/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()),ys) -> ys
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))
 app(app(flatwith(),f),app(leaf(),x)) -> app(app(cons(),app(f,x)),nil())
 app(app(flatwith(),f),app(node(),xs)) -> app(app(flatwithsub(),f),xs)
 app(app(flatwithsub(),f),nil()) -> nil()
 app(app(flatwithsub(),f),app(app(cons(),x),xs)) ->
 app(app(append(),app(app(flatwith(),f),x)),app(app(flatwithsub(),f),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   flatwithsub ==> flatwithsub0/0 flatwithsub1/1 flatwithsub2/2
   node ==> node0/0 node1/1
   leaf ==> leaf0/0 leaf1/1
   flatwith ==> flatwith0/0 flatwith1/1 flatwith2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   append ==> append0/0 append1/1 append2/2
   
  uncurry-rules:
   app(append1(x4),x5) -> append2(x4,x5)
   app(append0(),x4) -> append1(x4)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(flatwith1(x11),x12) -> flatwith2(x11,x12)
   app(flatwith0(),x11) -> flatwith1(x11)
   app(leaf0(),x14) -> leaf1(x14)
   app(node0(),x16) -> node1(x16)
   app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
   app(flatwithsub0(),x18) -> flatwithsub1(x18)
  eta-rules:
   
  problem:
   append2(nil0(),ys) -> ys
   append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
   flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
   flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
   flatwithsub2(f,nil0()) -> nil0()
   flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
   app(append1(x4),x5) -> append2(x4,x5)
   app(append0(),x4) -> append1(x4)
   app(cons1(x8),x9) -> cons2(x8,x9)
   app(cons0(),x8) -> cons1(x8)
   app(flatwith1(x11),x12) -> flatwith2(x11,x12)
   app(flatwith0(),x11) -> flatwith1(x11)
   app(leaf0(),x14) -> leaf1(x14)
   app(node0(),x16) -> node1(x16)
   app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
   app(flatwithsub0(),x18) -> flatwithsub1(x18)
  DP Processor:
   DPs:
    append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
    flatwith{2,#}(f,leaf1(x)) -> app#(f,x)
    flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
    flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
    flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
    flatwithsub{2,#}(f,cons2(x,xs)) -> append{2,#}(flatwith2(f,x),flatwithsub2(f,xs))
    app#(append1(x4),x5) -> append{2,#}(x4,x5)
    app#(flatwith1(x11),x12) -> flatwith{2,#}(x11,x12)
    app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19)
   TRS:
    append2(nil0(),ys) -> ys
    append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
    flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
    flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
    flatwithsub2(f,nil0()) -> nil0()
    flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
    app(append1(x4),x5) -> append2(x4,x5)
    app(append0(),x4) -> append1(x4)
    app(cons1(x8),x9) -> cons2(x8,x9)
    app(cons0(),x8) -> cons1(x8)
    app(flatwith1(x11),x12) -> flatwith2(x11,x12)
    app(flatwith0(),x11) -> flatwith1(x11)
    app(leaf0(),x14) -> leaf1(x14)
    app(node0(),x16) -> node1(x16)
    app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
    app(flatwithsub0(),x18) -> flatwithsub1(x18)
   TDG Processor:
    DPs:
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     flatwith{2,#}(f,leaf1(x)) -> app#(f,x)
     flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
     flatwithsub{2,#}(f,cons2(x,xs)) -> append{2,#}(flatwith2(f,x),flatwithsub2(f,xs))
     app#(append1(x4),x5) -> append{2,#}(x4,x5)
     app#(flatwith1(x11),x12) -> flatwith{2,#}(x11,x12)
     app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19)
    TRS:
     append2(nil0(),ys) -> ys
     append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
     flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
     flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
     flatwithsub2(f,nil0()) -> nil0()
     flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
     app(append1(x4),x5) -> append2(x4,x5)
     app(append0(),x4) -> append1(x4)
     app(cons1(x8),x9) -> cons2(x8,x9)
     app(cons0(),x8) -> cons1(x8)
     app(flatwith1(x11),x12) -> flatwith2(x11,x12)
     app(flatwith0(),x11) -> flatwith1(x11)
     app(leaf0(),x14) -> leaf1(x14)
     app(node0(),x16) -> node1(x16)
     app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
     app(flatwithsub0(),x18) -> flatwithsub1(x18)
    graph:
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> append{2,#}(flatwith2(f,x),flatwithsub2(f,xs))
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x) ->
     flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x) ->
     flatwith{2,#}(f,leaf1(x)) -> app#(f,x)
     flatwithsub{2,#}(f,cons2(x,xs)) -> append{2,#}(flatwith2(f,x),flatwithsub2(f,xs)) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> append{2,#}(flatwith2(f,x),flatwithsub2(f,xs))
     app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
     app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
     app#(flatwith1(x11),x12) -> flatwith{2,#}(x11,x12) ->
     flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
     app#(flatwith1(x11),x12) -> flatwith{2,#}(x11,x12) ->
     flatwith{2,#}(f,leaf1(x)) -> app#(f,x)
     app#(append1(x4),x5) -> append{2,#}(x4,x5) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> append{2,#}(flatwith2(f,x),flatwithsub2(f,xs))
     flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
     flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs) ->
     flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
     flatwith{2,#}(f,leaf1(x)) -> app#(f,x) ->
     app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19)
     flatwith{2,#}(f,leaf1(x)) -> app#(f,x) ->
     app#(flatwith1(x11),x12) -> flatwith{2,#}(x11,x12)
     flatwith{2,#}(f,leaf1(x)) -> app#(f,x) ->
     app#(append1(x4),x5) -> append{2,#}(x4,x5)
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
    SCC Processor:
     #sccs: 2
     #rules: 7
     #arcs: 19/81
     DPs:
      flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
      flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
      flatwith{2,#}(f,leaf1(x)) -> app#(f,x)
      app#(flatwith1(x11),x12) -> flatwith{2,#}(x11,x12)
      flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
      app#(flatwithsub1(x18),x19) -> flatwithsub{2,#}(x18,x19)
     TRS:
      append2(nil0(),ys) -> ys
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
      flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
      flatwithsub2(f,nil0()) -> nil0()
      flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
      app(append1(x4),x5) -> append2(x4,x5)
      app(append0(),x4) -> append1(x4)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(flatwith1(x11),x12) -> flatwith2(x11,x12)
      app(flatwith0(),x11) -> flatwith1(x11)
      app(leaf0(),x14) -> leaf1(x14)
      app(node0(),x16) -> node1(x16)
      app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
      app(flatwithsub0(),x18) -> flatwithsub1(x18)
     Subterm Criterion Processor:
      simple projection:
       pi(flatwith{2,#}) = 0
       pi(app#) = 0
       pi(flatwithsub{2,#}) = 0
      problem:
       DPs:
        flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
        flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
        flatwith{2,#}(f,leaf1(x)) -> app#(f,x)
        flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
       TRS:
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
        flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
        flatwithsub2(f,nil0()) -> nil0()
        flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
        app(append1(x4),x5) -> append2(x4,x5)
        app(append0(),x4) -> append1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(flatwith1(x11),x12) -> flatwith2(x11,x12)
        app(flatwith0(),x11) -> flatwith1(x11)
        app(leaf0(),x14) -> leaf1(x14)
        app(node0(),x16) -> node1(x16)
        app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
        app(flatwithsub0(),x18) -> flatwithsub1(x18)
      SCC Processor:
       #sccs: 1
       #rules: 3
       #arcs: 12/16
       DPs:
        flatwithsub{2,#}(f,cons2(x,xs)) -> flatwithsub{2,#}(f,xs)
        flatwithsub{2,#}(f,cons2(x,xs)) -> flatwith{2,#}(f,x)
        flatwith{2,#}(f,node1(xs)) -> flatwithsub{2,#}(f,xs)
       TRS:
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
        flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
        flatwithsub2(f,nil0()) -> nil0()
        flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
        app(append1(x4),x5) -> append2(x4,x5)
        app(append0(),x4) -> append1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(flatwith1(x11),x12) -> flatwith2(x11,x12)
        app(flatwith0(),x11) -> flatwith1(x11)
        app(leaf0(),x14) -> leaf1(x14)
        app(node0(),x16) -> node1(x16)
        app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
        app(flatwithsub0(),x18) -> flatwithsub1(x18)
       Subterm Criterion Processor:
        simple projection:
         pi(flatwith{2,#}) = 1
         pi(flatwithsub{2,#}) = 1
        problem:
         DPs:
          
