/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))
 app(flatten(),app(app(node(),x),xs)) ->
 app(app(cons(),x),app(concat(),app(app(map(),flatten()),xs)))
 app(concat(),nil()) -> nil()
 app(concat(),app(app(cons(),x),xs)) -> app(app(append(),x),app(concat(),xs))
 app(app(append(),nil()),xs) -> xs
 app(app(append(),app(app(cons(),x),xs)),ys) -> app(app(cons(),x),app(app(append(),xs),ys))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   append ==> append0/0 append1/1 append2/2
   concat ==> concat0/0 concat1/1
   node ==> node0/0 node1/1 node2/2
   flatten ==> flatten0/0 flatten1/1
   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(flatten0(),x11) -> flatten1(x11)
   app(node1(x13),x14) -> node2(x13,x14)
   app(node0(),x13) -> node1(x13)
   app(concat0(),x16) -> concat1(x16)
   app(append1(x18),x19) -> append2(x18,x19)
   app(append0(),x18) -> append1(x18)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
   concat1(nil0()) -> nil0()
   concat1(cons2(x,xs)) -> append2(x,concat1(xs))
   append2(nil0(),xs) -> xs
   append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
   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(flatten0(),x11) -> flatten1(x11)
   app(node1(x13),x14) -> node2(x13,x14)
   app(node0(),x13) -> node1(x13)
   app(concat0(),x16) -> concat1(x16)
   app(append1(x18),x19) -> append2(x18,x19)
   app(append0(),x18) -> append1(x18)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten0(),xs)
    flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten0(),xs))
    concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
    concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
    append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
    app#(map1(x4),x5) -> map{2,#}(x4,x5)
    app#(flatten0(),x11) -> flatten{1,#}(x11)
    app#(concat0(),x16) -> concat{1,#}(x16)
    app#(append1(x18),x19) -> append{2,#}(x18,x19)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
    concat1(nil0()) -> nil0()
    concat1(cons2(x,xs)) -> append2(x,concat1(xs))
    append2(nil0(),xs) -> xs
    append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
    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(flatten0(),x11) -> flatten1(x11)
    app(node1(x13),x14) -> node2(x13,x14)
    app(node0(),x13) -> node1(x13)
    app(concat0(),x16) -> concat1(x16)
    app(append1(x18),x19) -> append2(x18,x19)
    app(append0(),x18) -> append1(x18)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten0(),xs)
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten0(),xs))
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     app#(map1(x4),x5) -> map{2,#}(x4,x5)
     app#(flatten0(),x11) -> flatten{1,#}(x11)
     app#(concat0(),x16) -> concat{1,#}(x16)
     app#(append1(x18),x19) -> append{2,#}(x18,x19)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
     concat1(nil0()) -> nil0()
     concat1(cons2(x,xs)) -> append2(x,concat1(xs))
     append2(nil0(),xs) -> xs
     append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
     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(flatten0(),x11) -> flatten1(x11)
     app(node1(x13),x14) -> node2(x13,x14)
     app(node0(),x13) -> node1(x13)
     app(concat0(),x16) -> concat1(x16)
     app(append1(x18),x19) -> append2(x18,x19)
     app(append0(),x18) -> append1(x18)
    graph:
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs)) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs) ->
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs) ->
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten0(),xs)) ->
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten0(),xs)) ->
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten0(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten0(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(append1(x18),x19) -> append{2,#}(x18,x19) ->
     append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     app#(concat0(),x16) -> concat{1,#}(x16) ->
     concat{1,#}(cons2(x,xs)) -> append{2,#}(x,concat1(xs))
     app#(concat0(),x16) -> concat{1,#}(x16) ->
     concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     app#(flatten0(),x11) -> flatten{1,#}(x11) ->
     flatten{1,#}(node2(x,xs)) -> concat{1,#}(map2(flatten0(),xs))
     app#(flatten0(),x11) -> flatten{1,#}(x11) ->
     flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten0(),xs)
