/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem:
 a(b(x)) -> b(a(a(x)))
 b(c(x)) -> c(b(b(x)))
 c(a(x)) -> a(c(c(x)))
 u(a(x)) -> x
 v(b(x)) -> x
 w(c(x)) -> x
 a(u(x)) -> x
 b(v(x)) -> x
 c(w(x)) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [v](x0) = 4x0,
   
   [a](x0) = x0,
   
   [u](x0) = 2x0 + 4,
   
   [w](x0) = 8x0,
   
   [b](x0) = x0,
   
   [c](x0) = x0
  orientation:
   a(b(x)) = x >= x = b(a(a(x)))
   
   b(c(x)) = x >= x = c(b(b(x)))
   
   c(a(x)) = x >= x = a(c(c(x)))
   
   u(a(x)) = 2x + 4 >= x = x
   
   v(b(x)) = 4x >= x = x
   
   w(c(x)) = 8x >= x = x
   
   a(u(x)) = 2x + 4 >= x = x
   
   b(v(x)) = 4x >= x = x
   
   c(w(x)) = 8x >= x = x
  problem:
   a(b(x)) -> b(a(a(x)))
   b(c(x)) -> c(b(b(x)))
   c(a(x)) -> a(c(c(x)))
   v(b(x)) -> x
   w(c(x)) -> x
   b(v(x)) -> x
   c(w(x)) -> x
  String Reversal Processor:
   b(a(x)) -> a(a(b(x)))
   c(b(x)) -> b(b(c(x)))
   a(c(x)) -> c(c(a(x)))
   b(v(x)) -> x
   c(w(x)) -> x
   v(b(x)) -> x
   w(c(x)) -> x
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [v](x0) = x0 + 2,
     
     [a](x0) = x0,
     
     [w](x0) = 2x0,
     
     [b](x0) = x0,
     
     [c](x0) = x0
    orientation:
     b(a(x)) = x >= x = a(a(b(x)))
     
     c(b(x)) = x >= x = b(b(c(x)))
     
     a(c(x)) = x >= x = c(c(a(x)))
     
     b(v(x)) = x + 2 >= x = x
     
     c(w(x)) = 2x >= x = x
     
     v(b(x)) = x + 2 >= x = x
     
     w(c(x)) = 2x >= x = x
    problem:
     b(a(x)) -> a(a(b(x)))
     c(b(x)) -> b(b(c(x)))
     a(c(x)) -> c(c(a(x)))
     c(w(x)) -> x
     w(c(x)) -> x
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [a](x0) = x0,
      
      [w](x0) = 2x0 + 8,
      
      [b](x0) = x0,
      
      [c](x0) = x0
     orientation:
      b(a(x)) = x >= x = a(a(b(x)))
      
      c(b(x)) = x >= x = b(b(c(x)))
      
      a(c(x)) = x >= x = c(c(a(x)))
      
      c(w(x)) = 2x + 8 >= x = x
      
      w(c(x)) = 2x + 8 >= x = x
     problem:
      b(a(x)) -> a(a(b(x)))
      c(b(x)) -> b(b(c(x)))
      a(c(x)) -> c(c(a(x)))
     Bounds Processor:
      bound: 0
      enrichment: match
      automaton:
       final states: {8,5,1}
       transitions:
        a0(3) -> 4*
        a0(4) -> 1*
        a0(2) -> 9*
        f60() -> 2*
        b0(2) -> 3*
        b0(6) -> 7*
        b0(7) -> 5*
        c0(2) -> 6*
        c0(10) -> 8*
        c0(9) -> 10*
        8 -> 9*
        1 -> 3*
        5 -> 6*
      problem:
       
      Qed