/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))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   
  uncurry-rules:
   app(map1(x3),x4) -> map2(x3,x4)
   app(map0(),x3) -> map1(x3)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   app(map1(x3),x4) -> map2(x3,x4)
   app(map0(),x3) -> map1(x3)
   app(cons1(x7),x8) -> cons2(x7,x8)
   app(cons0(),x7) -> cons1(x7)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    app#(map1(x3),x4) -> map{2,#}(x3,x4)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    app(map1(x3),x4) -> map2(x3,x4)
    app(map0(),x3) -> map1(x3)
    app(cons1(x7),x8) -> cons2(x7,x8)
    app(cons0(),x7) -> cons1(x7)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x3),x4) -> map{2,#}(x3,x4)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     app(map1(x3),x4) -> map2(x3,x4)
     app(map0(),x3) -> map1(x3)
     app(cons1(x7),x8) -> cons2(x7,x8)
     app(cons0(),x7) -> cons1(x7)
    graph:
     app#(map1(x3),x4) -> map{2,#}(x3,x4) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x3),x4) -> map{2,#}(x3,x4) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x3),x4) -> map{2,#}(x3,x4)
     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)
    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))
       app(map1(x3),x4) -> map2(x3,x4)
       app(map0(),x3) -> map1(x3)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons0(),x7) -> cons1(x7)
     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))
       app(map1(x3),x4) -> map2(x3,x4)
       app(map0(),x3) -> map1(x3)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons0(),x7) -> cons1(x7)
      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))
         app(map1(x3),x4) -> map2(x3,x4)
         app(map0(),x3) -> map1(x3)
         app(cons1(x7),x8) -> cons2(x7,x8)
         app(cons0(),x7) -> cons1(x7)
       Qed