/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /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:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 2]     [1]
   [f](x0) = [0 0]x0 + [0],
   
             [1 2]     [0]
   [d](x0) = [0 0]x0 + [1],
   
             [1 2]     [1]
   [g](x0) = [0 0]x0 + [1],
   
             [1 0]  
   [a](x0) = [0 0]x0,
   
             [1 2]     [1]
   [b](x0) = [0 0]x0 + [1],
   
             [1 2]     [1]
   [c](x0) = [0 0]x0 + [1]
  orientation:
              [1 2]     [4]    [1 2]     [3]           
   b(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(d(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] = c(f(x1))
   
                 [1 2]     [4]    [1 2]     [4]           
   d(d(d(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = g(c(x1))
   
           [1 2]     [1]    [1 2]     [1]           
   f(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(g(x1))
   
           [1 2]     [1]    [1 2]     [1]              
   g(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = d(a(b(x1)))
   
              [1 2]     [4]    [1 2]     [4]           
   g(g(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(x1))
  problem:
   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))
  String Reversal Processor:
   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=3
    
    interpretation:
               [1 0 0]     [0]
     [f](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 1 0]     [0]
     [d](x0) = [0 0 1]x0 + [0]
               [0 0 0]     [1],
     
               [1 1 0]     [0]
     [g](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
     
               [1 0 0]     [0]
     [a](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
     
               [1 1 0]  
     [b](x0) = [0 0 0]x0
               [0 0 0]  ,
     
               [1 1 0]     [0]
     [c](x0) = [0 0 1]x0 + [1]
               [0 1 0]     [0]
    orientation:
                [1 1 1]     [1]    [1 1 1]     [1]              
     c(c(x1)) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [1] = d(d(d(x1)))
                [0 0 1]     [1]    [0 0 0]     [1]              
     
             [1 1 0]     [0]    [1 1 0]     [0]        
     c(x1) = [0 0 1]x1 + [1] >= [0 0 0]x1 + [1] = g(x1)
             [0 1 0]     [0]    [0 0 0]     [0]        
     
                [1 1 1]     [0]    [1 1 0]     [0]           
     d(d(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = f(c(x1))
                [0 0 0]     [1]    [0 0 0]     [0]           
     
                   [1 1 1]     [1]    [1 1 0]     [1]           
     d(d(d(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(g(x1))
                   [0 0 0]     [1]    [0 0 0]     [1]           
     
             [1 0 0]     [0]    [1 0 0]     [0]           
     f(x1) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = g(a(x1))
             [0 0 0]     [0]    [0 0 0]     [0]           
     
             [1 1 0]     [0]    [1 1 0]                
     g(x1) = [0 0 0]x1 + [1] >= [0 0 0]x1 = b(a(d(x1)))
             [0 0 0]     [0]    [0 0 0]                
     
                [1 1 0]     [1]    [1 1 0]     [0]           
     g(g(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(b(x1))
                [0 0 0]     [0]    [0 0 0]     [0]           
    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)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]  
      [f](x0) = [0 1 0]x0
                [0 0 0]  ,
      
                [1 0 1]     [0]
      [d](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1],
      
                [1 0 1]  
      [g](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 0 0]     [0]
      [a](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0],
      
                [1 0 0]  
      [b](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 0 1]     [1]
      [c](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0]
     orientation:
                 [1 1 1]     [2]    [1 0 1]     [2]              
      c(c(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = d(d(d(x1)))
                 [0 0 0]     [1]    [0 0 0]     [1]              
      
              [1 0 1]     [1]    [1 0 1]          
      c(x1) = [0 0 0]x1 + [1] >= [0 0 0]x1 = g(x1)
              [0 1 0]     [0]    [0 0 0]          
      
                 [1 0 1]     [1]    [1 0 1]     [1]           
      d(d(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = f(c(x1))
                 [0 0 0]     [1]    [0 0 0]     [0]           
      
                    [1 0 1]     [2]    [1 0 1]     [1]           
      d(d(d(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(g(x1))
                    [0 0 0]     [1]    [0 0 0]     [0]           
      
