p1(x)) -> id{1,#}(x) ->
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
     id{1,#}(p1(x)) -> id{1,#}(x) ->
     id{1,#}(p1(x)) -> id{1,#}(x)
     div{2,#}(s1(x),s1(y)) -> id{1,#}(y) ->
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
     div{2,#}(s1(x),s1(y)) -> id{1,#}(y) ->
     id{1,#}(p1(x)) -> id{1,#}(x)
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y)) ->
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y))
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y)) ->
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y))
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y)) ->
     div{2,#}(s1(x),s1(y)) -> id{1,#}(y)
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y)) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y)) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y)) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(y))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y))) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y))) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y))) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(y))
     app#(id0(),x22) -> id{1,#}(x22) ->
     id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
     app#(id0(),x22) -> id{1,#}(x22) ->
     id{1,#}(p1(x)) -> id{1,#}(x)
     app#(div1(x19),x20) -> div{2,#}(x19,x20) ->
     div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y))
     app#(div1(x19),x20) -> div{2,#}(x19,x20) ->
     div{2,#}(s1(x),s1(y)) -> minus{2,#}(x,id1(y))
     app#(div1(x19),x20) -> div{2,#}(x19,x20) ->
     div{2,#}(s1(x),s1(y)) -> id{1,#}(y)
     app#(minus1(x11),x12) -> minus{2,#}(x11,x12) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
     app#(minus1(x11),x12) -> minus{2,#}(x11,x12) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(x))
     app#(minus1(x11),x12) -> minus{2,#}(x11,x12) ->
     minus{2,#}(s1(x),s1(y)) -> p{1,#}(s1(y))
     app#(map1(x4),x5) -> map{2,#}(x4,x5) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x4),x5) -> map{2,#}(x4,x5) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(id0(),x22) -> id{1,#}(x22)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(div1(x19),x20) -> div{2,#}(x19,x20)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(p0(),x17) -> p{1,#}(x17)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(minus1(x11),x12) -> minus{2,#}(x11,x12)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) -> map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    SCC Processor:
     #sccs: 4
     #rules: 7
     #arcs: 32/225
     DPs:
      app#(map1(x4),x5) -> map{2,#}(x4,x5)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,00()) -> x
      minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      div2(00(),s1(y)) -> 00()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
      id1(x) -> x
      id1(x) -> s1(s1(s1(x)))
      id1(p1(x)) -> id1(s1(id1(x)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map0(),x4) -> map1(x4)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(minus1(x11),x12) -> minus2(x11,x12)
      app(minus0(),x11) -> minus1(x11)
      app(s0(),x15) -> s1(x15)
      app(p0(),x17) -> p1(x17)
      app(div1(x19),x20) -> div2(x19,x20)
      app(div0(),x19) -> div1(x19)
      app(id0(),x22) -> id1(x22)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 0
       pi(app#) = 0
      problem:
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
        map{2,#}(f,cons2(x,xs)) -> app#(f,x)
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,00()) -> x
        minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        div2(00(),s1(y)) -> 00()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
        id1(x) -> x
        id1(x) -> s1(s1(s1(x)))
        id1(p1(x)) -> id1(s1(id1(x)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map0(),x4) -> map1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(minus1(x11),x12) -> minus2(x11,x12)
        app(minus0(),x11) -> minus1(x11)
        app(s0(),x15) -> s1(x15)
        app(p0(),x17) -> p1(x17)
        app(div1(x19),x20) -> div2(x19,x20)
        app(div0(),x19) -> div1(x19)
        app(id0(),x22) -> id1(x22)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 5/4
       DPs:
        map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,00()) -> x
        minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        div2(00(),s1(y)) -> 00()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
        id1(x) -> x
        id1(x) -> s1(s1(s1(x)))
        id1(p1(x)) -> id1(s1(id1(x)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map0(),x4) -> map1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(minus1(x11),x12) -> minus2(x11,x12)
        app(minus0(),x11) -> minus1(x11)
        app(s0(),x15) -> s1(x15)
        app(p0(),x17) -> p1(x17)
        app(div1(x19),x20) -> div2(x19,x20)
        app(div0(),x19) -> div1(x19)
        app(id0(),x22) -> id1(x22)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          map2(f,nil0()) -> nil0()
          map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
          minus2(x,00()) -> x
          minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
          p1(s1(x)) -> x
          div2(00(),s1(y)) -> 00()
          div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
          id1(x) -> x
          id1(x) -> s1(s1(s1(x)))
          id1(p1(x)) -> id1(s1(id1(x)))
          app(map1(x4),x5) -> map2(x4,x5)
          app(map0(),x4) -> map1(x4)
          app(cons1(x8),x9) -> cons2(x8,x9)
          app(cons0(),x8) -> cons1(x8)
          app(minus1(x11),x12) -> minus2(x11,x12)
          app(minus0(),x11) -> minus1(x11)
          app(s0(),x15) -> s1(x15)
          app(p0(),x17) -> p1(x17)
          app(div1(x19),x20) -> div2(x19,x20)
          app(div0(),x19) -> div1(x19)
          app(id0(),x22) -> id1(x22)
        Qed
     
