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


--------------------------------------------------------------------------------


YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(b(c(b(x1))))
  b(x1) -> a(x1)
  c(c(c(x1))) -> x1
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> c#(b(x1))
    b#(a(x1)) -> b#(c(b(x1)))
    b#(a(x1)) -> a#(b(c(b(x1))))
    b#(x1) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(b(c(b(x1))))
    b(x1) -> a(x1)
    c(c(c(x1))) -> x1
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> a#(b(c(b(x1))))
     b#(x1) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(b(c(b(x1))))
     b(x1) -> a(x1)
     c(c(c(x1))) -> x1
    graph:
     b#(a(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(x1)
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> a#(b(c(b(x1))))
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(x1) -> a#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(c(b(x1))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 10/25
     DPs:
      b#(a(x1)) -> b#(c(b(x1)))
      b#(a(x1)) -> b#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(b(c(b(x1))))
      b(x1) -> a(x1)
      c(c(c(x1))) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> a(b(c(b(x1))))
       b(x1) -> a(x1)
       c(c(c(x1))) -> x1
      interpretation:
       [b#](x0) = [0 0]x0 + [-4],
       
                 [-3 0 ]     [2]
       [c](x0) = [-1 1 ]x0 + [3],
       
                 [2 1]     [3]
       [b](x0) = [0 0]x0 + [0],
       
                 [1  1 ]     [3 ]
       [a](x0) = [-& 0 ]x0 + [-&]
      orientation:
       b#(a(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = b#(c(b(x1)))
       
       b#(a(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [-4] = b#(x1)
       
               [1  1 ]     [3 ]           
       a(x1) = [-& 0 ]x1 + [-&] >= x1 = x1
       
                  [3 3]     [5]    [3 3]     [5]                 
       b(a(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = a(b(c(b(x1))))
       
               [2 1]     [3]    [1  1 ]     [3 ]        
       b(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [-&] = a(x1)
       
                     [0 2]     [4]           
       c(c(c(x1))) = [1 3]x1 + [5] >= x1 = x1
      problem:
       DPs:
        b#(a(x1)) -> b#(c(b(x1)))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(b(c(b(x1))))
        b(x1) -> a(x1)
        c(c(c(x1))) -> x1
      Restore Modifier:
       DPs:
        b#(a(x1)) -> b#(c(b(x1)))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(b(c(b(x1))))
        b(x1) -> a(x1)
        c(c(c(x1))) -> x1
       EDG Processor:
        DPs:
         b#(a(x1)) -> b#(c(b(x1)))
        TRS:
         a(x1) -> x1
         b(a(x1)) -> a(b(c(b(x1))))
         b(x1) -> a(x1)
         c(c(c(x1))) -> x1
        graph:
         b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(c(b(x1)))
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(a(x1)) -> a(b(c(b(x1))))
          b(x1) -> a(x1)
          c(c(c(x1))) -> x1
         interpretation:
          [b#](x0) = [0  -&]x0 + [0],
          
                    [-4 0 ]     [0]
          [c](x0) = [-1 1 ]x0 + [0],
          
                    [2 1]     [1]
          [b](x0) = [0 0]x0 + [0],
          
                    [1  1 ]     [1]
          [a](x0) = [-& 0 ]x0 + [0]
         orientation:
          b#(a(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(c(b(x1)))
          
                  [1  1 ]     [1]           
          a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
          
                     [3 3]     [3]    [3 3]     [3]                 
          b(a(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(c(b(x1))))
          
                  [2 1]     [1]    [1  1 ]     [1]        
          b(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = a(x1)
          
                        [0 2]     [1]           
          c(c(c(x1))) = [1 3]x1 + [2] >= x1 = x1
         problem:
          DPs:
           
          TRS:
           a(x1) -> x1
           b(a(x1)) -> a(b(c(b(x1))))
           b(x1) -> a(x1)
           c(c(c(x1))) -> x1
         Qed