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

Proof:
 String Reversal Processor:
  b(b(x1)) -> d(c(x1))
  c(c(x1)) -> d(d(d(x1)))
  c(x1) -> g(x1)
  d(d(x1)) -> f(c(x1))
  d(d(d(x1))) -> c(g(x1))
  f(x1) -> g(a(x1))
  g(x1) -> b(a(d(x1)))
  g(g(x1)) -> c(b(x1))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
              [1 0]  
    [a](x0) = [0 0]x0,
    
              [1 0]     [1]
    [f](x0) = [0 0]x0 + [1],
    
              [1 2]     [1]
    [g](x0) = [0 0]x0 + [1],
    
              [1 2]     [1]
    [c](x0) = [0 0]x0 + [1],
    
              [1 2]     [0]
    [d](x0) = [0 0]x0 + [1],
    
              [1 2]     [1]
    [b](x0) = [0 0]x0 + [1]
   orientation:
               [1 2]     [4]    [1 2]     [3]           
    b(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(c(x1))
    
               [1 2]     [4]    [1 2]     [4]              
    c(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(d(d(x1)))
    
            [1 2]     [1]    [1 2]     [1]        
    c(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = g(x1)
    
               [1 2]     [2]    [1 2]     [2]           
    d(d(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = f(c(x1))
    
                  [1 2]     [4]    [1 2]     [4]           
    d(d(d(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(g(x1))
    
            [1 0]     [1]    [1 0]     [1]           
    f(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = g(a(x1))
    
            [1 2]     [1]    [1 2]     [1]              
    g(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(d(x1)))
    
               [1 2]     [4]    [1 2]     [4]           
    g(g(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(b(x1))
   problem:
    c(c(x1)) -> d(d(d(x1)))
    c(x1) -> g(x1)
    d(d(x1)) -> f(c(x1))
    d(d(d(x1))) -> c(g(x1))
    f(x1) -> g(a(x1))
    g(x1) -> b(a(d(x1)))
    g(g(x1)) -> c(b(x1))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
               [1 0]  
     [a](x0) = [0 0]x0,
     
               [1 0]     [2]
     [f](x0) = [0 0]x0 + [2],
     
               [1 2]     [0]
     [g](x0) = [0 1]x0 + [1],
     
               [1 3]     [0]
     [c](x0) = [0 1]x0 + [2],
     
               [1 2]     [0]
     [d](x0) = [0 1]x0 + [1],
     
               [1 1]  
     [b](x0) = [0 1]x0
    orientation:
                [1 6]     [6]    [1 6]     [6]              
     c(c(x1)) = [0 1]x1 + [4] >= [0 1]x1 + [3] = d(d(d(x1)))
     
             [1 3]     [0]    [1 2]     [0]        
     c(x1) = [0 1]x1 + [2] >= [0 1]x1 + [1] = g(x1)
     
                [1 4]     [2]    [1 3]     [2]           
     d(d(x1)) = [0 1]x1 + [2] >= [0 0]x1 + [2] = f(c(x1))
     
                   [1 6]     [6]    [1 5]     [3]           
     d(d(d(x1))) = [0 1]x1 + [3] >= [0 1]x1 + [3] = c(g(x1))
     
             [1 0]     [2]    [1 0]     [0]           
     f(x1) = [0 0]x1 + [2] >= [0 0]x1 + [1] = g(a(x1))
     
             [1 2]     [0]    [1 2]                
     g(x1) = [0 1]x1 + [1] >= [0 0]x1 = b(a(d(x1)))
     
                [1 4]     [2]    [1 4]     [0]           
     g(g(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = c(b(x1))
    problem:
     c(c(x1)) -> d(d(d(x1)))
     c(x1) -> g(x1)
     d(d(x1)) -> f(c(x1))
     g(x1) -> b(a(d(x1)))
    String Reversal Processor:
     c(c(x1)) -> d(d(d(x1)))
     c(x1) -> g(x1)
     d(d(x1)) -> c(f(x1))
     g(x1) -> d(a(b(x1)))
     Bounds Processor:
      bound: 3
      enrichment: match
      automaton:
       final states: {8,6,5,1}
       transitions:
        d1(33) -> 34*
        a1(32) -> 33*
        b1(31) -> 32*
        c1(22) -> 23*
        c1(19) -> 20*
        f1(69) -> 70*
        f1(71) -> 72*
        f1(21) -> 22*
        f1(18) -> 19*
        g1(11) -> 12*
        d2(45) -> 46*
        a2(44) -> 45*
        f60() -> 2*
        b2(43) -> 44*
        d0(10) -> 8*
        d0(2) -> 3*
        d0(4) -> 1*
        d0(3) -> 4*
        g2(35) -> 36*
        g2(41) -> 42*
        g0(2) -> 5*
        d3(65) -> 66*
        d3(53) -> 54*
        c0(7) -> 6*
        a3(52) -> 53*
        a3(64) -> 65*
        f0(2) -> 7*
        b3(51) -> 52*
        b3(63) -> 64*
        a0(9) -> 10*
        b0(2) -> 9*
        2 -> 31,18
        3 -> 21*
        6 -> 3,21
        7 -> 11*
        11 -> 43*
        12 -> 6*
        19 -> 41*
        20 -> 4*
        22 -> 35*
        23 -> 1*
        34 -> 5*
        35 -> 51*
        36 -> 23,1
        41 -> 63*
        42 -> 20,4
        45 -> 71*
        46 -> 12,6
        54 -> 36,23
        65 -> 69*
        66 -> 42*
        70 -> 22*
        72 -> 19*
      problem:
       
      Qed