/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(append(),nil()),l) -> l
 app(app(append(),app(app(cons(),h),t)),l) -> app(app(cons(),h),app(app(append(),t),l))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
 app(app(append(),app(app(append(),l1),l2)),l3) -> app(app(append(),l1),app(app(append(),l2),l3))
 app(app(map(),f),app(app(append(),l1),l2)) ->
 app(app(append(),app(app(map(),f),l1)),app(app(map(),f),l2))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   map ==> map0/0 map1/1 map2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   append ==> append0/0 append1/1 append2/2
   
  uncurry-rules:
   app(append1(x7),x8) -> append2(x7,x8)
   app(append0(),x7) -> append1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(map1(x14),x15) -> map2(x14,x15)
   app(map0(),x14) -> map1(x14)
  eta-rules:
   
  problem:
   append2(nil0(),l) -> l
   append2(cons2(h,t),l) -> cons2(h,append2(t,l))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
   append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
   map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
   app(append1(x7),x8) -> append2(x7,x8)
   app(append0(),x7) -> append1(x7)
   app(cons1(x11),x12) -> cons2(x11,x12)
   app(cons0(),x11) -> cons1(x11)
   app(map1(x14),x15) -> map2(x14,x15)
   app(map0(),x14) -> map1(x14)
  DP Processor:
   DPs:
    append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
    map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
    map{2,#}(f,cons2(h,t)) -> app#(f,h)
    append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
    append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
    map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
    map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
    map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2))
    app#(append1(x7),x8) -> append{2,#}(x7,x8)
    app#(map1(x14),x15) -> map{2,#}(x14,x15)
   TRS:
    append2(nil0(),l) -> l
    append2(cons2(h,t),l) -> cons2(h,append2(t,l))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
    append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
    map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
    app(append1(x7),x8) -> append2(x7,x8)
    app(append0(),x7) -> append1(x7)
    app(cons1(x11),x12) -> cons2(x11,x12)
    app(cons0(),x11) -> cons1(x11)
    app(map1(x14),x15) -> map2(x14,x15)
    app(map0(),x14) -> map1(x14)
   TDG Processor:
    DPs:
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2))
     app#(append1(x7),x8) -> append{2,#}(x7,x8)
     app#(map1(x14),x15) -> map{2,#}(x14,x15)
    TRS:
     append2(nil0(),l) -> l
     append2(cons2(h,t),l) -> cons2(h,append2(t,l))
     map2(f,nil0()) -> nil0()
     map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
     append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
     map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
     app(append1(x7),x8) -> append2(x7,x8)
     app(append0(),x7) -> append1(x7)
     app(cons1(x11),x12) -> cons2(x11,x12)
     app(cons0(),x11) -> cons1(x11)
     app(map1(x14),x15) -> map2(x14,x15)
     app(map0(),x14) -> map1(x14)
    graph:
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2))
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     app#(map1(x14),x15) -> map{2,#}(x14,x15) ->
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     app#(append1(x7),x8) -> append{2,#}(x7,x8) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     app#(append1(x7),x8) -> append{2,#}(x7,x8) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
     app#(append1(x7),x8) -> append{2,#}(x7,x8) ->
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
     map{2,#}(f,cons2(h,t)) -> app#(f,h) ->
     app#(map1(x14),x15) -> map{2,#}(x14,x15)
     map{2,#}(f,cons2(h,t)) -> app#(f,h) ->
     app#(append1(x7),x8) -> append{2,#}(x7,x8)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2))
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t) ->
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2) ->
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2))
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2) ->
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2) ->
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1) ->
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2))
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1) ->
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1) ->
     map{2,#}(f,cons2(h,t)) -> app#(f,h)
     map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1) ->
     map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2)) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2)) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
     map{2,#}(f,append2(l1,l2)) -> append{2,#}(map2(f,l1),map2(f,l2)) ->
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l) ->
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3) ->
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3)) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3)) ->
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
     append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3)) ->
     append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
    SCC Processor:
     #sccs: 2
     #rules: 8
     #arcs: 37/100
     DPs:
      app#(map1(x14),x15) -> map{2,#}(x14,x15)
      map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
      map{2,#}(f,cons2(h,t)) -> app#(f,h)
      map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
      map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
     TRS:
      append2(nil0(),l) -> l
      append2(cons2(h,t),l) -> cons2(h,append2(t,l))
      map2(f,nil0()) -> nil0()
      map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
      append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
      map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
      app(append1(x7),x8) -> append2(x7,x8)
      app(append0(),x7) -> append1(x7)
      app(cons1(x11),x12) -> cons2(x11,x12)
      app(cons0(),x11) -> cons1(x11)
      app(map1(x14),x15) -> map2(x14,x15)
      app(map0(),x14) -> map1(x14)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 0
       pi(app#) = 0
      problem:
       DPs:
        map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
        map{2,#}(f,cons2(h,t)) -> app#(f,h)
        map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
        map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
       TRS:
        append2(nil0(),l) -> l
        append2(cons2(h,t),l) -> cons2(h,append2(t,l))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
        append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
        map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
        app(append1(x7),x8) -> append2(x7,x8)
        app(append0(),x7) -> append1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(map1(x14),x15) -> map2(x14,x15)
        app(map0(),x14) -> map1(x14)
      SCC Processor:
       #sccs: 1
       #rules: 3
       #arcs: 17/16
       DPs:
        map{2,#}(f,cons2(h,t)) -> map{2,#}(f,t)
        map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l2)
        map{2,#}(f,append2(l1,l2)) -> map{2,#}(f,l1)
       TRS:
        append2(nil0(),l) -> l
        append2(cons2(h,t),l) -> cons2(h,append2(t,l))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
        append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
        map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
        app(append1(x7),x8) -> append2(x7,x8)
        app(append0(),x7) -> append1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(map1(x14),x15) -> map2(x14,x15)
        app(map0(),x14) -> map1(x14)
       Subterm Criterion Processor:
        simple projection:
         pi(map{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          append2(nil0(),l) -> l
          append2(cons2(h,t),l) -> cons2(h,append2(t,l))
          map2(f,nil0()) -> nil0()
          map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
          append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
          map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
          app(append1(x7),x8) -> append2(x7,x8)
          app(append0(),x7) -> append1(x7)
          app(cons1(x11),x12) -> cons2(x11,x12)
          app(cons0(),x11) -> cons1(x11)
          app(map1(x14),x15) -> map2(x14,x15)
          app(map0(),x14) -> map1(x14)
        Qed
     
