/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 a(x1) -> x1
 a(b(b(x1))) -> b(b(b(a(c(x1)))))
 c(b(x1)) -> a(x1)

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