/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(x1) -> b(c(x1))
 b(a(b(x1))) -> a(a(a(x1)))
 c(c(x1)) -> a(x1)

Proof:
 String Reversal Processor:
  a(x1) -> c(b(x1))
  b(a(b(x1))) -> a(a(a(x1)))
  c(c(x1)) -> a(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> c#(b(x1))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(a(x1))
    b#(a(b(x1))) -> a#(a(a(x1)))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> c(b(x1))
    b(a(b(x1))) -> a(a(a(x1)))
    c(c(x1)) -> a(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(x1)
     b#(a(b(x1))) -> a#(a(x1))
     b#(a(b(x1))) -> a#(a(a(x1)))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> c(b(x1))
     b(a(b(x1))) -> a(a(a(x1)))
     c(c(x1)) -> a(x1)
    graph:
     c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
     c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(x1) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(a(a(x1)))
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1))
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> c(b(x1))
      b(a(b(x1))) -> a(a(a(x1)))
      c(c(x1)) -> a(x1)
     interpretation:
      [c#](x0) = [2 0]x0 + [0],
      
      [b#](x0) = [-& 1 ]x0 + [0],
      
      [a#](x0) = [-& 2 ]x0 + [2],
      
                [-& 0 ]     [0]
      [b](x0) = [-& 2 ]x0 + [2],
      
                [2  0 ]     [0]
      [c](x0) = [0  -&]x0 + [0],
      
                [-& 2 ]     [2]
      [a](x0) = [-& 0 ]x0 + [0]
     orientation:
      a#(x1) = [-& 2 ]x1 + [2] >= [-& 1 ]x1 + [0] = b#(x1)
      
      a#(x1) = [-& 2 ]x1 + [2] >= [-& 2 ]x1 + [2] = c#(b(x1))
      
      b#(a(b(x1))) = [-& 3 ]x1 + [3] >= [-& 2 ]x1 + [2] = a#(x1)
      
      b#(a(b(x1))) = [-& 3 ]x1 + [3] >= [-& 2 ]x1 + [2] = a#(a(x1))
      
      b#(a(b(x1))) = [-& 3 ]x1 + [3] >= [-& 2 ]x1 + [2] = a#(a(a(x1)))
      
      c#(c(x1)) = [4 2]x1 + [2] >= [-& 2 ]x1 + [2] = a#(x1)
      
              [-& 2 ]     [2]    [-& 2 ]     [2]           
      a(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = c(b(x1))
      
                    [-& 2 ]     [2]    [-& 2 ]     [2]              
      b(a(b(x1))) = [-& 4 ]x1 + [4] >= [-& 0 ]x1 + [0] = a(a(a(x1)))
      
                 [4 2]     [2]    [-& 2 ]     [2]        
      c(c(x1)) = [2 0]x1 + [0] >= [-& 0 ]x1 + [0] = a(x1)
     problem:
      DPs:
       a#(x1) -> c#(b(x1))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> c(b(x1))
       b(a(b(x1))) -> a(a(a(x1)))
       c(c(x1)) -> a(x1)
     Restore Modifier:
      DPs:
       a#(x1) -> c#(b(x1))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> c(b(x1))
       b(a(b(x1))) -> a(a(a(x1)))
       c(c(x1)) -> a(x1)
      EDG Processor:
       DPs:
        a#(x1) -> c#(b(x1))
        c#(c(x1)) -> a#(x1)
       TRS:
        a(x1) -> c(b(x1))
        b(a(b(x1))) -> a(a(a(x1)))
        c(c(x1)) -> a(x1)
       graph:
        c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
        a#(x1) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         a(x1) -> c(b(x1))
         b(a(b(x1))) -> a(a(a(x1)))
         c(c(x1)) -> a(x1)
        interpretation:
         [c#](x0) = [-& 0  0 ]x0 + [0],
         
         [a#](x0) = [0  1  -&]x0 + [1],
         
                   [1  1  0 ]     [1]
         [b](x0) = [-& 0  -&]x0 + [0]
                   [-& 0  -&]     [0],
         
                   [-& -& -&]     [0]
         [c](x0) = [-& 0  0 ]x0 + [0]
                   [0  1  1 ]     [1],
         
                   [-& -& -&]     [0]
         [a](x0) = [0  0  -&]x0 + [0]
                   [1  1  0 ]     [1]
        orientation:
         a#(x1) = [0  1  -&]x1 + [1] >= [-& 0  -&]x1 + [0] = c#(b(x1))
         
         c#(c(x1)) = [0 1 1]x1 + [1] >= [0  1  -&]x1 + [1] = a#(x1)
         
                 [-& -& -&]     [0]    [-& -& -&]     [0]           
         a(x1) = [0  0  -&]x1 + [0] >= [-& 0  -&]x1 + [0] = c(b(x1))
                 [1  1  0 ]     [1]    [1  1  0 ]     [1]           
         
                       [2 2 1]     [2]    [-& -& -&]     [0]              
         b(a(b(x1))) = [1 1 0]x1 + [1] >= [0  0  -&]x1 + [0] = a(a(a(x1)))
                       [1 1 0]     [1]    [1  1  0 ]     [1]              
         
                    [-& -& -&]     [0]    [-& -& -&]     [0]        
         c(c(x1)) = [0  1  1 ]x1 + [1] >= [0  0  -&]x1 + [0] = a(x1)
                    [1  2  2 ]     [2]    [1  1  0 ]     [1]        
        problem:
         DPs:
          c#(c(x1)) -> a#(x1)
         TRS:
          a(x1) -> c(b(x1))
          b(a(b(x1))) -> a(a(a(x1)))
          c(c(x1)) -> a(x1)
        Restore Modifier:
         DPs:
          c#(c(x1)) -> a#(x1)
         TRS:
          a(x1) -> c(b(x1))
          b(a(b(x1))) -> a(a(a(x1)))
          c(c(x1)) -> a(x1)
         EDG Processor:
          DPs:
           c#(c(x1)) -> a#(x1)
          TRS:
           a(x1) -> c(b(x1))
           b(a(b(x1))) -> a(a(a(x1)))
           c(c(x1)) -> a(x1)
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1