     DPs:
      append{2,#}(cons2(h,t),l) -> append{2,#}(t,l)
      append{2,#}(append2(l1,l2),l3) -> append{2,#}(l2,l3)
      append{2,#}(append2(l1,l2),l3) -> append{2,#}(l1,append2(l2,l3))
     TRS:
      append2(nil0(),l) -> l
      append2(cons2(h,t),l) -> cons2(h,append2(t,l))
      map2(f,nil0()) -> nil0()
      map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
      append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
      map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
      app(append1(x7),x8) -> append2(x7,x8)
      app(append0(),x7) -> append1(x7)
      app(cons1(x11),x12) -> cons2(x11,x12)
      app(cons0(),x11) -> cons1(x11)
      app(map1(x14),x15) -> map2(x14,x15)
      app(map0(),x14) -> map1(x14)
     Subterm Criterion Processor:
      simple projection:
       pi(append{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        append2(nil0(),l) -> l
        append2(cons2(h,t),l) -> cons2(h,append2(t,l))
        map2(f,nil0()) -> nil0()
        map2(f,cons2(h,t)) -> cons2(app(f,h),map2(f,t))
        append2(append2(l1,l2),l3) -> append2(l1,append2(l2,l3))
        map2(f,append2(l1,l2)) -> append2(map2(f,l1),map2(f,l2))
        app(append1(x7),x8) -> append2(x7,x8)
        app(append0(),x7) -> append1(x7)
        app(cons1(x11),x12) -> cons2(x11,x12)
        app(cons0(),x11) -> cons1(x11)
        app(map1(x14),x15) -> map2(x14,x15)
        app(map0(),x14) -> map1(x14)
      Qed