         TRS:
          append2(nil0(),ys) -> ys
          append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
          flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
          flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
          flatwithsub2(f,nil0()) -> nil0()
          flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
          app(append1(x4),x5) -> append2(x4,x5)
          app(append0(),x4) -> append1(x4)
          app(cons1(x8),x9) -> cons2(x8,x9)
          app(cons0(),x8) -> cons1(x8)
          app(flatwith1(x11),x12) -> flatwith2(x11,x12)
          app(flatwith0(),x11) -> flatwith1(x11)
          app(leaf0(),x14) -> leaf1(x14)
          app(node0(),x16) -> node1(x16)
          app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
          app(flatwithsub0(),x18) -> flatwithsub1(x18)
        Qed
     
     DPs:
      append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     TRS:
      append2(nil0(),ys) -> ys
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
      flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
      flatwithsub2(f,nil0()) -> nil0()
      flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
      app(append1(x4),x5) -> append2(x4,x5)
      app(append0(),x4) -> append1(x4)
      app(cons1(x8),x9) -> cons2(x8,x9)
      app(cons0(),x8) -> cons1(x8)
      app(flatwith1(x11),x12) -> flatwith2(x11,x12)
      app(flatwith0(),x11) -> flatwith1(x11)
      app(leaf0(),x14) -> leaf1(x14)
      app(node0(),x16) -> node1(x16)
      app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
      app(flatwithsub0(),x18) -> flatwithsub1(x18)
     Subterm Criterion Processor:
      simple projection:
       pi(append{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        append2(nil0(),ys) -> ys
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        flatwith2(f,leaf1(x)) -> cons2(app(f,x),nil0())
        flatwith2(f,node1(xs)) -> flatwithsub2(f,xs)
        flatwithsub2(f,nil0()) -> nil0()
        flatwithsub2(f,cons2(x,xs)) -> append2(flatwith2(f,x),flatwithsub2(f,xs))
        app(append1(x4),x5) -> append2(x4,x5)
        app(append0(),x4) -> append1(x4)
        app(cons1(x8),x9) -> cons2(x8,x9)
        app(cons0(),x8) -> cons1(x8)
        app(flatwith1(x11),x12) -> flatwith2(x11,x12)
        app(flatwith0(),x11) -> flatwith1(x11)
        app(leaf0(),x14) -> leaf1(x14)
        app(node0(),x16) -> node1(x16)
        app(flatwithsub1(x18),x19) -> flatwithsub2(x18,x19)
        app(flatwithsub0(),x18) -> flatwithsub1(x18)
      Qed