/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:
 b(x,y) -> c(a(c(y),a(0(),x)))
 a(y,x) -> y
 a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 1 0]     [1 0 0]  
   [a](x0, x1) = [0 1 1]x0 + [0 0 1]x1
                 [1 1 1]     [1 0 0]  ,
   
         [0]
   [0] = [0]
         [1],
   
             [1 0 0]  
   [c](x0) = [0 0 0]x0
             [0 1 0]  ,
   
                 [1 1 0]     [1 0 0]     [0]
   [b](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                 [1 0 0]     [0 1 0]     [1]
  orientation:
            [1 1 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [0]                      
   b(x,y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = c(a(c(y),a(0(),x)))
            [1 0 0]    [0 1 0]    [1]    [1 0 0]    [0 1 0]    [1]                      
   
            [1 0 0]    [1 1 0]          
   a(y,x) = [0 0 1]x + [0 1 1]y >= y = y
            [1 0 0]    [1 1 1]          
   
                             [1 0 1]    [1 1 0]    [1]    [1 0 1]    [1 0 0]    [0]                          
   a(y,c(b(a(0(),x),0()))) = [0 0 0]x + [0 1 1]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = b(a(c(b(0(),y)),x),0())
                             [1 0 1]    [1 1 1]    [1]    [1 0 0]    [1 0 0]    [1]                          
  problem:
   b(x,y) -> c(a(c(y),a(0(),x)))
   a(y,x) -> y
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                       [1 0 0]  
    [a](x0, x1) = x0 + [0 0 0]x1
                       [0 0 0]  ,
    
          [0]
    [0] = [0]
          [0],
    
              [1 0 0]  
    [c](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                  [1 0 0]     [1 0 0]     [1]
    [b](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                  [0 0 0]     [0 0 0]     [0]
   orientation:
             [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]                       
    b(x,y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = c(a(c(y),a(0(),x)))
             [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                       
    
             [1 0 0]              
    a(y,x) = [0 0 0]x + y >= y = y
             [0 0 0]              
   problem:
    a(y,x) -> y
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                        [1 0 0]     [1]
     [a](x0, x1) = x0 + [0 0 0]x1 + [0]
                        [0 0 0]     [0]
    orientation:
              [1 0 0]        [1]         
     a(y,x) = [0 0 0]x + y + [0] >= y = y
              [0 0 0]        [0]         
    problem:
     
    Qed