/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(0()) -> 1()
 f(s(x)) -> g(f(x))
 g(x) -> +(x,s(x))
 f(s(x)) -> +(f(x),s(f(x)))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                 [1 1]     [2 0]     [1]
   [+](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
   
             [3 2]     [3]
   [g](x0) = [0 0]x0 + [0],
   
             [1 0]     [0]
   [s](x0) = [2 3]x0 + [2],
   
         [0]
   [1] = [0],
   
             [1 2]  
   [f](x0) = [1 0]x0,
   
         [0]
   [0] = [3]
  orientation:
            [6]    [0]      
   f(0()) = [0] >= [0] = 1()
   
             [5 6]    [4]    [5 6]    [3]          
   f(s(x)) = [1 0]x + [0] >= [0 0]x + [0] = g(f(x))
   
          [3 2]    [3]    [3 1]    [1]            
   g(x) = [0 0]x + [0] >= [0 0]x + [0] = +(x,s(x))
   
             [5 6]    [4]    [4 6]    [1]                  
   f(s(x)) = [1 0]x + [0] >= [0 0]x + [0] = +(f(x),s(f(x)))
  problem:
   
  Qed