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

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