     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#(append1(x18),x19) -> append{2,#}(x18,x19)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(concat0(),x16) -> concat{1,#}(x16)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(flatten0(),x11) -> flatten{1,#}(x11)
     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: 3
     #rules: 7
     #arcs: 21/121
     DPs:
      flatten{1,#}(node2(x,xs)) -> map{2,#}(flatten0(),xs)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x4),x5) -> map{2,#}(x4,x5)
      app#(flatten0(),x11) -> flatten{1,#}(x11)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
      concat1(nil0()) -> nil0()
      concat1(cons2(x,xs)) -> append2(x,concat1(xs))
      append2(nil0(),xs) -> xs
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      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(flatten0(),x11) -> flatten1(x11)
      app(node1(x13),x14) -> node2(x13,x14)
      app(node0(),x13) -> node1(x13)
      app(concat0(),x16) -> concat1(x16)
      app(append1(x18),x19) -> append2(x18,x19)
      app(append0(),x18) -> append1(x18)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
       pi(flatten{1,#}) = 0
      problem:
       DPs:
        app#(map1(x4),x5) -> map{2,#}(x4,x5)
        app#(flatten0(),x11) -> flatten{1,#}(x11)
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
        concat1(nil0()) -> nil0()
        concat1(cons2(x,xs)) -> append2(x,concat1(xs))
        append2(nil0(),xs) -> xs
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        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(flatten0(),x11) -> flatten1(x11)
        app(node1(x13),x14) -> node2(x13,x14)
        app(node0(),x13) -> node1(x13)
        app(concat0(),x16) -> concat1(x16)
        app(append1(x18),x19) -> append2(x18,x19)
        app(append0(),x18) -> append1(x18)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 9/4
       
     
     DPs:
      concat{1,#}(cons2(x,xs)) -> concat{1,#}(xs)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
      concat1(nil0()) -> nil0()
      concat1(cons2(x,xs)) -> append2(x,concat1(xs))
      append2(nil0(),xs) -> xs
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      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(flatten0(),x11) -> flatten1(x11)
      app(node1(x13),x14) -> node2(x13,x14)
      app(node0(),x13) -> node1(x13)
      app(concat0(),x16) -> concat1(x16)
      app(append1(x18),x19) -> append2(x18,x19)
      app(append0(),x18) -> append1(x18)
     Subterm Criterion Processor:
      simple projection:
       pi(concat{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
        concat1(nil0()) -> nil0()
        concat1(cons2(x,xs)) -> append2(x,concat1(xs))
        append2(nil0(),xs) -> xs
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        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(flatten0(),x11) -> flatten1(x11)
        app(node1(x13),x14) -> node2(x13,x14)
        app(node0(),x13) -> node1(x13)
        app(concat0(),x16) -> concat1(x16)
        app(append1(x18),x19) -> append2(x18,x19)
        app(append0(),x18) -> append1(x18)
      Qed
     
     DPs:
      append{2,#}(cons2(x,xs),ys) -> append{2,#}(xs,ys)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
      concat1(nil0()) -> nil0()
      concat1(cons2(x,xs)) -> append2(x,concat1(xs))
      append2(nil0(),xs) -> xs
      append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
      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(flatten0(),x11) -> flatten1(x11)
      app(node1(x13),x14) -> node2(x13,x14)
      app(node0(),x13) -> node1(x13)
      app(concat0(),x16) -> concat1(x16)
      app(append1(x18),x19) -> append2(x18,x19)
      app(append0(),x18) -> append1(x18)
     Subterm Criterion Processor:
      simple projection:
       pi(append{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        flatten1(node2(x,xs)) -> cons2(x,concat1(map2(flatten0(),xs)))
        concat1(nil0()) -> nil0()
        concat1(cons2(x,xs)) -> append2(x,concat1(xs))
        append2(nil0(),xs) -> xs
        append2(cons2(x,xs),ys) -> cons2(x,append2(xs,ys))
        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(flatten0(),x11) -> flatten1(x11)
        app(node1(x13),x14) -> node2(x13,x14)
        app(node0(),x13) -> node1(x13)
        app(concat0(),x16) -> concat1(x16)
        app(append1(x18),x19) -> append2(x18,x19)
        app(append0(),x18) -> append1(x18)
      Qed