/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(f(x)) -> f(c(f(x)))
 f(f(x)) -> f(d(f(x)))
 g(c(x)) -> x
 g(d(x)) -> x
 g(c(0())) -> g(d(1()))
 g(c(1())) -> g(d(0()))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
         [0]
   [1] = [0]
         [1],
   
         [0]
   [0] = [0]
         [1],
   
             [1 1 0]  
   [g](x0) = [1 0 1]x0
             [0 1 0]  ,
   
             [1 0 0]  
   [d](x0) = [0 0 1]x0
             [0 1 0]  ,
   
             [1 1 0]  
   [c](x0) = [0 0 1]x0
             [0 0 0]  ,
   
             [1 0 1]     [0]
   [f](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [1]
  orientation:
             [1 0 1]    [1]    [1 0 1]    [0]             
   f(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(c(f(x)))
             [0 0 0]    [1]    [0 0 0]    [1]             
   
             [1 0 1]    [1]    [1 0 1]    [0]             
   f(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(d(f(x)))
             [0 0 0]    [1]    [0 0 0]    [1]             
   
             [1 1 1]          
   g(c(x)) = [1 1 0]x >= x = x
             [0 0 1]          
   
             [1 0 1]          
   g(d(x)) = [1 1 0]x >= x = x
             [0 0 1]          
   
               [1]    [1]            
   g(c(0())) = [0] >= [0] = g(d(1()))
               [1]    [1]            
   
               [1]    [1]            
   g(c(1())) = [0] >= [0] = g(d(0()))
               [1]    [1]            
  problem:
   g(c(x)) -> x
   g(d(x)) -> x
   g(c(0())) -> g(d(1()))
   g(c(1())) -> g(d(0()))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [1] = 2,
    
    [0] = 2,
    
    [g](x0) = x0 + 5,
    
    [d](x0) = x0,
    
    [c](x0) = x0
   orientation:
    g(c(x)) = x + 5 >= x = x
    
    g(d(x)) = x + 5 >= x = x
    
    g(c(0())) = 7 >= 7 = g(d(1()))
    
    g(c(1())) = 7 >= 7 = g(d(0()))
   problem:
    g(c(0())) -> g(d(1()))
    g(c(1())) -> g(d(0()))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
           [0]
     [1] = [0]
           [0],
     
           [0]
     [0] = [0]
           [0],
     
               [1 0 1]  
     [g](x0) = [0 0 0]x0
               [0 0 0]  ,
     
               [1 0 0]  
     [d](x0) = [0 0 0]x0
               [0 0 0]  ,
     
               [1 0 0]     [0]
     [c](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1]
    orientation:
                 [1]    [0]            
     g(c(0())) = [0] >= [0] = g(d(1()))
                 [0]    [0]            
     
                 [1]    [0]            
     g(c(1())) = [0] >= [0] = g(d(0()))
                 [0]    [0]            
    problem:
     
    Qed