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


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YES

Problem:
 fib(0()) -> 0()
 fib(s(0())) -> s(0())
 fib(s(s(x))) -> +(fib(s(x)),fib(x))

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