/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:
 a__from(X) -> cons(mark(X),from(s(X)))
 a__length(nil()) -> 0()
 a__length(cons(X,Y)) -> s(a__length1(Y))
 a__length1(X) -> a__length(X)
 mark(from(X)) -> a__from(mark(X))
 mark(length(X)) -> a__length(X)
 mark(length1(X)) -> a__length1(X)
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 mark(nil()) -> nil()
 mark(0()) -> 0()
 a__from(X) -> from(X)
 a__length(X) -> length(X)
 a__length1(X) -> length1(X)

Proof:
 DP Processor:
  DPs:
   a__from#(X) -> mark#(X)
   a__length#(cons(X,Y)) -> a__length1#(Y)
   a__length1#(X) -> a__length#(X)
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(length(X)) -> a__length#(X)
   mark#(length1(X)) -> a__length1#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__from(X) -> cons(mark(X),from(s(X)))
   a__length(nil()) -> 0()
   a__length(cons(X,Y)) -> s(a__length1(Y))
   a__length1(X) -> a__length(X)
   mark(from(X)) -> a__from(mark(X))
   mark(length(X)) -> a__length(X)
   mark(length1(X)) -> a__length1(X)
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   mark(nil()) -> nil()
   mark(0()) -> 0()
   a__from(X) -> from(X)
   a__length(X) -> length(X)
   a__length1(X) -> length1(X)
  TDG Processor:
   DPs:
    a__from#(X) -> mark#(X)
    a__length#(cons(X,Y)) -> a__length1#(Y)
    a__length1#(X) -> a__length#(X)
    mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X))
    mark#(length(X)) -> a__length#(X)
    mark#(length1(X)) -> a__length1#(X)
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__from(X) -> cons(mark(X),from(s(X)))
    a__length(nil()) -> 0()
    a__length(cons(X,Y)) -> s(a__length1(Y))
    a__length1(X) -> a__length(X)
    mark(from(X)) -> a__from(mark(X))
    mark(length(X)) -> a__length(X)
    mark(length1(X)) -> a__length1(X)
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    mark(0()) -> 0()
    a__from(X) -> from(X)
    a__length(X) -> length(X)
    a__length1(X) -> length1(X)
   graph:
    a__length1#(X) -> a__length#(X) ->
    a__length#(cons(X,Y)) -> a__length1#(Y)
    a__length#(cons(X,Y)) -> a__length1#(Y) ->
    a__length1#(X) -> a__length#(X)
    mark#(length1(X)) -> a__length1#(X) ->
    a__length1#(X) -> a__length#(X)
    mark#(length(X)) -> a__length#(X) ->
    a__length#(cons(X,Y)) -> a__length1#(Y)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length1(X)) -> a__length1#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    a__from#(X) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X)
   SCC Processor:
    #sccs: 2
    #rules: 7
    #arcs: 29/81
    DPs:
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> mark#(X)
     mark#(from(X)) -> a__from#(mark(X))
     a__from#(X) -> mark#(X)
     mark#(s(X)) -> mark#(X)
    TRS:
     a__from(X) -> cons(mark(X),from(s(X)))
     a__length(nil()) -> 0()
     a__length(cons(X,Y)) -> s(a__length1(Y))
     a__length1(X) -> a__length(X)
     mark(from(X)) -> a__from(mark(X))
     mark(length(X)) -> a__length(X)
     mark(length1(X)) -> a__length1(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__from(X) -> from(X)
     a__length(X) -> length(X)
     a__length1(X) -> length1(X)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a__from(X) -> cons(mark(X),from(s(X)))
      a__length(nil()) -> 0()
      a__length(cons(X,Y)) -> s(a__length1(Y))
      a__length1(X) -> a__length(X)
      mark(from(X)) -> a__from(mark(X))
      mark(length(X)) -> a__length(X)
      mark(length1(X)) -> a__length1(X)
      mark(cons(X1,X2)) -> cons(mark(X1),X2)
      mark(s(X)) -> s(mark(X))
      mark(nil()) -> nil()
      mark(0()) -> 0()
      a__from(X) -> from(X)
      a__length(X) -> length(X)
      a__length1(X) -> length1(X)
     interpretation:
      [mark#](x0) = 2x0,
      
      [a__from#](x0) = 5x0 + 0,
      
      [length1](x0) = x0 + 2,
      
      [length](x0) = x0,
      
      [a__length1](x0) = x0 + 2,
      
      [0] = 5,
      
      [a__length](x0) = x0,
      
      [nil] = 5,
      
      [cons](x0, x1) = 2x0 + x1 + 3,
      
      [from](x0) = 3x0 + 4,
      
      [s](x0) = x0 + 0,
      
      [mark](x0) = x0 + 1,
      
      [a__from](x0) = 3x0 + 4
     orientation:
      mark#(cons(X1,X2)) = 4X1 + 2X2 + 5 >= 2X1 = mark#(X1)
      
      mark#(from(X)) = 5X + 6 >= 2X = mark#(X)
      
      mark#(from(X)) = 5X + 6 >= 5X + 6 = a__from#(mark(X))
      
      a__from#(X) = 5X + 0 >= 2X = mark#(X)
      
      mark#(s(X)) = 2X + 2 >= 2X = mark#(X)
      
      a__from(X) = 3X + 4 >= 3X + 4 = cons(mark(X),from(s(X)))
      
