/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(mapt(),f),app(leaf(),x)) -> app(leaf(),app(f,x))
 app(app(mapt(),f),app(node(),xs)) -> app(node(),app(app(maptlist(),f),xs))
 app(app(maptlist(),f),nil()) -> nil()
 app(app(maptlist(),f),app(app(cons(),x),xs)) ->
 app(app(cons(),app(app(mapt(),f),x)),app(app(maptlist(),f),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   maptlist ==> maptlist0/0 maptlist1/1 maptlist2/2
   node ==> node0/0 node1/1
   leaf ==> leaf0/0 leaf1/1
   mapt ==> mapt0/0 mapt1/1 mapt2/2
   
  uncurry-rules:
   app(mapt1(x3),x4) -> mapt2(x3,x4)
   app(mapt0(),x3) -> mapt1(x3)
   app(leaf0(),x6) -> leaf1(x6)
   app(node0(),x8) -> node1(x8)
   app(maptlist1(x10),x11) -> maptlist2(x10,x11)
   app(maptlist0(),x10) -> maptlist1(x10)
   app(cons1(x14),x15) -> cons2(x14,x15)
   app(cons0(),x14) -> cons1(x14)
  eta-rules:
   
  problem:
   mapt2(f,leaf1(x)) -> leaf1(app(f,x))
   mapt2(f,node1(xs)) -> node1(maptlist2(f,xs))
   maptlist2(f,nil0()) -> nil0()
   maptlist2(f,cons2(x,xs)) -> cons2(mapt2(f,x),maptlist2(f,xs))
   app(mapt1(x3),x4) -> mapt2(x3,x4)
   app(mapt0(),x3) -> mapt1(x3)
   app(leaf0(),x6) -> leaf1(x6)
   app(node0(),x8) -> node1(x8)
   app(maptlist1(x10),x11) -> maptlist2(x10,x11)
   app(maptlist0(),x10) -> maptlist1(x10)
   app(cons1(x14),x15) -> cons2(x14,x15)
   app(cons0(),x14) -> cons1(x14)
  DP Processor:
   DPs:
    mapt{2,#}(f,leaf1(x)) -> app#(f,x)
    mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs)
    maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
    maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
    app#(mapt1(x3),x4) -> mapt{2,#}(x3,x4)
    app#(maptlist1(x10),x11) -> maptlist{2,#}(x10,x11)
   TRS:
    mapt2(f,leaf1(x)) -> leaf1(app(f,x))
    mapt2(f,node1(xs)) -> node1(maptlist2(f,xs))
    maptlist2(f,nil0()) -> nil0()
    maptlist2(f,cons2(x,xs)) -> cons2(mapt2(f,x),maptlist2(f,xs))
    app(mapt1(x3),x4) -> mapt2(x3,x4)
    app(mapt0(),x3) -> mapt1(x3)
    app(leaf0(),x6) -> leaf1(x6)
    app(node0(),x8) -> node1(x8)
    app(maptlist1(x10),x11) -> maptlist2(x10,x11)
    app(maptlist0(),x10) -> maptlist1(x10)
    app(cons1(x14),x15) -> cons2(x14,x15)
    app(cons0(),x14) -> cons1(x14)
   TDG Processor:
    DPs:
     mapt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs)
     maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
     maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
     app#(mapt1(x3),x4) -> mapt{2,#}(x3,x4)
     app#(maptlist1(x10),x11) -> maptlist{2,#}(x10,x11)
    TRS:
     mapt2(f,leaf1(x)) -> leaf1(app(f,x))
     mapt2(f,node1(xs)) -> node1(maptlist2(f,xs))
     maptlist2(f,nil0()) -> nil0()
     maptlist2(f,cons2(x,xs)) -> cons2(mapt2(f,x),maptlist2(f,xs))
     app(mapt1(x3),x4) -> mapt2(x3,x4)
     app(mapt0(),x3) -> mapt1(x3)
     app(leaf0(),x6) -> leaf1(x6)
     app(node0(),x8) -> node1(x8)
     app(maptlist1(x10),x11) -> maptlist2(x10,x11)
     app(maptlist0(),x10) -> maptlist1(x10)
     app(cons1(x14),x15) -> cons2(x14,x15)
     app(cons0(),x14) -> cons1(x14)
    graph:
     maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs) ->
     maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
     maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs) ->
     maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
     maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x) ->
     mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs)
     maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x) ->
     mapt{2,#}(f,leaf1(x)) -> app#(f,x)
     app#(maptlist1(x10),x11) -> maptlist{2,#}(x10,x11) ->
     maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
     app#(maptlist1(x10),x11) -> maptlist{2,#}(x10,x11) ->
     maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
     app#(mapt1(x3),x4) -> mapt{2,#}(x3,x4) ->
     mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs)
     app#(mapt1(x3),x4) -> mapt{2,#}(x3,x4) ->
     mapt{2,#}(f,leaf1(x)) -> app#(f,x)
     mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs) ->
     maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
     mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs) ->
     maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
     mapt{2,#}(f,leaf1(x)) -> app#(f,x) ->
     app#(maptlist1(x10),x11) -> maptlist{2,#}(x10,x11)
     mapt{2,#}(f,leaf1(x)) -> app#(f,x) -> app#(mapt1(x3),x4) -> mapt{2,#}(x3,x4)
    Subterm Criterion Processor:
     simple projection:
      pi(mapt{2,#}) = 0
      pi(app#) = 0
      pi(maptlist{2,#}) = 0
     problem:
      DPs:
       mapt{2,#}(f,leaf1(x)) -> app#(f,x)
       mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs)
       maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
       maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
      TRS:
       mapt2(f,leaf1(x)) -> leaf1(app(f,x))
       mapt2(f,node1(xs)) -> node1(maptlist2(f,xs))
       maptlist2(f,nil0()) -> nil0()
       maptlist2(f,cons2(x,xs)) -> cons2(mapt2(f,x),maptlist2(f,xs))
       app(mapt1(x3),x4) -> mapt2(x3,x4)
       app(mapt0(),x3) -> mapt1(x3)
       app(leaf0(),x6) -> leaf1(x6)
       app(node0(),x8) -> node1(x8)
       app(maptlist1(x10),x11) -> maptlist2(x10,x11)
       app(maptlist0(),x10) -> maptlist1(x10)
       app(cons1(x14),x15) -> cons2(x14,x15)
       app(cons0(),x14) -> cons1(x14)
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 12/16
      DPs:
       maptlist{2,#}(f,cons2(x,xs)) -> maptlist{2,#}(f,xs)
       maptlist{2,#}(f,cons2(x,xs)) -> mapt{2,#}(f,x)
       mapt{2,#}(f,node1(xs)) -> maptlist{2,#}(f,xs)
      TRS:
       mapt2(f,leaf1(x)) -> leaf1(app(f,x))
       mapt2(f,node1(xs)) -> node1(maptlist2(f,xs))
       maptlist2(f,nil0()) -> nil0()
       maptlist2(f,cons2(x,xs)) -> cons2(mapt2(f,x),maptlist2(f,xs))
       app(mapt1(x3),x4) -> mapt2(x3,x4)
       app(mapt0(),x3) -> mapt1(x3)
       app(leaf0(),x6) -> leaf1(x6)
       app(node0(),x8) -> node1(x8)
       app(maptlist1(x10),x11) -> maptlist2(x10,x11)
       app(maptlist0(),x10) -> maptlist1(x10)
       app(cons1(x14),x15) -> cons2(x14,x15)
       app(cons0(),x14) -> cons1(x14)
      Subterm Criterion Processor:
       simple projection:
        pi(mapt{2,#}) = 1
        pi(maptlist{2,#}) = 1
       problem:
        DPs:
         
        TRS:
         mapt2(f,leaf1(x)) -> leaf1(app(f,x))
         mapt2(f,node1(xs)) -> node1(maptlist2(f,xs))
         maptlist2(f,nil0()) -> nil0()
         maptlist2(f,cons2(x,xs)) -> cons2(mapt2(f,x),maptlist2(f,xs))
         app(mapt1(x3),x4) -> mapt2(x3,x4)
         app(mapt0(),x3) -> mapt1(x3)
         app(leaf0(),x6) -> leaf1(x6)
         app(node0(),x8) -> node1(x8)
         app(maptlist1(x10),x11) -> maptlist2(x10,x11)
         app(maptlist0(),x10) -> maptlist1(x10)
         app(cons1(x14),x15) -> cons2(x14,x15)
         app(cons0(),x14) -> cons1(x14)
       Qed