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

Proof:
 DP Processor:
  DPs:
   a#(b(b(x1))) -> c#(x1)
   a#(b(b(x1))) -> a#(c(x1))
   a#(b(b(x1))) -> a#(a(c(x1)))
  TRS:
   a(x1) -> x1
   a(b(b(x1))) -> b(b(b(a(a(c(x1))))))
   c(b(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(b(x1))) -> c#(x1)
    a#(b(b(x1))) -> a#(c(x1))
    a#(b(b(x1))) -> a#(a(c(x1)))
   TRS:
    a(x1) -> x1
    a(b(b(x1))) -> b(b(b(a(a(c(x1))))))
    c(b(x1)) -> x1
   graph:
    a#(b(b(x1))) -> a#(c(x1)) -> a#(b(b(x1))) -> a#(a(c(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)
    a#(b(b(x1))) -> a#(a(c(x1))) -> a#(b(b(x1))) -> a#(a(c(x1)))
    a#(b(b(x1))) -> a#(a(c(x1))) -> a#(b(b(x1))) -> a#(c(x1))
    a#(b(b(x1))) -> a#(a(c(x1))) -> a#(b(b(x1))) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     a#(b(b(x1))) -> a#(c(x1))
     a#(b(b(x1))) -> a#(a(c(x1)))
    TRS:
     a(x1) -> x1
     a(b(b(x1))) -> b(b(b(a(a(c(x1))))))
     c(b(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 4
     usable rules:
      a(x1) -> x1
      a(b(b(x1))) -> b(b(b(a(a(c(x1))))))
      c(b(x1)) -> x1
     interpretation:
      [a#](x0) = [0  -& 0  0 ]x0 + [0],
      
                [0  -& -& 0 ]     [0]
                [0  0  0  1 ]     [1]
      [c](x0) = [0  -& -& 0 ]x0 + [0]
                [0  -& -& 0 ]     [0],
      
                [0  -& 0  0 ]     [0]
                [0  -& -& 0 ]     [0]
      [b](x0) = [-& 0  -& 1 ]x0 + [0]
                [0  -& -& -&]     [0],
      
                [0  -& 0  0 ]     [0]
                [0  0  0  -&]     [0]
      [a](x0) = [0  -& 0  0 ]x0 + [0]
                [0  -& 0  0 ]     [0]
     orientation:
      a#(b(b(x1))) = [1 0 0 1]x1 + [1] >= [0  -& -& 0 ]x1 + [0] = a#(c(x1))
      
      a#(b(b(x1))) = [1 0 0 1]x1 + [1] >= [0  -& -& 0 ]x1 + [0] = a#(a(c(x1)))
      
              [0  -& 0  0 ]     [0]           
              [0  0  0  -&]     [0]           
      a(x1) = [0  -& 0  0 ]x1 + [0] >= x1 = x1
              [0  -& 0  0 ]     [0]           
      
                    [1 0 0 1]     [1]    [1  0  0  1 ]     [1]                       
                    [1 0 0 1]     [1]    [1  0  0  1 ]     [1]                       
      a(b(b(x1))) = [1 0 0 1]x1 + [1] >= [1  -& -& 1 ]x1 + [1] = b(b(b(a(a(c(x1))))))
                    [1 0 0 1]     [1]    [1  0  0  1 ]     [1]                       
      
                 [0  -& 0  0 ]     [0]           
                 [1  0  0  1 ]     [1]           
      c(b(x1)) = [0  -& 0  0 ]x1 + [0] >= x1 = x1
                 [0  -& 0  0 ]     [0]           
     problem:
      DPs:
       
      TRS:
       a(x1) -> x1
       a(b(b(x1))) -> b(b(b(a(a(c(x1))))))
       c(b(x1)) -> x1
     Qed