/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:
 strict:
  g(c(x,s(y))) -> g(c(s(x),y))
  f(c(s(x),y)) -> f(c(x,s(y)))
  f(f(x)) -> f(d(f(x)))
  f(x) -> x
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [1 0]     [0]
   [rand](x0) = [0 2]x0 + [1],
   
             [1 0]  
   [d](x0) = [0 0]x0,
   
                  [1]
   [f](x0) = x0 + [0],
   
             [2 0]     [2]
   [g](x0) = [2 0]x0 + [1],
   
                 [1 0]     [1 0]  
   [c](x0, x1) = [0 0]x0 + [0 2]x1,
   
             [1 0]  
   [s](x0) = [0 0]x0
  orientation:
                  [2 0]    [2 0]    [2]    [2 0]    [2 0]    [2]               
   g(c(x,s(y))) = [2 0]x + [2 0]y + [1] >= [2 0]x + [2 0]y + [1] = g(c(s(x),y))
   
                  [1 0]    [1 0]    [1]    [1 0]    [1 0]    [1]               
   f(c(s(x),y)) = [0 0]x + [0 2]y + [0] >= [0 0]x + [0 0]y + [0] = f(c(x,s(y)))
   
                 [2]    [1 0]    [2]             
   f(f(x)) = x + [0] >= [0 0]x + [0] = f(d(f(x)))
   
              [1]         
   f(x) = x + [0] >= x = x
   
             [1 0]    [0]         
   rand(x) = [0 2]x + [1] >= x = x
   
             [1 0]    [0]    [1 0]    [0]             
   rand(x) = [0 2]x + [1] >= [0 0]x + [1] = rand(s(x))
  problem:
   strict:
    g(c(x,s(y))) -> g(c(s(x),y))
    f(c(s(x),y)) -> f(c(x,s(y)))
    f(f(x)) -> f(d(f(x)))
   weak:
    rand(x) -> x
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                 [2 0]     [1]
    [rand](x0) = [2 1]x0 + [1],
    
              [1 0]  
    [d](x0) = [0 0]x0,
    
              [1 1]  
    [f](x0) = [1 1]x0,
    
              [1 0]     [3]
    [g](x0) = [2 0]x0 + [0],
    
                  [1 0]     [1 0]     [0]
    [c](x0, x1) = [2 2]x0 + [0 0]x1 + [1],
    
                
    [s](x0) = x0
   orientation:
                   [1 0]    [1 0]    [3]    [1 0]    [1 0]    [3]               
    g(c(x,s(y))) = [2 0]x + [2 0]y + [0] >= [2 0]x + [2 0]y + [0] = g(c(s(x),y))
    
                   [3 2]    [1 0]    [1]    [3 2]    [1 0]    [1]               
    f(c(s(x),y)) = [3 2]x + [1 0]y + [1] >= [3 2]x + [1 0]y + [1] = f(c(x,s(y)))
    
              [2 2]     [1 1]              
    f(f(x)) = [2 2]x >= [1 1]x = f(d(f(x)))
    
              [2 0]    [1]         
    rand(x) = [2 1]x + [1] >= x = x
    
              [2 0]    [1]    [2 0]    [1]             
    rand(x) = [2 1]x + [1] >= [2 1]x + [1] = rand(s(x))
   problem:
    strict:
     g(c(x,s(y))) -> g(c(s(x),y))
     f(c(s(x),y)) -> f(c(x,s(y)))
     f(f(x)) -> f(d(f(x)))
    weak:
     rand(x) -> rand(s(x))
   Bounds Processor:
    bound: 1
    enrichment: match-rt
    automaton:
     final states: {7}
     transitions:
      c1(7,14) -> 15*
      s1(7) -> 14*
      s1(14) -> 14*
      f1(15) -> 7*
      f1(7) -> 7*
      d1(7) -> 15*
      g0(7) -> 7*
      rand1(14) -> 7*
      c0(7,7) -> 7*
      s0(7) -> 7*
      f0(7) -> 7*
      d0(7) -> 7*
      rand0(7) -> 7*
    problem:
     strict:
      g(c(x,s(y))) -> g(c(s(x),y))
      f(f(x)) -> f(d(f(x)))
     weak:
      rand(x) -> rand(s(x))
    Matrix Interpretation Processor: dim=2
     
     interpretation:
                   [1 0]  
      [rand](x0) = [0 0]x0,
      
                     [0]
      [d](x0) = x0 + [1],
      
                [1 0]     [0]
      [f](x0) = [0 0]x0 + [1],
      
                [1 1]  
      [g](x0) = [2 0]x0,
      
                    [1 0]     [1 0]  
      [c](x0, x1) = [2 0]x0 + [2 1]x1,
      
                [1 0]     [0]
      [s](x0) = [0 2]x0 + [1]
     orientation:
                     [3 0]    [3 2]    [1]    [3 0]    [3 1]                
      g(c(x,s(y))) = [2 0]x + [2 0]y + [0] >= [2 0]x + [2 0]y = g(c(s(x),y))
      
                [1 0]    [0]    [1 0]    [0]             
      f(f(x)) = [0 0]x + [1] >= [0 0]x + [1] = f(d(f(x)))
      
                [1 0]     [1 0]              
      rand(x) = [0 0]x >= [0 0]x = rand(s(x))
     problem:
      strict:
       f(f(x)) -> f(d(f(x)))
      weak:
       rand(x) -> rand(s(x))
     String Reversal Processor:
      strict:
       f(f(x)) -> f(d(f(x)))
      weak:
       rand(x) -> s(rand(x))
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
                     [4 2]  
        [rand](x0) = [4 6]x0,
        
                  [0  0 ]  
        [d](x0) = [-& -&]x0,
        
                  [0 5]  
        [f](x0) = [0 4]x0,
        
                  [0  -&]  
        [s](x0) = [-& -&]x0
       orientation:
                  [5 9]     [0 5]              
        f(f(x)) = [4 8]x >= [0 5]x = f(d(f(x)))
        
                  [4 2]     [4  2 ]              
        rand(x) = [4 6]x >= [-& -&]x = s(rand(x))
       problem:
        strict:
         
        weak:
         rand(x) -> s(rand(x))
       Qed