/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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(append(),xs),nil()) -> xs
 app(app(append(),nil()),ys) -> ys
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
 app(app(zip(),nil()),yss) -> yss
 app(app(zip(),xss),nil()) -> xss
 app(app(zip(),app(app(cons(),xs),xss)),app(app(cons(),ys),yss)) ->
 app(app(cons(),app(app(append(),xs),ys)),app(app(zip(),xss),yss))
 app(app(combine(),xs),nil()) -> xs
 app(app(combine(),xs),app(app(cons(),ys),yss)) -> app(app(combine(),app(app(zip(),xs),ys)),yss)
 app(levels(),app(app(node(),x),xs)) ->
 app(app(cons(),app(app(cons(),x),nil())),app(app(combine(),nil()),app(app(map(),levels()),xs)))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   node ==> node0/0 node1/1 node2/2
   levels ==> levels0/0 levels1/1
   combine ==> combine0/0 combine1/1 combine2/2
   zip ==> zip0/0 zip1/1 zip2/2
   append ==> append0/0 append1/1 append2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   
  uncurry-rules:
   app(map1(x6),x7) -> map2(x6,x7)
   app(map0(),x6) -> map1(x6)
   app(cons1(x10),x11) -> cons2(x10,x11)
   app(cons0(),x10) -> cons1(x10)
   app(append1(x13),x14) -> append2(x13,x14)
   app(append0(),x13) -> append1(x13)
   app(zip1(x16),x17) -> zip2(x16,x17)
   app(zip0(),x16) -> zip1(x16)
   app(combine1(x19),x20) -> combine2(x19,x20)
   app(combine0(),x19) -> combine1(x19)
   app(levels0(),x22) -> levels1(x22)
   app(node1(x24),x25) -> node2(x24,x25)
   app(node0(),x24) -> node1(x24)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   append2(xs,nil0()) -> xs
   append2(nil0(),ys) -> ys
   append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
   zip2(nil0(),yss) -> yss
   zip2(xss,nil0()) -> xss
   zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
   combine2(xs,nil0()) -> xs
   combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
   levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
   app(map1(x6),x7) -> map2(x6,x7)
   app(map0(),x6) -> map1(x6)
   app(cons1(x10),x11) -> cons2(x10,x11)
   app(cons0(),x10) -> cons1(x10)
   app(append1(x13),x14) -> append2(x13,x14)
   app(append0(),x13) -> append1(x13)
   app(zip1(x16),x17) -> zip2(x16,x17)
   app(zip0(),x16) -> zip1(x16)
   app(combine1(x19),x20) -> combine2(x19,x20)
   app(combine0(),x19) -> combine1(x19)
   app(levels0(),x22) -> levels1(x22)
   app(node1(x24),x25) -> node2(x24,x25)
   app(node0(),x24) -> node1(x24)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
    zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss)
    zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> append{2,#}(xs,ys)
    combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys)
    combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss)
    levels{1,#}(node2(x,xs)) -> map{2,#}(levels0(),xs)
    levels{1,#}(node2(x,xs)) -> combine{2,#}(nil0(),map2(levels0(),xs))
    app#(map1(x6),x7) -> map{2,#}(x6,x7)
    app#(append1(x13),x14) -> append{2,#}(x13,x14)
    app#(zip1(x16),x17) -> zip{2,#}(x16,x17)
    app#(combine1(x19),x20) -> combine{2,#}(x19,x20)
    app#(levels0(),x22) -> levels{1,#}(x22)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    append2(xs,nil0()) -> xs
    append2(nil0(),ys) -> ys
    append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
    zip2(nil0(),yss) -> yss
    zip2(xss,nil0()) -> xss
    zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
    combine2(xs,nil0()) -> xs
    combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
    levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
    app(map1(x6),x7) -> map2(x6,x7)
    app(map0(),x6) -> map1(x6)
    app(cons1(x10),x11) -> cons2(x10,x11)
    app(cons0(),x10) -> cons1(x10)
    app(append1(x13),x14) -> append2(x13,x14)
    app(append0(),x13) -> append1(x13)
    app(zip1(x16),x17) -> zip2(x16,x17)
    app(zip0(),x16) -> zip1(x16)
    app(combine1(x19),x20) -> combine2(x19,x20)
    app(combine0(),x19) -> combine1(x19)
    app(levels0(),x22) -> levels1(x22)
    app(node1(x24),x25) -> node2(x24,x25)
    app(node0(),x24) -> node1(x24)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss)
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> append{2,#}(xs,ys)
     combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys)
     combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss)
     levels{1,#}(node2(x,xs)) -> map{2,#}(levels0(),xs)
     levels{1,#}(node2(x,xs)) -> combine{2,#}(nil0(),map2(levels0(),xs))
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     app#(append1(x13),x14) -> append{2,#}(x13,x14)
     app#(zip1(x16),x17) -> zip{2,#}(x16,x17)
     app#(combine1(x19),x20) -> combine{2,#}(x19,x20)
     app#(levels0(),x22) -> levels{1,#}(x22)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     append2(xs,nil0()) -> xs
     append2(nil0(),ys) -> ys
     append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
     zip2(nil0(),yss) -> yss
     zip2(xss,nil0()) -> xss
     zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
     combine2(xs,nil0()) -> xs
     combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
     levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
     app(map1(x6),x7) -> map2(x6,x7)
     app(map0(),x6) -> map1(x6)
     app(cons1(x10),x11) -> cons2(x10,x11)
     app(cons0(),x10) -> cons1(x10)
     app(append1(x13),x14) -> append2(x13,x14)
     app(append0(),x13) -> append1(x13)
     app(zip1(x16),x17) -> zip2(x16,x17)
     app(zip0(),x16) -> zip1(x16)
     app(combine1(x19),x20) -> combine2(x19,x20)
     app(combine0(),x19) -> combine1(x19)
     app(levels0(),x22) -> levels1(x22)
     app(node1(x24),x25) -> node2(x24,x25)
     app(node0(),x24) -> node1(x24)
    graph:
     levels{1,#}(node2(x,xs)) -> combine{2,#}(nil0(),map2(levels0(),xs)) ->
     combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss)
     levels{1,#}(node2(x,xs)) -> combine{2,#}(nil0(),map2(levels0(),xs)) ->
     combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys)
     levels{1,#}(node2(x,xs)) -> map{2,#}(levels0(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     levels{1,#}(node2(x,xs)) -> map{2,#}(levels0(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss) ->
     combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss)
     combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss) ->
     combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys)
     combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys) ->
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> append{2,#}(xs,ys)
     combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys) ->
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss)
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss) ->
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> append{2,#}(xs,ys)
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss) ->
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss)
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> append{2,#}(xs,ys) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     app#(levels0(),x22) -> levels{1,#}(x22) ->
     levels{1,#}(node2(x,xs)) -> combine{2,#}(nil0(),map2(levels0(),xs))
     app#(levels0(),x22) -> levels{1,#}(x22) ->
     levels{1,#}(node2(x,xs)) -> map{2,#}(levels0(),xs)
     app#(combine1(x19),x20) -> combine{2,#}(x19,x20) ->
     combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss)
     app#(combine1(x19),x20) -> combine{2,#}(x19,x20) ->
     combine{2,#}(xs,cons2(ys,yss)) -> zip{2,#}(xs,ys)
     app#(zip1(x16),x17) -> zip{2,#}(x16,x17) ->
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> append{2,#}(xs,ys)
     app#(zip1(x16),x17) -> zip{2,#}(x16,x17) ->
     zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss)
     app#(append1(x13),x14) -> append{2,#}(x13,x14) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(levels0(),x22) -> levels{1,#}(x22)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(combine1(x19),x20) -> combine{2,#}(x19,x20)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(zip1(x16),x17) -> zip{2,#}(x16,x17)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(append1(x13),x14) -> append{2,#}(x13,x14)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     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: 8
     #arcs: 28/196
     DPs:
      levels{1,#}(node2(x,xs)) -> map{2,#}(levels0(),xs)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x6),x7) -> map{2,#}(x6,x7)
      app#(levels0(),x22) -> levels{1,#}(x22)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      append2(xs,nil0()) -> xs