     DPs:
      div{2,#}(s1(x),s1(y)) -> div{2,#}(minus2(x,id1(y)),s1(y))
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,00()) -> x
      minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      div2(00(),s1(y)) -> 00()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
      id1(x) -> x
      id1(x) -> s1(s1(s1(x)))
      id1(p1(x)) -> id1(s1(id1(x)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map0(),x4) -> map1(x4)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(minus1(x11),x12) -> minus2(x11,x12)
      app(minus0(),x11) -> minus1(x11)
      app(s0(),x15) -> s1(x15)
      app(p0(),x17) -> p1(x17)
      app(div1(x19),x20) -> div2(x19,x20)
      app(div0(),x19) -> div1(x19)
      app(id0(),x22) -> id1(x22)
     Subterm Criterion Processor:
      simple projection:
       pi(minus2) = 0
       pi(p1) = 0
       pi(div{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,00()) -> x
        minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        div2(00(),s1(y)) -> 00()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
        id1(x) -> x
        id1(x) -> s1(s1(s1(x)))
        id1(p1(x)) -> id1(s1(id1(x)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map0(),x4) -> map1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(minus1(x11),x12) -> minus2(x11,x12)
        app(minus0(),x11) -> minus1(x11)
        app(s0(),x15) -> s1(x15)
        app(p0(),x17) -> p1(x17)
        app(div1(x19),x20) -> div2(x19,x20)
        app(div0(),x19) -> div1(x19)
        app(id0(),x22) -> id1(x22)
      Qed
     
     DPs:
      minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,00()) -> x
      minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      div2(00(),s1(y)) -> 00()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
      id1(x) -> x
      id1(x) -> s1(s1(s1(x)))
      id1(p1(x)) -> id1(s1(id1(x)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map0(),x4) -> map1(x4)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(minus1(x11),x12) -> minus2(x11,x12)
      app(minus0(),x11) -> minus1(x11)
      app(s0(),x15) -> s1(x15)
      app(p0(),x17) -> p1(x17)
      app(div1(x19),x20) -> div2(x19,x20)
      app(div0(),x19) -> div1(x19)
      app(id0(),x22) -> id1(x22)
     Usable Rule Processor:
      DPs:
       minus{2,#}(s1(x),s1(y)) -> minus{2,#}(p1(s1(x)),p1(s1(y)))
      TRS:
       p1(s1(x)) -> x
      Semantic Labeling Processor:
       dimension: 2
       usable rules:
        
       interpretation:
                   [1 1]  
        [p1](x0) = [1 0]x0,
        
                   [1 1]     [0]
        [s1](x0) = [1 1]x0 + [1]
        labeled:
         minus{2,#}
         s1
        usable (for model):
         minus{2,#}
         s1
         p1
        argument filtering:
         pi(s1) = 0
         pi(p1) = 0
         pi(minus{2,#}) = []
       precedence:
        minus{2,#} ~ p1 ~ s1
       problem:
        DPs:
         
