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

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [1 0]  
   [rand](x0) = [0 2]x0,
   
             [1 0]  
   [s](x0) = [0 0]x0,
   
                 [1 0]     [1 2]  
   [f](x0, x1) = [0 0]x0 + [1 2]x1,
   
             [1 2]     [0]
   [c](x0) = [1 0]x0 + [1]
  orientation:
               [1 0]    [3 2]    [2]    [1 0]    [2 2]                  
   f(x,c(y)) = [0 0]x + [3 2]y + [2] >= [0 0]x + [2 2]y = f(x,s(f(y,y)))
   
               [1 0]    [1 2]     [1 0]    [1 2]                
   f(s(x),y) = [0 0]x + [1 2]y >= [0 0]x + [1 2]y = f(x,s(c(y)))
   
             [1 0]          
   rand(x) = [0 2]x >= x = x
   
             [1 0]     [1 0]              
   rand(x) = [0 2]x >= [0 0]x = rand(s(x))
  problem:
   strict:
    f(s(x),y) -> f(x,s(c(y)))
   weak:
    rand(x) -> x
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                 [1 0]     [1]
    [rand](x0) = [0 2]x0 + [0],
    
              [1 0]  
    [s](x0) = [0 0]x0,
    
                  [2 0]     [1 0]     [1]
    [f](x0, x1) = [0 0]x0 + [2 0]x1 + [0],
    
              [1 0]  
    [c](x0) = [0 0]x0
   orientation:
                [2 0]    [1 0]    [1]    [2 0]    [1 0]    [1]               
    f(s(x),y) = [0 0]x + [2 0]y + [0] >= [0 0]x + [2 0]y + [0] = f(x,s(c(y)))
    
              [1 0]    [1]         
    rand(x) = [0 2]x + [0] >= x = x
    
              [1 0]    [1]    [1 0]    [1]             
    rand(x) = [0 2]x + [0] >= [0 0]x + [0] = rand(s(x))
   problem:
    strict:
     f(s(x),y) -> f(x,s(c(y)))
    weak:
     rand(x) -> rand(s(x))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                  [1 0]     [2]
     [rand](x0) = [0 0]x0 + [0],
     
                    [0]
     [s](x0) = x0 + [2],
     
                   [2 1]     [2 0]     [0]
     [f](x0, x1) = [0 0]x0 + [0 0]x1 + [2],
     
               [1 0]  
     [c](x0) = [0 2]x0
    orientation:
                 [2 1]    [2 0]    [2]    [2 1]    [2 0]    [0]               
     f(s(x),y) = [0 0]x + [0 0]y + [2] >= [0 0]x + [0 0]y + [2] = f(x,s(c(y)))
     
               [1 0]    [2]    [1 0]    [2]             
     rand(x) = [0 0]x + [0] >= [0 0]x + [0] = rand(s(x))
    problem:
     strict:
      
     weak:
      rand(x) -> rand(s(x))
    Qed