      append2(nil0(),ys) -> ys
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      zip2(nil0(),yss) -> yss
      zip2(xss,nil0()) -> xss
      zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
      combine2(xs,nil0()) -> xs
      combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
      levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
      app(map1(x6),x7) -> map2(x6,x7)
      app(map0(),x6) -> map1(x6)
      app(cons1(x10),x11) -> cons2(x10,x11)
      app(cons0(),x10) -> cons1(x10)
      app(append1(x13),x14) -> append2(x13,x14)
      app(append0(),x13) -> append1(x13)
      app(zip1(x16),x17) -> zip2(x16,x17)
      app(zip0(),x16) -> zip1(x16)
      app(combine1(x19),x20) -> combine2(x19,x20)
      app(combine0(),x19) -> combine1(x19)
      app(levels0(),x22) -> levels1(x22)
      app(node1(x24),x25) -> node2(x24,x25)
      app(node0(),x24) -> node1(x24)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
       pi(levels{1,#}) = 0
      problem:
       DPs:
        app#(map1(x6),x7) -> map{2,#}(x6,x7)
        app#(levels0(),x22) -> levels{1,#}(x22)
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        append2(xs,nil0()) -> xs
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        zip2(nil0(),yss) -> yss
        zip2(xss,nil0()) -> xss
        zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
        combine2(xs,nil0()) -> xs
        combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
        levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
        app(map1(x6),x7) -> map2(x6,x7)
        app(map0(),x6) -> map1(x6)
        app(cons1(x10),x11) -> cons2(x10,x11)
        app(cons0(),x10) -> cons1(x10)
        app(append1(x13),x14) -> append2(x13,x14)
        app(append0(),x13) -> append1(x13)
        app(zip1(x16),x17) -> zip2(x16,x17)
        app(zip0(),x16) -> zip1(x16)
        app(combine1(x19),x20) -> combine2(x19,x20)
        app(combine0(),x19) -> combine1(x19)
        app(levels0(),x22) -> levels1(x22)
        app(node1(x24),x25) -> node2(x24,x25)
        app(node0(),x24) -> node1(x24)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 9/4
       
     
     DPs:
      combine{2,#}(xs,cons2(ys,yss)) -> combine{2,#}(zip2(xs,ys),yss)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      append2(xs,nil0()) -> xs
      append2(nil0(),ys) -> ys
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      zip2(nil0(),yss) -> yss
      zip2(xss,nil0()) -> xss
      zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
      combine2(xs,nil0()) -> xs
      combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
      levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
      app(map1(x6),x7) -> map2(x6,x7)
      app(map0(),x6) -> map1(x6)
      app(cons1(x10),x11) -> cons2(x10,x11)
      app(cons0(),x10) -> cons1(x10)
      app(append1(x13),x14) -> append2(x13,x14)
      app(append0(),x13) -> append1(x13)
      app(zip1(x16),x17) -> zip2(x16,x17)
      app(zip0(),x16) -> zip1(x16)
      app(combine1(x19),x20) -> combine2(x19,x20)
      app(combine0(),x19) -> combine1(x19)
      app(levels0(),x22) -> levels1(x22)
      app(node1(x24),x25) -> node2(x24,x25)
      app(node0(),x24) -> node1(x24)
     Subterm Criterion Processor:
      simple projection:
       pi(combine{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        append2(xs,nil0()) -> xs
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        zip2(nil0(),yss) -> yss
        zip2(xss,nil0()) -> xss
        zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
        combine2(xs,nil0()) -> xs
        combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
        levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
        app(map1(x6),x7) -> map2(x6,x7)
        app(map0(),x6) -> map1(x6)
        app(cons1(x10),x11) -> cons2(x10,x11)
        app(cons0(),x10) -> cons1(x10)
        app(append1(x13),x14) -> append2(x13,x14)
        app(append0(),x13) -> append1(x13)
        app(zip1(x16),x17) -> zip2(x16,x17)
        app(zip0(),x16) -> zip1(x16)
        app(combine1(x19),x20) -> combine2(x19,x20)
        app(combine0(),x19) -> combine1(x19)
        app(levels0(),x22) -> levels1(x22)
        app(node1(x24),x25) -> node2(x24,x25)
        app(node0(),x24) -> node1(x24)
