/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__2nd(cons(X,cons(Y,Z))) -> mark(Y)
 a__from(X) -> cons(mark(X),from(s(X)))
 mark(2nd(X)) -> a__2nd(mark(X))
 mark(from(X)) -> a__from(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 a__2nd(X) -> 2nd(X)
 a__from(X) -> from(X)

Proof:
 DP Processor:
  DPs:
   a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y)
   a__from#(X) -> mark#(X)
   mark#(2nd(X)) -> mark#(X)
   mark#(2nd(X)) -> a__2nd#(mark(X))
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
   a__from(X) -> cons(mark(X),from(s(X)))
   mark(2nd(X)) -> a__2nd(mark(X))
   mark(from(X)) -> a__from(mark(X))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   a__2nd(X) -> 2nd(X)
   a__from(X) -> from(X)
  TDG Processor:
   DPs:
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y)
    a__from#(X) -> mark#(X)
    mark#(2nd(X)) -> mark#(X)
    mark#(2nd(X)) -> a__2nd#(mark(X))
    mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
    a__from(X) -> cons(mark(X),from(s(X)))
    mark(2nd(X)) -> a__2nd(mark(X))
    mark(from(X)) -> a__from(mark(X))
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    a__2nd(X) -> 2nd(X)
    a__from(X) -> from(X)
   graph:
    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#(from(X)) -> a__from#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(2nd(X)) -> mark#(X)
    mark#(2nd(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(2nd(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(2nd(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X))
    mark#(2nd(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X)
    mark#(2nd(X)) -> a__2nd#(mark(X)) ->
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y)
    mark#(from(X)) -> a__from#(mark(X)) -> a__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#(from(X)) -> a__from#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(2nd(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#(from(X)) -> a__from#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> a__2nd#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(2nd(X)) -> mark#(X)
    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#(from(X)) -> a__from#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(2nd(X)) -> a__2nd#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(2nd(X)) -> mark#(X)
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y) ->
    mark#(s(X)) -> mark#(X)
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y) ->
    mark#(from(X)) -> a__from#(mark(X))
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y) ->
    mark#(from(X)) -> mark#(X)
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y) ->
    mark#(2nd(X)) -> a__2nd#(mark(X))
    a__2nd#(cons(X,cons(Y,Z))) -> mark#(Y) -> mark#(2nd(X)) -> mark#(X)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
     a__from(X) -> cons(mark(X),from(s(X)))
     mark(2nd(X)) -> a__2nd(mark(X))
     mark(from(X)) -> a__from(mark(X))
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     a__2nd(X) -> 2nd(X)
     a__from(X) -> from(X)
    interpretation:
     [a__from#](x0) = 4x0 + 0,
     
     [mark#](x0) = x0 + 0,
     
     [a__2nd#](x0) = x0 + 4,
     
     [2nd](x0) = x0 + 4,
     
     [from](x0) = 4x0,
     
     [s](x0) = x0,
     
     [a__from](x0) = 4x0,
     
     [mark](x0) = x0,
     
     [a__2nd](x0) = x0 + 4,
     
     [cons](x0, x1) = 1x0 + x1
    orientation:
     a__2nd#(cons(X,cons(Y,Z))) = 1X + 1Y + Z + 4 >= Y + 0 = mark#(Y)
     
     a__from#(X) = 4X + 0 >= X + 0 = mark#(X)
     
     mark#(2nd(X)) = X + 4 >= X + 0 = mark#(X)
     
     mark#(2nd(X)) = X + 4 >= X + 4 = a__2nd#(mark(X))
     
     mark#(from(X)) = 4X + 0 >= X + 0 = mark#(X)
     
     mark#(from(X)) = 4X + 0 >= 4X + 0 = a__from#(mark(X))
     
     mark#(cons(X1,X2)) = 1X1 + X2 + 0 >= X1 + 0 = mark#(X1)
     
     mark#(s(X)) = X + 0 >= X + 0 = mark#(X)
     
     a__2nd(cons(X,cons(Y,Z))) = 1X + 1Y + Z + 4 >= Y = mark(Y)
     
     a__from(X) = 4X >= 4X = cons(mark(X),from(s(X)))
     
     mark(2nd(X)) = X + 4 >= X + 4 = a__2nd(mark(X))
     
     mark(from(X)) = 4X >= 4X = a__from(mark(X))
     
     mark(cons(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = cons(mark(X1),X2)
     
     mark(s(X)) = X >= X = s(mark(X))
     
     a__2nd(X) = X + 4 >= X + 4 = 2nd(X)
     
