/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem:
 and(tt(),X) -> activate(X)
 plus(N,0()) -> N
 plus(N,s(M)) -> s(plus(N,M))
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                         [1 0 1]  
   [plus](x0, x1) = x0 + [0 0 0]x1
                         [0 0 1]  ,
   
                   [1 0 0]          [1]
   [and](x0, x1) = [0 0 0]x0 + x1 + [0]
                   [0 0 0]          [0],
   
         [0]
   [0] = [0]
         [0],
   
                  [0]
   [s](x0) = x0 + [0]
                  [1],
   
          [0]
   [tt] = [0]
          [0],
   
                      
   [activate](x0) = x0
                      
  orientation:
                     [1]                   
   and(tt(),X) = X + [0] >= X = activate(X)
                     [0]                   
   
                           
   plus(N,0()) = N >= N = N
                           
   
                  [1 0 1]        [1]    [1 0 1]        [0]               
   plus(N,s(M)) = [0 0 0]M + N + [0] >= [0 0 0]M + N + [0] = s(plus(N,M))
                  [0 0 1]        [1]    [0 0 1]        [1]               
   
                           
   activate(X) = X >= X = X
                           
  problem:
   plus(N,0()) -> N
   activate(X) -> X
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                          [1 0 0]     [1]
    [plus](x0, x1) = x0 + [0 0 0]x1 + [1]
                          [0 0 0]     [0],
    
          [0]
    [0] = [0]
          [0],
    
                       
    [activate](x0) = x0
                       
   orientation:
                      [1]         
    plus(N,0()) = N + [1] >= N = N
                      [0]         
    
                            
    activate(X) = X >= X = X
                            
   problem:
    activate(X) -> X
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                           [1]
     [activate](x0) = x0 + [0]
                           [0]
    orientation:
                       [1]         
     activate(X) = X + [0] >= X = X
                       [0]         
    problem:
     
    Qed