/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:
 f(0(x1)) -> s(0(x1))
 d(0(x1)) -> 0(x1)
 d(s(x1)) -> s(s(d(x1)))
 f(s(x1)) -> d(f(x1))

Proof:
 String Reversal Processor:
  0(f(x1)) -> 0(s(x1))
  0(d(x1)) -> 0(x1)
  s(d(x1)) -> d(s(s(x1)))
  s(f(x1)) -> f(d(x1))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [d](x0) = [0 0 0]x0
              [1 0 0]  ,
    
              [1 0 0]     [0]
    [s](x0) = [0 1 1]x0 + [1]
              [0 1 1]     [0],
    
              [1 1 0]     [1]
    [f](x0) = [1 0 1]x0 + [0]
              [1 0 0]     [0],
    
              [1 0 0]  
    [0](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
               [1 1 0]     [1]    [1 0 0]             
    0(f(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 0(s(x1))
               [0 0 0]     [0]    [0 0 0]             
    
               [1 0 0]      [1 0 0]          
    0(d(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 0(x1)
               [0 0 0]      [0 0 0]          
    
               [1 0 0]     [0]    [1 0 0]                
    s(d(x1)) = [1 0 0]x1 + [1] >= [0 0 0]x1 = d(s(s(x1)))
               [1 0 0]     [0]    [1 0 0]                
    
               [1 1 0]     [1]    [1 0 0]     [1]           
    s(f(x1)) = [2 0 1]x1 + [1] >= [2 0 0]x1 + [0] = f(d(x1))
               [2 0 1]     [0]    [1 0 0]     [0]           
   problem:
    0(d(x1)) -> 0(x1)
    s(d(x1)) -> d(s(s(x1)))
    s(f(x1)) -> f(d(x1))
   String Reversal Processor:
    d(0(x1)) -> 0(x1)
    d(s(x1)) -> s(s(d(x1)))
    f(s(x1)) -> d(f(x1))
    Bounds Processor:
     bound: 0
     enrichment: match
     automaton:
      final states: {6,3,1}
      transitions:
       f40() -> 2*
       00(2) -> 1*
       s0(5) -> 3*
       s0(4) -> 5*
       d0(7) -> 6*
       d0(2) -> 4*
       f0(2) -> 7*
       1 -> 4*
       3 -> 4*
       6 -> 7*
     problem:
      
     Qed