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


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


YES

Problem:
 a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
 a(d(x1)) -> c(x1)
 a(f(f(x1))) -> g(x1)
 b(g(x1)) -> g(b(x1))
 c(x1) -> f(f(x1))
 c(a(c(x1))) -> b(c(a(b(c(x1)))))
 c(d(x1)) -> a(a(x1))
 g(x1) -> c(a(x1))
 g(x1) -> d(d(d(d(x1))))

Proof:
 String Reversal Processor:
  a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
  d(a(x1)) -> c(x1)
  f(f(a(x1))) -> g(x1)
  g(b(x1)) -> b(g(x1))
  c(x1) -> f(f(x1))
  c(a(c(x1))) -> c(b(a(c(b(x1)))))
  d(c(x1)) -> a(a(x1))
  g(x1) -> a(c(x1))
  g(x1) -> d(d(d(d(x1))))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0) = x0 + 13,
    
    [f](x0) = x0 + 4,
    
    [d](x0) = x0 + 3,
    
    [b](x0) = x0,
    
    [c](x0) = x0 + 8,
    
    [a](x0) = x0 + 5
   orientation:
    a(c(b(a(x1)))) = x1 + 18 >= x1 + 18 = b(a(b(c(a(b(x1))))))
    
    d(a(x1)) = x1 + 8 >= x1 + 8 = c(x1)
    
    f(f(a(x1))) = x1 + 13 >= x1 + 13 = g(x1)
    
    g(b(x1)) = x1 + 13 >= x1 + 13 = b(g(x1))
    
    c(x1) = x1 + 8 >= x1 + 8 = f(f(x1))
    
    c(a(c(x1))) = x1 + 21 >= x1 + 21 = c(b(a(c(b(x1)))))
    
    d(c(x1)) = x1 + 11 >= x1 + 10 = a(a(x1))
    
    g(x1) = x1 + 13 >= x1 + 13 = a(c(x1))
    
    g(x1) = x1 + 13 >= x1 + 12 = d(d(d(d(x1))))
   problem:
    a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
    d(a(x1)) -> c(x1)
    f(f(a(x1))) -> g(x1)
    g(b(x1)) -> b(g(x1))
    c(x1) -> f(f(x1))
    c(a(c(x1))) -> c(b(a(c(b(x1)))))
    g(x1) -> a(c(x1))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0) = 4x0 + 2,
     
     [f](x0) = x0,
     
     [d](x0) = 2x0 + 14,
     
     [b](x0) = x0,
     
     [c](x0) = x0,
     
     [a](x0) = 4x0 + 2
    orientation:
     a(c(b(a(x1)))) = 16x1 + 10 >= 16x1 + 10 = b(a(b(c(a(b(x1))))))
     
     d(a(x1)) = 8x1 + 18 >= x1 = c(x1)
     
     f(f(a(x1))) = 4x1 + 2 >= 4x1 + 2 = g(x1)
     
     g(b(x1)) = 4x1 + 2 >= 4x1 + 2 = b(g(x1))
     
     c(x1) = x1 >= x1 = f(f(x1))
     
     c(a(c(x1))) = 4x1 + 2 >= 4x1 + 2 = c(b(a(c(b(x1)))))
     
     g(x1) = 4x1 + 2 >= 4x1 + 2 = a(c(x1))
    problem:
     a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
     f(f(a(x1))) -> g(x1)
     g(b(x1)) -> b(g(x1))
     c(x1) -> f(f(x1))
     c(a(c(x1))) -> c(b(a(c(b(x1)))))
     g(x1) -> a(c(x1))
    String Reversal Processor:
     a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
     a(f(f(x1))) -> g(x1)
     b(g(x1)) -> g(b(x1))
     c(x1) -> f(f(x1))
     c(a(c(x1))) -> b(c(a(b(c(x1)))))
     g(x1) -> c(a(x1))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [g](x0) = 4x0 + 2,
       
       [f](x0) = x0 + 1,
       
       [b](x0) = x0,
       
       [c](x0) = x0 + 2,
       
       [a](x0) = 4x0
      orientation:
       a(b(c(a(x1)))) = 16x1 + 8 >= 16x1 + 8 = b(a(c(b(a(b(x1))))))
       
       a(f(f(x1))) = 4x1 + 8 >= 4x1 + 2 = g(x1)
       
       b(g(x1)) = 4x1 + 2 >= 4x1 + 2 = g(b(x1))
       
       c(x1) = x1 + 2 >= x1 + 2 = f(f(x1))
       
       c(a(c(x1))) = 4x1 + 10 >= 4x1 + 10 = b(c(a(b(c(x1)))))
       
       g(x1) = 4x1 + 2 >= 4x1 + 2 = c(a(x1))
      problem:
       a(b(c(a(x1)))) -> b(a(c(b(a(b(x1))))))
       b(g(x1)) -> g(b(x1))
       c(x1) -> f(f(x1))
       c(a(c(x1))) -> b(c(a(b(c(x1)))))
       g(x1) -> c(a(x1))
      String Reversal Processor:
       a(c(b(a(x1)))) -> b(a(b(c(a(b(x1))))))
       g(b(x1)) -> b(g(x1))
       c(x1) -> f(f(x1))
       c(a(c(x1))) -> c(b(a(c(b(x1)))))
       g(x1) -> a(c(x1))
       Bounds Processor:
        bound: 2
        enrichment: match
        automaton:
         final states: {16,12,10,8,1}
         transitions:
          f0(2) -> 11*
          f0(11) -> 10*
          a1(55) -> 56*
          a1(58) -> 59*
          a1(43) -> 44*
          c1(42) -> 43*
          c1(56) -> 57*
          f1(40) -> 41*
          f1(30) -> 31*
          f1(27) -> 28*
          f1(39) -> 40*
          f1(19) -> 20*
          f1(31) -> 32*
          f1(28) -> 29*
          f1(18) -> 19*
          f2(72) -> 73*
          f2(52) -> 53*
          f2(71) -> 72*
          f2(51) -> 52*
          b1(57) -> 58*
          b1(59) -> 60*
          b1(54) -> 55*
          f60() -> 2*
          b0(5) -> 6*
          b0(7) -> 1*
          b0(2) -> 3*
          b0(14) -> 15*
          b0(9) -> 8*
          a0(17) -> 16*
          a0(6) -> 7*
          a0(13) -> 14*
          a0(3) -> 4*
          c0(15) -> 12*
          c0(2) -> 17*
          c0(4) -> 5*
          c0(3) -> 13*
          g0(2) -> 9*
          1 -> 44,16,9,14
          2 -> 42,18
          3 -> 27*
          4 -> 30*
          8 -> 9*
          12 -> 43,17
          13 -> 54*
          15 -> 39*
          20 -> 17*
          29 -> 13*
          32 -> 5*
          41 -> 12*
          42 -> 51*
          44 -> 9*
          53 -> 43*
          56 -> 71*
          60 -> 44,9,16
          73 -> 57*
        problem:
         
        Qed