/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(mapbt(),f),app(leaf(),x)) -> app(leaf(),app(f,x))
 app(app(mapbt(),f),app(app(app(branch(),x),l),r)) ->
 app(app(app(branch(),app(f,x)),app(app(mapbt(),f),l)),app(app(mapbt(),f),r))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   branch ==> branch0/0 branch1/1 branch2/2 branch3/3
   leaf ==> leaf0/0 leaf1/1
   mapbt ==> mapbt0/0 mapbt1/1 mapbt2/2
   
  uncurry-rules:
   app(mapbt1(x4),x5) -> mapbt2(x4,x5)
   app(mapbt0(),x4) -> mapbt1(x4)
   app(leaf0(),x7) -> leaf1(x7)
   app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
   app(branch1(x9),x10) -> branch2(x9,x10)
   app(branch0(),x9) -> branch1(x9)
  eta-rules:
   
  problem:
   mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
   mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
   app(mapbt1(x4),x5) -> mapbt2(x4,x5)
   app(mapbt0(),x4) -> mapbt1(x4)
   app(leaf0(),x7) -> leaf1(x7)
   app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
   app(branch1(x9),x10) -> branch2(x9,x10)
   app(branch0(),x9) -> branch1(x9)
  DP Processor:
   DPs:
    mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
    mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
    mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
    mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
    app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5)
   TRS:
    mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
    mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
    app(mapbt1(x4),x5) -> mapbt2(x4,x5)
    app(mapbt0(),x4) -> mapbt1(x4)
    app(leaf0(),x7) -> leaf1(x7)
    app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
    app(branch1(x9),x10) -> branch2(x9,x10)
    app(branch0(),x9) -> branch1(x9)
   TDG Processor:
    DPs:
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5)
    TRS:
     mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
     mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
     app(mapbt1(x4),x5) -> mapbt2(x4,x5)
     app(mapbt0(),x4) -> mapbt1(x4)
     app(leaf0(),x7) -> leaf1(x7)
     app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
     app(branch1(x9),x10) -> branch2(x9,x10)
     app(branch0(),x9) -> branch1(x9)
    graph:
     app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5) ->
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x) ->
     app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r) ->
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
     mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l) ->
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapbt{2,#}(f,leaf1(x)) -> app#(f,x) -> app#(mapbt1(x4),x5) -> mapbt{2,#}(x4,x5)
    Subterm Criterion Processor:
     simple projection:
      pi(mapbt{2,#}) = 0
      pi(app#) = 0
     problem:
      DPs:
       mapbt{2,#}(f,leaf1(x)) -> app#(f,x)
       mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
       mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
       mapbt{2,#}(f,branch3(x,l,r)) -> app#(f,x)
      TRS:
       mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
       mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
       app(mapbt1(x4),x5) -> mapbt2(x4,x5)
       app(mapbt0(),x4) -> mapbt1(x4)
       app(leaf0(),x7) -> leaf1(x7)
       app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
       app(branch1(x9),x10) -> branch2(x9,x10)
       app(branch0(),x9) -> branch1(x9)
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 14/16
      DPs:
       mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,r)
       mapbt{2,#}(f,branch3(x,l,r)) -> mapbt{2,#}(f,l)
      TRS:
       mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
       mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
       app(mapbt1(x4),x5) -> mapbt2(x4,x5)
       app(mapbt0(),x4) -> mapbt1(x4)
       app(leaf0(),x7) -> leaf1(x7)
       app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
       app(branch1(x9),x10) -> branch2(x9,x10)
       app(branch0(),x9) -> branch1(x9)
      Subterm Criterion Processor:
       simple projection:
        pi(mapbt{2,#}) = 1
       problem:
        DPs:
         
        TRS:
         mapbt2(f,leaf1(x)) -> leaf1(app(f,x))
         mapbt2(f,branch3(x,l,r)) -> branch3(app(f,x),mapbt2(f,l),mapbt2(f,r))
         app(mapbt1(x4),x5) -> mapbt2(x4,x5)
         app(mapbt0(),x4) -> mapbt1(x4)
         app(leaf0(),x7) -> leaf1(x7)
         app(branch2(x9,x10),x11) -> branch3(x9,x10,x11)
         app(branch1(x9),x10) -> branch2(x9,x10)
         app(branch0(),x9) -> branch1(x9)
       Qed