     a__from(X) = 4X >= 4X = from(X)
    problem:
     DPs:
      a__from#(X) -> mark#(X)
      mark#(2nd(X)) -> mark#(X)
      mark#(2nd(X)) -> a__2nd#(mark(X))
      mark#(from(X)) -> mark#(X)
      mark#(from(X)) -> a__from#(mark(X))
      mark#(cons(X1,X2)) -> mark#(X1)
      mark#(s(X)) -> mark#(X)
     TRS:
      a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
      a__from(X) -> cons(mark(X),from(s(X)))
      mark(2nd(X)) -> a__2nd(mark(X))
      mark(from(X)) -> a__from(mark(X))
      mark(cons(X1,X2)) -> cons(mark(X1),X2)
      mark(s(X)) -> s(mark(X))
      a__2nd(X) -> 2nd(X)
      a__from(X) -> from(X)
    Restore Modifier:
     DPs:
      a__from#(X) -> mark#(X)
      mark#(2nd(X)) -> mark#(X)
      mark#(2nd(X)) -> a__2nd#(mark(X))
      mark#(from(X)) -> mark#(X)
      mark#(from(X)) -> a__from#(mark(X))
      mark#(cons(X1,X2)) -> mark#(X1)
      mark#(s(X)) -> mark#(X)
     TRS:
      a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
      a__from(X) -> cons(mark(X),from(s(X)))
      mark(2nd(X)) -> a__2nd(mark(X))
      mark(from(X)) -> a__from(mark(X))
      mark(cons(X1,X2)) -> cons(mark(X1),X2)
      mark(s(X)) -> s(mark(X))
      a__2nd(X) -> 2nd(X)
      a__from(X) -> from(X)
     SCC Processor:
      #sccs: 1
      #rules: 6
      #arcs: 38/49
      DPs:
       a__from#(X) -> mark#(X)
       mark#(2nd(X)) -> mark#(X)
       mark#(from(X)) -> mark#(X)
       mark#(from(X)) -> a__from#(mark(X))
       mark#(cons(X1,X2)) -> mark#(X1)
       mark#(s(X)) -> mark#(X)
      TRS:
       a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
       a__from(X) -> cons(mark(X),from(s(X)))
       mark(2nd(X)) -> a__2nd(mark(X))
       mark(from(X)) -> a__from(mark(X))
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       a__2nd(X) -> 2nd(X)
       a__from(X) -> from(X)
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
        a__from(X) -> cons(mark(X),from(s(X)))
        mark(2nd(X)) -> a__2nd(mark(X))
        mark(from(X)) -> a__from(mark(X))
        mark(cons(X1,X2)) -> cons(mark(X1),X2)
        mark(s(X)) -> s(mark(X))
        a__2nd(X) -> 2nd(X)
        a__from(X) -> from(X)
       interpretation:
        [a__from#](x0) = 2x0,
        
        [mark#](x0) = 1x0,
        
        [2nd](x0) = 4x0,
        
        [from](x0) = 5x0,
        
        [s](x0) = x0,
        
        [a__from](x0) = 5x0,
        
        [mark](x0) = x0,
        
        [a__2nd](x0) = 4x0,
        
        [cons](x0, x1) = 1x0 + x1
       orientation:
        a__from#(X) = 2X >= 1X = mark#(X)
        
        mark#(2nd(X)) = 5X >= 1X = mark#(X)
        
        mark#(from(X)) = 6X >= 1X = mark#(X)
        
        mark#(from(X)) = 6X >= 2X = a__from#(mark(X))
        
        mark#(cons(X1,X2)) = 2X1 + 1X2 >= 1X1 = mark#(X1)
        
        mark#(s(X)) = 1X >= 1X = mark#(X)
        
        a__2nd(cons(X,cons(Y,Z))) = 5X + 5Y + 4Z >= Y = mark(Y)
        
        a__from(X) = 5X >= 5X = cons(mark(X),from(s(X)))
        
        mark(2nd(X)) = 4X >= 4X = a__2nd(mark(X))
        
        mark(from(X)) = 5X >= 5X = a__from(mark(X))
        
        mark(cons(X1,X2)) = 1X1 + X2 >= 1X1 + X2 = cons(mark(X1),X2)
        
        mark(s(X)) = X >= X = s(mark(X))
        
        a__2nd(X) = 4X >= 4X = 2nd(X)
        
        a__from(X) = 5X >= 5X = from(X)
       problem:
        DPs:
         mark#(s(X)) -> mark#(X)
        TRS:
         a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
         a__from(X) -> cons(mark(X),from(s(X)))
         mark(2nd(X)) -> a__2nd(mark(X))
         mark(from(X)) -> a__from(mark(X))
         mark(cons(X1,X2)) -> cons(mark(X1),X2)
         mark(s(X)) -> s(mark(X))
         a__2nd(X) -> 2nd(X)
         a__from(X) -> from(X)
       Restore Modifier:
        DPs:
         mark#(s(X)) -> mark#(X)
        TRS:
         a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
         a__from(X) -> cons(mark(X),from(s(X)))
         mark(2nd(X)) -> a__2nd(mark(X))
         mark(from(X)) -> a__from(mark(X))
         mark(cons(X1,X2)) -> cons(mark(X1),X2)
         mark(s(X)) -> s(mark(X))
         a__2nd(X) -> 2nd(X)
         a__from(X) -> from(X)
        Size-Change Termination Processor:
         DPs:
          
         TRS:
          a__2nd(cons(X,cons(Y,Z))) -> mark(Y)
          a__from(X) -> cons(mark(X),from(s(X)))
          mark(2nd(X)) -> a__2nd(mark(X))
          mark(from(X)) -> a__from(mark(X))
          mark(cons(X1,X2)) -> cons(mark(X1),X2)
          mark(s(X)) -> s(mark(X))
          a__2nd(X) -> 2nd(X)
          a__from(X) -> from(X)
         The DP: mark#(s(X)) -> mark#(X) has the edges:
           0 >   0
         Qed