        TRS:
         p1(s1(x)) -> x
       Qed
     
     DPs:
      id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
      id{1,#}(p1(x)) -> id{1,#}(x)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      minus2(x,00()) -> x
      minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
      p1(s1(x)) -> x
      div2(00(),s1(y)) -> 00()
      div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
      id1(x) -> x
      id1(x) -> s1(s1(s1(x)))
      id1(p1(x)) -> id1(s1(id1(x)))
      app(map1(x4),x5) -> map2(x4,x5)
      app(map0(),x4) -> map1(x4)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(minus1(x11),x12) -> minus2(x11,x12)
      app(minus0(),x11) -> minus1(x11)
      app(s0(),x15) -> s1(x15)
      app(p0(),x17) -> p1(x17)
      app(div1(x19),x20) -> div2(x19,x20)
      app(div0(),x19) -> div1(x19)
      app(id0(),x22) -> id1(x22)
     EDG Processor:
      DPs:
       id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
       id{1,#}(p1(x)) -> id{1,#}(x)
      TRS:
       map2(f,nil0()) -> nil0()
       map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
       minus2(x,00()) -> x
       minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
       p1(s1(x)) -> x
       div2(00(),s1(y)) -> 00()
       div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
       id1(x) -> x
       id1(x) -> s1(s1(s1(x)))
       id1(p1(x)) -> id1(s1(id1(x)))
       app(map1(x4),x5) -> map2(x4,x5)
       app(map0(),x4) -> map1(x4)
       app(cons1(x8),x9) -> cons2(x8,x9)
       app(cons0(),x8) -> cons1(x8)
       app(minus1(x11),x12) -> minus2(x11,x12)
       app(minus0(),x11) -> minus1(x11)
       app(s0(),x15) -> s1(x15)
       app(p0(),x17) -> p1(x17)
       app(div1(x19),x20) -> div2(x19,x20)
       app(div0(),x19) -> div1(x19)
       app(id0(),x22) -> id1(x22)
      graph:
       id{1,#}(p1(x)) -> id{1,#}(x) -> id{1,#}(p1(x)) -> id{1,#}(x)
       id{1,#}(p1(x)) -> id{1,#}(x) -> id{1,#}(p1(x)) -> id{1,#}(s1(id1(x)))
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 2/4
       DPs:
        id{1,#}(p1(x)) -> id{1,#}(x)
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        minus2(x,00()) -> x
        minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
        p1(s1(x)) -> x
        div2(00(),s1(y)) -> 00()
        div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
        id1(x) -> x
        id1(x) -> s1(s1(s1(x)))
        id1(p1(x)) -> id1(s1(id1(x)))
        app(map1(x4),x5) -> map2(x4,x5)
        app(map0(),x4) -> map1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(minus1(x11),x12) -> minus2(x11,x12)
        app(minus0(),x11) -> minus1(x11)
        app(s0(),x15) -> s1(x15)
        app(p0(),x17) -> p1(x17)
        app(div1(x19),x20) -> div2(x19,x20)
        app(div0(),x19) -> div1(x19)
        app(id0(),x22) -> id1(x22)
       Size-Change Termination Processor:
        DPs:
         
        TRS:
         map2(f,nil0()) -> nil0()
         map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
         minus2(x,00()) -> x
         minus2(s1(x),s1(y)) -> minus2(p1(s1(x)),p1(s1(y)))
         p1(s1(x)) -> x
         div2(00(),s1(y)) -> 00()
         div2(s1(x),s1(y)) -> s1(div2(minus2(x,id1(y)),s1(y)))
         id1(x) -> x
         id1(x) -> s1(s1(s1(x)))
         id1(p1(x)) -> id1(s1(id1(x)))
         app(map1(x4),x5) -> map2(x4,x5)
         app(map0(),x4) -> map1(x4)
         app(cons1(x8),x9) -> cons2(x8,x9)
         app(cons0(),x8) -> cons1(x8)
         app(minus1(x11),x12) -> minus2(x11,x12)
         app(minus0(),x11) -> minus1(x11)
         app(s0(),x15) -> s1(x15)
         app(p0(),x17) -> p1(x17)
         app(div1(x19),x20) -> div2(x19,x20)
         app(div0(),x19) -> div1(x19)
         app(id0(),x22) -> id1(x22)
        The DP: id{1,#}(p1(x)) -> id{1,#}(x) has the edges:
          0 >   0
        Qed