              [1 0 0]      [1 0 0]             
      f(x1) = [0 1 0]x1 >= [0 0 0]x1 = g(a(x1))
              [0 0 0]      [0 0 0]             
      
              [1 0 1]      [1 0 1]                
      g(x1) = [0 0 0]x1 >= [0 0 0]x1 = b(a(d(x1)))
              [0 0 0]      [0 0 0]                
     problem:
      c(c(x1)) -> d(d(d(x1)))
      d(d(x1)) -> f(c(x1))
      f(x1) -> g(a(x1))
      g(x1) -> b(a(d(x1)))
     String Reversal Processor:
      c(c(x1)) -> d(d(d(x1)))
      d(d(x1)) -> c(f(x1))
      f(x1) -> a(g(x1))
      g(x1) -> d(a(b(x1)))
      Bounds Processor:
       bound: 4
       enrichment: match
       automaton:
        final states: {7}
        transitions:
         b2(62) -> 63*
         c0(7) -> 7*
         a4(127) -> 128*
         a4(146) -> 147*
         a4(135) -> 136*
         a4(115) -> 116*
         g2(59) -> 60*
         g2(82) -> 83*
         b1(26) -> 27*
         d3(103) -> 104*
         d3(124) -> 125*
         c1(17) -> 18*
         f0(7) -> 7*
         b4(145) -> 146*
         b4(153) -> 154*
         b4(134) -> 135*
         b4(114) -> 115*
         b4(126) -> 127*
         d0(7) -> 7*
         a1(27) -> 28*
         a1(24) -> 25*
         d1(71) -> 72*
         d1(12) -> 13*
         d1(33) -> 34*
         d1(14) -> 15*
         d1(13) -> 14*
         a0(7) -> 7*
         a3(90) -> 91*
         a3(112) -> 113*
         a3(102) -> 103*
         a3(80) -> 81*
         a3(123) -> 124*
         a3(93) -> 94*
         f2(105) -> 106*
         f2(35) -> 36*
         f2(73) -> 74*
         f2(52) -> 53*
         f2(45) -> 46*
         b0(7) -> 7*
         d4(136) -> 137*
         d4(128) -> 129*
         d4(147) -> 148*
         d4(116) -> 117*
         b3(122) -> 123*
         b3(101) -> 102*
         g0(7) -> 7*
         f1(16) -> 17*
         f1(43) -> 44*
         g3(111) -> 112*
         g3(79) -> 80*
         g3(89) -> 90*
         g3(92) -> 93*
         g3(138) -> 139*
         d2(64) -> 65*
         a2(60) -> 61*
         a2(83) -> 84*
         a2(63) -> 64*
         c2(53) -> 54*
         c2(46) -> 47*
         c2(36) -> 37*
         g1(23) -> 24*
         94 -> 36*
         43 -> 82*
         92 -> 126*
         74 -> 46*
         148 -> 112*
         154 -> 115*
         47 -> 14*
         17 -> 33*
         35 -> 92*
         137 -> 80*
         113 -> 74*
         7 -> 26,23,16,12
         104 -> 60*
         12 -> 45*
         14 -> 52,43
         16 -> 59*
         106 -> 46*
         45 -> 89*
         28 -> 14*
         117 -> 139,90
         82 -> 122*
         105 -> 138*
         52 -> 79*
         54 -> 13*
         138 -> 153*
         72 -> 13*
         36 -> 71*
         91 -> 106,46
         79 -> 134*
         125 -> 83*
         73 -> 111*
         44 -> 17*
         139 -> 90*
         13 -> 35*
         71 -> 105*
         65 -> 24*
         34 -> 13*
         59 -> 101*
         37 -> 15*
         18 -> 13,7
         84 -> 44*
         129 -> 93*
         15 -> 7*
         81 -> 53*
         89 -> 114*
         61 -> 17*
         25 -> 7*
         111 -> 145*
         23 -> 62*
         33 -> 73*
       problem:
        
       Qed