      Qed
     
     DPs:
      zip{2,#}(cons2(xs,xss),cons2(ys,yss)) -> zip{2,#}(xss,yss)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      append2(xs,nil0()) -> xs
      append2(nil0(),ys) -> ys
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      zip2(nil0(),yss) -> yss
      zip2(xss,nil0()) -> xss
      zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
      combine2(xs,nil0()) -> xs
      combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
      levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
      app(map1(x6),x7) -> map2(x6,x7)
      app(map0(),x6) -> map1(x6)
      app(cons1(x10),x11) -> cons2(x10,x11)
      app(cons0(),x10) -> cons1(x10)
      app(append1(x13),x14) -> append2(x13,x14)
      app(append0(),x13) -> append1(x13)
      app(zip1(x16),x17) -> zip2(x16,x17)
      app(zip0(),x16) -> zip1(x16)
      app(combine1(x19),x20) -> combine2(x19,x20)
      app(combine0(),x19) -> combine1(x19)
      app(levels0(),x22) -> levels1(x22)
      app(node1(x24),x25) -> node2(x24,x25)
      app(node0(),x24) -> node1(x24)
     Subterm Criterion Processor:
      simple projection:
       pi(zip{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        append2(xs,nil0()) -> xs
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        zip2(nil0(),yss) -> yss
        zip2(xss,nil0()) -> xss
        zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
        combine2(xs,nil0()) -> xs
        combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
        levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
        app(map1(x6),x7) -> map2(x6,x7)
        app(map0(),x6) -> map1(x6)
        app(cons1(x10),x11) -> cons2(x10,x11)
        app(cons0(),x10) -> cons1(x10)
        app(append1(x13),x14) -> append2(x13,x14)
        app(append0(),x13) -> append1(x13)
        app(zip1(x16),x17) -> zip2(x16,x17)
        app(zip0(),x16) -> zip1(x16)
        app(combine1(x19),x20) -> combine2(x19,x20)
        app(combine0(),x19) -> combine1(x19)
        app(levels0(),x22) -> levels1(x22)
        app(node1(x24),x25) -> node2(x24,x25)
        app(node0(),x24) -> node1(x24)
      Qed
     
     DPs:
      append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      append2(xs,nil0()) -> xs
      append2(nil0(),ys) -> ys
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      zip2(nil0(),yss) -> yss
      zip2(xss,nil0()) -> xss
      zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
      combine2(xs,nil0()) -> xs
      combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
      levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
      app(map1(x6),x7) -> map2(x6,x7)
      app(map0(),x6) -> map1(x6)
      app(cons1(x10),x11) -> cons2(x10,x11)
      app(cons0(),x10) -> cons1(x10)
      app(append1(x13),x14) -> append2(x13,x14)
      app(append0(),x13) -> append1(x13)
      app(zip1(x16),x17) -> zip2(x16,x17)
      app(zip0(),x16) -> zip1(x16)
      app(combine1(x19),x20) -> combine2(x19,x20)
      app(combine0(),x19) -> combine1(x19)
      app(levels0(),x22) -> levels1(x22)
      app(node1(x24),x25) -> node2(x24,x25)
      app(node0(),x24) -> node1(x24)
     Subterm Criterion Processor:
      simple projection:
       pi(append{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        append2(xs,nil0()) -> xs
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        zip2(nil0(),yss) -> yss
        zip2(xss,nil0()) -> xss
        zip2(cons2(xs,xss),cons2(ys,yss)) -> cons2(append2(xs,ys),zip2(xss,yss))
        combine2(xs,nil0()) -> xs
        combine2(xs,cons2(ys,yss)) -> combine2(zip2(xs,ys),yss)
        levels1(node2(x,xs)) -> cons2(cons2(x,nil0()),combine2(nil0(),map2(levels0(),xs)))
        app(map1(x6),x7) -> map2(x6,x7)
        app(map0(),x6) -> map1(x6)
        app(cons1(x10),x11) -> cons2(x10,x11)
        app(cons0(),x10) -> cons1(x10)
        app(append1(x13),x14) -> append2(x13,x14)
        app(append0(),x13) -> append1(x13)
        app(zip1(x16),x17) -> zip2(x16,x17)
        app(zip0(),x16) -> zip1(x16)
        app(combine1(x19),x20) -> combine2(x19,x20)
        app(combine0(),x19) -> combine1(x19)
        app(levels0(),x22) -> levels1(x22)
        app(node1(x24),x25) -> node2(x24,x25)
        app(node0(),x24) -> node1(x24)
      Qed