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


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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=2
  
  interpretation:
             [1 1]  
   [w](x0) = [0 2]x0,
   
             [1 0]     [1]
   [v](x0) = [0 2]x0 + [0],
   
             [1 0]     [0]
   [u](x0) = [2 1]x0 + [1],
   
               
   [c](x0) = x0,
   
               
   [a](x0) = x0,
   
               
   [b](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)))
   
             [1 0]    [0]         
   u(a(x)) = [2 1]x + [1] >= x = x
   
             [1 0]    [1]         
   v(b(x)) = [0 2]x + [0] >= x = x
   
             [1 1]          
   w(c(x)) = [0 2]x >= x = x
   
             [1 0]    [0]         
   a(u(x)) = [2 1]x + [1] >= x = x
   
             [1 0]    [1]         
   b(v(x)) = [0 2]x + [0] >= x = x
   
             [1 1]          
   c(w(x)) = [0 2]x >= x = x
  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
   w(c(x)) -> x
   a(u(x)) -> x
   c(w(x)) -> x
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [w](x0) = x0 + 2,
    
    [u](x0) = 10x0,
    
    [c](x0) = x0,
    
    [a](x0) = x0,
    
    [b](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)) = 10x >= x = x
    
    w(c(x)) = x + 2 >= x = x
    
    a(u(x)) = 10x >= x = x
    
    c(w(x)) = x + 2 >= x = x
   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
    a(u(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)))
    a(u(x)) -> x
    u(a(x)) -> x
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [u](x0) = x0 + 1,
      
      [c](x0) = x0,
      
      [a](x0) = x0,
      
      [b](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)))
      
      a(u(x)) = x + 1 >= x = x
      
      u(a(x)) = x + 1 >= 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(2) -> 9*
        a0(4) -> 1*
        a0(3) -> 4*
        b0(7) -> 5*
        b0(2) -> 3*
        b0(6) -> 7*
        c0(10) -> 8*
        c0(2) -> 6*
        c0(9) -> 10*
        f60() -> 2*
        1 -> 3*
        5 -> 6*
        8 -> 9*
      problem:
       
      Qed