/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:
 sum(0()) -> 0()
 sum(s(x)) -> +(sum(x),s(x))
 sum1(0()) -> 0()
 sum1(s(x)) -> s(+(sum1(x),+(x,x)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                [1 1 1]     [1]
   [sum1](x0) = [1 1 1]x0 + [0]
                [1 1 1]     [1],
   
                 [1 0 0]     [1 0 0]  
   [+](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
             [1 1 0]     [0]
   [s](x0) = [1 0 0]x0 + [0]
             [1 0 1]     [1],
   
               [1 0 1]  
   [sum](x0) = [0 0 0]x0
               [0 0 0]  ,
   
         [0]
   [0] = [0]
         [0]
  orientation:
              [0]    [0]      
   sum(0()) = [0] >= [0] = 0()
              [0]    [0]      
   
               [2 1 1]    [1]    [2 1 1]                  
   sum(s(x)) = [0 0 0]x + [0] >= [0 0 0]x = +(sum(x),s(x))
               [0 0 0]    [0]    [0 0 0]                  
   
               [1]    [0]      
   sum1(0()) = [0] >= [0] = 0()
               [1]    [0]      
   
                [3 1 1]    [2]    [3 1 1]    [1]                       
   sum1(s(x)) = [3 1 1]x + [1] >= [3 1 1]x + [1] = s(+(sum1(x),+(x,x)))
                [3 1 1]    [2]    [3 1 1]    [2]                       
  problem:
   sum(0()) -> 0()
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                [1 0 0]     [1]
    [sum](x0) = [0 0 0]x0 + [0]
                [0 0 1]     [0],
    
          [0]
    [0] = [0]
          [1]
   orientation:
               [1]    [0]      
    sum(0()) = [0] >= [0] = 0()
               [1]    [1]      
   problem:
    
   Qed