      a__length(nil()) = 5 >= 5 = 0()
      
      a__length(cons(X,Y)) = 2X + Y + 3 >= Y + 2 = s(a__length1(Y))
      
      a__length1(X) = X + 2 >= X = a__length(X)
      
      mark(from(X)) = 3X + 4 >= 3X + 4 = a__from(mark(X))
      
      mark(length(X)) = X + 1 >= X = a__length(X)
      
      mark(length1(X)) = X + 2 >= X + 2 = a__length1(X)
      
      mark(cons(X1,X2)) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = cons(mark(X1),X2)
      
      mark(s(X)) = X + 1 >= X + 1 = s(mark(X))
      
      mark(nil()) = 5 >= 5 = nil()
      
      mark(0()) = 5 >= 5 = 0()
      
      a__from(X) = 3X + 4 >= 3X + 4 = from(X)
      
      a__length(X) = X >= X = length(X)
      
      a__length1(X) = X + 2 >= X + 2 = length1(X)
     problem:
      DPs:
       mark#(from(X)) -> a__from#(mark(X))
       mark#(s(X)) -> mark#(X)
      TRS:
       a__from(X) -> cons(mark(X),from(s(X)))
       a__length(nil()) -> 0()
       a__length(cons(X,Y)) -> s(a__length1(Y))
       a__length1(X) -> a__length(X)
       mark(from(X)) -> a__from(mark(X))
       mark(length(X)) -> a__length(X)
       mark(length1(X)) -> a__length1(X)
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       mark(nil()) -> nil()
       mark(0()) -> 0()
       a__from(X) -> from(X)
       a__length(X) -> length(X)
       a__length1(X) -> length1(X)
     Restore Modifier:
      DPs:
       mark#(from(X)) -> a__from#(mark(X))
       mark#(s(X)) -> mark#(X)
      TRS:
       a__from(X) -> cons(mark(X),from(s(X)))
       a__length(nil()) -> 0()
       a__length(cons(X,Y)) -> s(a__length1(Y))
       a__length1(X) -> a__length(X)
       mark(from(X)) -> a__from(mark(X))
       mark(length(X)) -> a__length(X)
       mark(length1(X)) -> a__length1(X)
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       mark(nil()) -> nil()
       mark(0()) -> 0()
       a__from(X) -> from(X)
       a__length(X) -> length(X)
       a__length1(X) -> length1(X)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 17/4
       DPs:
        mark#(s(X)) -> mark#(X)
       TRS:
        a__from(X) -> cons(mark(X),from(s(X)))
        a__length(nil()) -> 0()
        a__length(cons(X,Y)) -> s(a__length1(Y))
        a__length1(X) -> a__length(X)
        mark(from(X)) -> a__from(mark(X))
        mark(length(X)) -> a__length(X)
        mark(length1(X)) -> a__length1(X)
        mark(cons(X1,X2)) -> cons(mark(X1),X2)
        mark(s(X)) -> s(mark(X))
        mark(nil()) -> nil()
        mark(0()) -> 0()
        a__from(X) -> from(X)
        a__length(X) -> length(X)
        a__length1(X) -> length1(X)
       Size-Change Termination Processor:
        DPs:
         
        TRS:
         a__from(X) -> cons(mark(X),from(s(X)))
         a__length(nil()) -> 0()
         a__length(cons(X,Y)) -> s(a__length1(Y))
         a__length1(X) -> a__length(X)
         mark(from(X)) -> a__from(mark(X))
         mark(length(X)) -> a__length(X)
         mark(length1(X)) -> a__length1(X)
         mark(cons(X1,X2)) -> cons(mark(X1),X2)
         mark(s(X)) -> s(mark(X))
         mark(nil()) -> nil()
         mark(0()) -> 0()
         a__from(X) -> from(X)
         a__length(X) -> length(X)
         a__length1(X) -> length1(X)
        The DP: mark#(s(X)) -> mark#(X) has the edges:
          0 >   0
        Qed
    
    DPs:
     a__length1#(X) -> a__length#(X)
     a__length#(cons(X,Y)) -> a__length1#(Y)
    TRS:
     a__from(X) -> cons(mark(X),from(s(X)))
     a__length(nil()) -> 0()
     a__length(cons(X,Y)) -> s(a__length1(Y))
     a__length1(X) -> a__length(X)
     mark(from(X)) -> a__from(mark(X))
     mark(length(X)) -> a__length(X)
     mark(length1(X)) -> a__length1(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__from(X) -> from(X)
     a__length(X) -> length(X)
     a__length1(X) -> length1(X)
    Subterm Criterion Processor:
     simple projection:
      pi(a__length#) = 0
      pi(a__length1#) = 0
     problem:
      DPs:
       a__length1#(X) -> a__length#(X)
      TRS:
       a__from(X) -> cons(mark(X),from(s(X)))
       a__length(nil()) -> 0()
       a__length(cons(X,Y)) -> s(a__length1(Y))
       a__length1(X) -> a__length(X)
       mark(from(X)) -> a__from(mark(X))
       mark(length(X)) -> a__length(X)
       mark(length1(X)) -> a__length1(X)
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       mark(nil()) -> nil()
       mark(0()) -> 0()
       a__from(X) -> from(X)
       a__length(X) -> length(X)
       a__length1(X) -> length1(X)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 2/1