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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> c#(b(x1))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> c#(a(x1))
   c#(c(x1)) -> a#(x1)
   c#(c(x1)) -> b#(a(x1))
  TRS:
   a(a(x1)) -> c(b(x1))
   b(b(x1)) -> c(a(x1))
   c(c(x1)) -> b(a(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> c#(a(x1))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1))
   TRS:
    a(a(x1)) -> c(b(x1))
    b(b(x1)) -> c(a(x1))
    c(c(x1)) -> b(a(x1))
   graph:
    c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(a(x1))
    c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1)
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1))
    c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> b#(a(x1))
    b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
    a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(a(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     a(a(x1)) -> c(b(x1))
     b(b(x1)) -> c(a(x1))
     c(c(x1)) -> b(a(x1))
    interpretation:
     [c#](x0) = x0 + 0,
     
     [b#](x0) = x0 + 0,
     
     [a#](x0) = 8x0 + 0,
     
     [c](x0) = 8x0 + 0,
     
     [b](x0) = 8x0 + 0,
     
     [a](x0) = 8x0 + 0
    orientation:
     a#(a(x1)) = 16x1 + 8 >= x1 + 0 = b#(x1)
     
     a#(a(x1)) = 16x1 + 8 >= 8x1 + 0 = c#(b(x1))
     
     b#(b(x1)) = 8x1 + 0 >= 8x1 + 0 = a#(x1)
     
     b#(b(x1)) = 8x1 + 0 >= 8x1 + 0 = c#(a(x1))
     
     c#(c(x1)) = 8x1 + 0 >= 8x1 + 0 = a#(x1)
     
     c#(c(x1)) = 8x1 + 0 >= 8x1 + 0 = b#(a(x1))
     
     a(a(x1)) = 16x1 + 8 >= 16x1 + 8 = c(b(x1))
     
     b(b(x1)) = 16x1 + 8 >= 16x1 + 8 = c(a(x1))
     
     c(c(x1)) = 16x1 + 8 >= 16x1 + 8 = b(a(x1))
    problem:
     DPs:
      b#(b(x1)) -> a#(x1)
      b#(b(x1)) -> c#(a(x1))
      c#(c(x1)) -> a#(x1)
      c#(c(x1)) -> b#(a(x1))
     TRS:
      a(a(x1)) -> c(b(x1))
      b(b(x1)) -> c(a(x1))
      c(c(x1)) -> b(a(x1))
    Restore Modifier:
     DPs:
      b#(b(x1)) -> a#(x1)
      b#(b(x1)) -> c#(a(x1))
      c#(c(x1)) -> a#(x1)
      c#(c(x1)) -> b#(a(x1))
     TRS:
      a(a(x1)) -> c(b(x1))
      b(b(x1)) -> c(a(x1))
      c(c(x1)) -> b(a(x1))
     EDG Processor:
      DPs:
       b#(b(x1)) -> a#(x1)
       b#(b(x1)) -> c#(a(x1))
       c#(c(x1)) -> a#(x1)
       c#(c(x1)) -> b#(a(x1))
      TRS:
       a(a(x1)) -> c(b(x1))
       b(b(x1)) -> c(a(x1))
       c(c(x1)) -> b(a(x1))
      graph:
       c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1)
       c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(a(x1))
       b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
       b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> b#(a(x1))
      SCC Processor:
       #sccs: 1
       #rules: 2
       #arcs: 4/16
       DPs:
        c#(c(x1)) -> b#(a(x1))
        b#(b(x1)) -> c#(a(x1))
       TRS:
        a(a(x1)) -> c(b(x1))
        b(b(x1)) -> c(a(x1))
        c(c(x1)) -> b(a(x1))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(a(x1)) -> c(b(x1))
         b(b(x1)) -> c(a(x1))
         c(c(x1)) -> b(a(x1))
        interpretation:
         [c#](x0) = [-& 0 ]x0 + [3],
         
         [b#](x0) = [-& 0 ]x0 + [0],
         
                   [0  0 ]     [2]
         [c](x0) = [1  -&]x0 + [0],
         
                   [-& 0 ]     [0]
         [b](x0) = [0  1 ]x0 + [3],
         
                   [0  1 ]     [1]
         [a](x0) = [0  -&]x0 + [2]
        orientation:
         c#(c(x1)) = [1  -&]x1 + [3] >= [0  -&]x1 + [2] = b#(a(x1))
         
         b#(b(x1)) = [0 1]x1 + [3] >= [0  -&]x1 + [3] = c#(a(x1))
         
                    [1 1]     [3]    [0  1 ]     [3]           
         a(a(x1)) = [0 1]x1 + [2] >= [-& 1 ]x1 + [1] = c(b(x1))
         
                    [0 1]     [3]    [0 1]     [2]           
         b(b(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [2] = c(a(x1))
         
                    [1 0]     [2]    [0  -&]     [2]           
         c(c(x1)) = [1 1]x1 + [3] >= [1  1 ]x1 + [3] = b(a(x1))
        problem:
         DPs:
          b#(b(x1)) -> c#(a(x1))
         TRS:
          a(a(x1)) -> c(b(x1))
          b(b(x1)) -> c(a(x1))
          c(c(x1)) -> b(a(x1))
        Restore Modifier:
         DPs:
          b#(b(x1)) -> c#(a(x1))
         TRS:
          a(a(x1)) -> c(b(x1))
          b(b(x1)) -> c(a(x1))
          c(c(x1)) -> b(a(x1))
         EDG Processor:
          DPs:
           b#(b(x1)) -> c#(a(x1))
          TRS:
           a(a(x1)) -> c(b(x1))
           b(b(x1)) -> c(a(x1))
           c(c(x1)) -> b(a(x1))
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1