/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(fmap(),fnil()),x) -> nil()
 app(app(fmap(),app(app(fcons(),f),t)),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t),x))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   cons ==> cons0/0 cons1/1 cons2/2
   fcons ==> fcons0/0 fcons1/1 fcons2/2
   nil ==> nil0/0
   fnil ==> fnil0/0
   fmap ==> fmap0/0 fmap1/1 fmap2/2
   
  uncurry-rules:
   app(fmap1(x3),x4) -> fmap2(x3,x4)
   app(fmap0(),x3) -> fmap1(x3)
   app(fcons1(x8),x9) -> fcons2(x8,x9)
   app(fcons0(),x8) -> fcons1(x8)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
  eta-rules:
   
  problem:
   fmap2(fnil0(),x) -> nil0()
   fmap2(fcons2(f,t),x) -> cons2(app(f,x),fmap2(t,x))
   app(fmap1(x3),x4) -> fmap2(x3,x4)
   app(fmap0(),x3) -> fmap1(x3)
   app(fcons1(x8),x9) -> fcons2(x8,x9)
   app(fcons0(),x8) -> fcons1(x8)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
  DP Processor:
   DPs:
    fmap{2,#}(fcons2(f,t),x) -> fmap{2,#}(t,x)
    fmap{2,#}(fcons2(f,t),x) -> app#(f,x)
    app#(fmap1(x3),x4) -> fmap{2,#}(x3,x4)
   TRS:
    fmap2(fnil0(),x) -> nil0()
    fmap2(fcons2(f,t),x) -> cons2(app(f,x),fmap2(t,x))
    app(fmap1(x3),x4) -> fmap2(x3,x4)
    app(fmap0(),x3) -> fmap1(x3)
    app(fcons1(x8),x9) -> fcons2(x8,x9)
    app(fcons0(),x8) -> fcons1(x8)
    app(cons1(x11),x12) -> cons2(x11,x12)
    app(cons0(),x11) -> cons1(x11)
   TDG Processor:
    DPs:
     fmap{2,#}(fcons2(f,t),x) -> fmap{2,#}(t,x)
     fmap{2,#}(fcons2(f,t),x) -> app#(f,x)
     app#(fmap1(x3),x4) -> fmap{2,#}(x3,x4)
    TRS:
     fmap2(fnil0(),x) -> nil0()
     fmap2(fcons2(f,t),x) -> cons2(app(f,x),fmap2(t,x))
     app(fmap1(x3),x4) -> fmap2(x3,x4)
     app(fmap0(),x3) -> fmap1(x3)
     app(fcons1(x8),x9) -> fcons2(x8,x9)
     app(fcons0(),x8) -> fcons1(x8)
     app(cons1(x11),x12) -> cons2(x11,x12)
     app(cons0(),x11) -> cons1(x11)
    graph:
     app#(fmap1(x3),x4) -> fmap{2,#}(x3,x4) ->
     fmap{2,#}(fcons2(f,t),x) -> app#(f,x)
     app#(fmap1(x3),x4) -> fmap{2,#}(x3,x4) ->
     fmap{2,#}(fcons2(f,t),x) -> fmap{2,#}(t,x)
     fmap{2,#}(fcons2(f,t),x) -> app#(f,x) ->
     app#(fmap1(x3),x4) -> fmap{2,#}(x3,x4)
     fmap{2,#}(fcons2(f,t),x) -> fmap{2,#}(t,x) ->
     fmap{2,#}(fcons2(f,t),x) -> app#(f,x)
     fmap{2,#}(fcons2(f,t),x) -> fmap{2,#}(t,x) -> fmap{2,#}(fcons2(f,t),x) -> fmap{2,#}(t,x)
    Subterm Criterion Processor:
     simple projection:
      pi(fmap{2,#}) = 0
      pi(app#) = 0
     problem:
      DPs:
       
      TRS:
       fmap2(fnil0(),x) -> nil0()
       fmap2(fcons2(f,t),x) -> cons2(app(f,x),fmap2(t,x))
       app(fmap1(x3),x4) -> fmap2(x3,x4)
       app(fmap0(),x3) -> fmap1(x3)
       app(fcons1(x8),x9) -> fcons2(x8,x9)
       app(fcons0(),x8) -> fcons1(x8)
       app(cons1(x11),x12) -> cons2(x11,x12)
       app(cons0(),x11) -> cons1(x11)
     Qed