/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:
 f(X) -> cons(X,n__f(n__g(X)))
 g(0()) -> s(0())
 g(s(X)) -> s(s(g(X)))
 sel(0(),cons(X,Y)) -> X
 sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
 f(X) -> n__f(X)
 g(X) -> n__g(X)
 activate(n__f(X)) -> f(activate(X))
 activate(n__g(X)) -> g(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   g#(s(X)) -> g#(X)
   sel#(s(X),cons(Y,Z)) -> activate#(Z)
   sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
   activate#(n__f(X)) -> activate#(X)
   activate#(n__f(X)) -> f#(activate(X))
   activate#(n__g(X)) -> activate#(X)
   activate#(n__g(X)) -> g#(activate(X))
  TRS:
   f(X) -> cons(X,n__f(n__g(X)))
   g(0()) -> s(0())
   g(s(X)) -> s(s(g(X)))
   sel(0(),cons(X,Y)) -> X
   sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
   f(X) -> n__f(X)
   g(X) -> n__g(X)
   activate(n__f(X)) -> f(activate(X))
   activate(n__g(X)) -> g(activate(X))
   activate(X) -> X
  TDG Processor:
   DPs:
    g#(s(X)) -> g#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z)
    sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
    activate#(n__f(X)) -> activate#(X)
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__g(X)) -> activate#(X)
    activate#(n__g(X)) -> g#(activate(X))
   TRS:
    f(X) -> cons(X,n__f(n__g(X)))
    g(0()) -> s(0())
    g(s(X)) -> s(s(g(X)))
    sel(0(),cons(X,Y)) -> X
    sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
    f(X) -> n__f(X)
    g(X) -> n__g(X)
    activate(n__f(X)) -> f(activate(X))
    activate(n__g(X)) -> g(activate(X))
    activate(X) -> X
   graph:
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__g(X)) -> g#(activate(X))
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__g(X)) -> activate#(X)
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__f(X)) -> activate#(X) ->
    activate#(n__f(X)) -> activate#(X)
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__g(X)) -> g#(activate(X))
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__g(X)) -> activate#(X)
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__f(X)) -> f#(activate(X))
    activate#(n__g(X)) -> activate#(X) ->
    activate#(n__f(X)) -> activate#(X)
    activate#(n__g(X)) -> g#(activate(X)) -> g#(s(X)) -> g#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__g(X)) -> g#(activate(X))
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__g(X)) -> activate#(X)
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__f(X)) -> f#(activate(X))
    sel#(s(X),cons(Y,Z)) -> activate#(Z) ->
    activate#(n__f(X)) -> activate#(X)
    sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) ->
    sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
    sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) ->
    sel#(s(X),cons(Y,Z)) -> activate#(Z)
    g#(s(X)) -> g#(X) -> g#(s(X)) -> g#(X)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 16/49
    DPs:
     sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z))
    TRS:
     f(X) -> cons(X,n__f(n__g(X)))
     g(0()) -> s(0())
     g(s(X)) -> s(s(g(X)))
     sel(0(),cons(X,Y)) -> X
     sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
     f(X) -> n__f(X)
     g(X) -> n__g(X)
     activate(n__f(X)) -> f(activate(X))
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(sel#) = 0
     problem:
      DPs:
       
      TRS:
       f(X) -> cons(X,n__f(n__g(X)))
       g(0()) -> s(0())
       g(s(X)) -> s(s(g(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
       f(X) -> n__f(X)
       g(X) -> n__g(X)
       activate(n__f(X)) -> f(activate(X))
       activate(n__g(X)) -> g(activate(X))
       activate(X) -> X
     Qed
    
    DPs:
     activate#(n__f(X)) -> activate#(X)
     activate#(n__g(X)) -> activate#(X)
    TRS:
     f(X) -> cons(X,n__f(n__g(X)))
     g(0()) -> s(0())
     g(s(X)) -> s(s(g(X)))
     sel(0(),cons(X,Y)) -> X
     sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
     f(X) -> n__f(X)
     g(X) -> n__g(X)
     activate(n__f(X)) -> f(activate(X))
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(activate#) = 0
     problem:
      DPs:
       
      TRS:
       f(X) -> cons(X,n__f(n__g(X)))
       g(0()) -> s(0())
       g(s(X)) -> s(s(g(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
       f(X) -> n__f(X)
       g(X) -> n__g(X)
       activate(n__f(X)) -> f(activate(X))
       activate(n__g(X)) -> g(activate(X))
       activate(X) -> X
     Qed
    
    DPs:
     g#(s(X)) -> g#(X)
    TRS:
     f(X) -> cons(X,n__f(n__g(X)))
     g(0()) -> s(0())
     g(s(X)) -> s(s(g(X)))
     sel(0(),cons(X,Y)) -> X
     sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
     f(X) -> n__f(X)
     g(X) -> n__g(X)
     activate(n__f(X)) -> f(activate(X))
     activate(n__g(X)) -> g(activate(X))
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       f(X) -> cons(X,n__f(n__g(X)))
       g(0()) -> s(0())
       g(s(X)) -> s(s(g(X)))
       sel(0(),cons(X,Y)) -> X
       sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
       f(X) -> n__f(X)
       g(X) -> n__g(X)
       activate(n__f(X)) -> f(activate(X))
       activate(n__g(X)) -> g(activate(X))
       activate(X) -> X
     Qed