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

Proof:
 DP Processor:
  DPs:
   a#(b(b(x1))) -> b#(c(x1))
   a#(b(b(x1))) -> b#(b(c(x1)))
   a#(b(b(x1))) -> b#(b(b(c(x1))))
   b#(c(x1)) -> a#(x1)
   b#(c(x1)) -> a#(a(x1))
  TRS:
   a(x1) -> x1
   a(b(b(x1))) -> b(b(b(c(x1))))
   b(c(x1)) -> a(a(x1))
  TDG Processor:
   DPs:
    a#(b(b(x1))) -> b#(c(x1))
    a#(b(b(x1))) -> b#(b(c(x1)))
    a#(b(b(x1))) -> b#(b(b(c(x1))))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    a(b(b(x1))) -> b(b(b(c(x1))))
    b(c(x1)) -> a(a(x1))
   graph:
    b#(c(x1)) -> a#(a(x1)) -> a#(b(b(x1))) -> b#(b(b(c(x1))))
    b#(c(x1)) -> a#(a(x1)) -> a#(b(b(x1))) -> b#(b(c(x1)))
    b#(c(x1)) -> a#(a(x1)) -> a#(b(b(x1))) -> b#(c(x1))
    b#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> b#(b(b(c(x1))))
    b#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> b#(b(c(x1)))
    b#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> b#(c(x1))
    a#(b(b(x1))) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(x1))
    a#(b(b(x1))) -> b#(c(x1)) -> b#(c(x1)) -> a#(x1)
    a#(b(b(x1))) -> b#(b(c(x1))) -> b#(c(x1)) -> a#(a(x1))
    a#(b(b(x1))) -> b#(b(c(x1))) -> b#(c(x1)) -> a#(x1)
    a#(b(b(x1))) -> b#(b(b(c(x1)))) -> b#(c(x1)) -> a#(a(x1))
    a#(b(b(x1))) -> b#(b(b(c(x1)))) -> b#(c(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(x1) -> x1
     a(b(b(x1))) -> b(b(b(c(x1))))
     b(c(x1)) -> a(a(x1))
    interpretation:
     [b#](x0) = [-& 1 ]x0 + [0],
     
     [a#](x0) = [-& 1 ]x0 + [0],
     
               [-& -&]     [1]
     [c](x0) = [0  0 ]x0 + [3],
     
               [-& 0 ]     [3]
     [b](x0) = [1  0 ]x0 + [3],
     
               [0 0]     [3]
     [a](x0) = [0 0]x0 + [0]
    orientation:
     a#(b(b(x1))) = [2 2]x1 + [5] >= [1 1]x1 + [4] = b#(c(x1))
     
     a#(b(b(x1))) = [2 2]x1 + [5] >= [1 1]x1 + [4] = b#(b(c(x1)))
     
     a#(b(b(x1))) = [2 2]x1 + [5] >= [2 2]x1 + [5] = b#(b(b(c(x1))))
     
     b#(c(x1)) = [1 1]x1 + [4] >= [-& 1 ]x1 + [0] = a#(x1)
     
     b#(c(x1)) = [1 1]x1 + [4] >= [1 1]x1 + [1] = a#(a(x1))
     
             [0 0]     [3]           
     a(x1) = [0 0]x1 + [0] >= x1 = x1
     
                   [1 1]     [4]    [1 1]     [4]                 
     a(b(b(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = b(b(b(c(x1))))
     
                [0 0]     [3]    [0 0]     [3]           
     b(c(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [3] = a(a(x1))
    problem:
     DPs:
      a#(b(b(x1))) -> b#(b(b(c(x1))))
      b#(c(x1)) -> a#(x1)
      b#(c(x1)) -> a#(a(x1))
     TRS:
      a(x1) -> x1
      a(b(b(x1))) -> b(b(b(c(x1))))
      b(c(x1)) -> a(a(x1))
    Restore Modifier:
     DPs:
      a#(b(b(x1))) -> b#(b(b(c(x1))))
      b#(c(x1)) -> a#(x1)
      b#(c(x1)) -> a#(a(x1))
     TRS:
      a(x1) -> x1
      a(b(b(x1))) -> b(b(b(c(x1))))
      b(c(x1)) -> a(a(x1))
     EDG Processor:
      DPs:
       a#(b(b(x1))) -> b#(b(b(c(x1))))
       b#(c(x1)) -> a#(x1)
       b#(c(x1)) -> a#(a(x1))
      TRS:
       a(x1) -> x1
       a(b(b(x1))) -> b(b(b(c(x1))))
       b(c(x1)) -> a(a(x1))
      graph:
       b#(c(x1)) -> a#(a(x1)) -> a#(b(b(x1))) -> b#(b(b(c(x1))))
       b#(c(x1)) -> a#(x1) -> a#(b(b(x1))) -> b#(b(b(c(x1))))
       a#(b(b(x1))) -> b#(b(b(c(x1)))) -> b#(c(x1)) -> a#(x1)
       a#(b(b(x1))) -> b#(b(b(c(x1)))) -> b#(c(x1)) -> a#(a(x1))
      Matrix Interpretation Processor: dim=1
       
       usable rules:
        a(x1) -> x1
        a(b(b(x1))) -> b(b(b(c(x1))))
        b(c(x1)) -> a(a(x1))
       interpretation:
        [b#](x0) = 2x0 + 15/2,
        
        [a#](x0) = 4x0,
        
        [c](x0) = 2x0,
        
        [b](x0) = 1/2x0 + 3,
        
        [a](x0) = x0 + 1
       orientation:
        a#(b(b(x1))) = x1 + 18 >= x1 + 33/2 = b#(b(b(c(x1))))
        
        b#(c(x1)) = 4x1 + 15/2 >= 4x1 = a#(x1)
        
        b#(c(x1)) = 4x1 + 15/2 >= 4x1 + 4 = a#(a(x1))
        
        a(x1) = x1 + 1 >= x1 = x1
        
        a(b(b(x1))) = 1/4x1 + 11/2 >= 1/4x1 + 21/4 = b(b(b(c(x1))))
        
        b(c(x1)) = x1 + 3 >= x1 + 2 = a(a(x1))
       problem:
        DPs:
         
        TRS:
         a(x1) -> x1
         a(b(b(x1))) -> b(b(b(c(x1))))
         b(c(x1)) -> a(a(x1))
       Qed