/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(app(comp(),f),g),x) -> app(f,app(g,x))
 app(twice(),f) -> app(app(comp(),f),f)

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   twice ==> twice0/0 twice1/1
   comp ==> comp0/0 comp1/1 comp2/2 comp3/3
   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(comp2(x11,x12),x13) -> comp3(x11,x12,x13)
   app(comp1(x11),x12) -> comp2(x11,x12)
   app(comp0(),x11) -> comp1(x11)
   app(twice0(),x15) -> twice1(x15)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   comp3(f,g,x) -> app(f,app(g,x))
   twice1(f) -> comp2(f,f)
   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(comp2(x11,x12),x13) -> comp3(x11,x12,x13)
   app(comp1(x11),x12) -> comp2(x11,x12)
   app(comp0(),x11) -> comp1(x11)
   app(twice0(),x15) -> twice1(x15)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    comp{3,#}(f,g,x) -> app#(g,x)
    comp{3,#}(f,g,x) -> app#(f,app(g,x))
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
    app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13)
    app#(twice0(),x15) -> twice{1,#}(x15)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    comp3(f,g,x) -> app(f,app(g,x))
    twice1(f) -> comp2(f,f)
    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(comp2(x11,x12),x13) -> comp3(x11,x12,x13)
    app(comp1(x11),x12) -> comp2(x11,x12)
    app(comp0(),x11) -> comp1(x11)
    app(twice0(),x15) -> twice1(x15)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     comp{3,#}(f,g,x) -> app#(g,x)
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13)
     app#(twice0(),x15) -> twice{1,#}(x15)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     comp3(f,g,x) -> app(f,app(g,x))
     twice1(f) -> comp2(f,f)
     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(comp2(x11,x12),x13) -> comp3(x11,x12,x13)
     app(comp1(x11),x12) -> comp2(x11,x12)
     app(comp0(),x11) -> comp1(x11)
     app(twice0(),x15) -> twice1(x15)
    graph:
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(twice0(),x15) -> twice{1,#}(x15)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13)
     comp{3,#}(f,g,x) -> app#(g,x) ->
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(twice0(),x15) -> twice{1,#}(x15)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13)
     comp{3,#}(f,g,x) -> app#(f,app(g,x)) ->
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13) ->
     comp{3,#}(f,g,x) -> app#(f,app(g,x))
     app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13) ->
     comp{3,#}(f,g,x) -> app#(g,x)
     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#(twice0(),x15) -> twice{1,#}(x15)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13)
     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: 1
     #rules: 6
     #arcs: 15/49
     DPs:
      comp{3,#}(f,g,x) -> app#(g,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#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13)
      comp{3,#}(f,g,x) -> app#(f,app(g,x))
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      comp3(f,g,x) -> app(f,app(g,x))
      twice1(f) -> comp2(f,f)
      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(comp2(x11,x12),x13) -> comp3(x11,x12,x13)
      app(comp1(x11),x12) -> comp2(x11,x12)
      app(comp0(),x11) -> comp1(x11)
      app(twice0(),x15) -> twice1(x15)
     Size-Change Termination Processor:
      DPs:
       
      TRS:
       map2(f,nil0()) -> nil0()
       map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
       comp3(f,g,x) -> app(f,app(g,x))
       twice1(f) -> comp2(f,f)
       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(comp2(x11,x12),x13) -> comp3(x11,x12,x13)
       app(comp1(x11),x12) -> comp2(x11,x12)
       app(comp0(),x11) -> comp1(x11)
       app(twice0(),x15) -> twice1(x15)
      The DP: comp{3,#}(f,g,x) -> app#(g,x) has the edges:
        1 >=  0
        2 >=  1
      The DP: app#(map1(x4),x5) -> map{2,#}(x4,x5) has the edges:
        0 >   0
        1 >=  1
      The DP: map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) has the edges:
        0 >=  0
        1 >   1
      The DP: map{2,#}(f,cons2(x,xs)) -> app#(f,x) has the edges:
        0 >=  0
        1 >   1
      The DP: app#(comp2(x11,x12),x13) -> comp{3,#}(x11,x12,x13) has the edges:
        0 >   1
        0 >   0
        1 >=  2
      The DP: comp{3,#}(f,g,x) -> app#(f,app(g,x)) has the edges:
        0 >=  0
      Qed