/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem:
 -(x,0()) -> x
 -(0(),s(y)) -> 0()
 -(s(x),s(y)) -> -(x,y)
 f(0()) -> 0()
 f(s(x)) -> -(s(x),g(f(x)))
 g(0()) -> s(0())
 g(s(x)) -> -(s(x),f(g(x)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 2x0 + 1,
   
   [f](x0) = 2x0,
   
   [s](x0) = 4x0 + 1,
   
   [-](x0, x1) = x0 + x1,
   
   [0] = 0
  orientation:
   -(x,0()) = x >= x = x
   
   -(0(),s(y)) = 4y + 1 >= 0 = 0()
   
   -(s(x),s(y)) = 4x + 4y + 2 >= x + y = -(x,y)
   
   f(0()) = 0 >= 0 = 0()
   
   f(s(x)) = 8x + 2 >= 8x + 2 = -(s(x),g(f(x)))
   
   g(0()) = 1 >= 1 = s(0())
   
   g(s(x)) = 8x + 3 >= 8x + 3 = -(s(x),f(g(x)))
  problem:
   -(x,0()) -> x
   f(0()) -> 0()
   f(s(x)) -> -(s(x),g(f(x)))
   g(0()) -> s(0())
   g(s(x)) -> -(s(x),f(g(x)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0) = 4x0 + 4,
    
    [f](x0) = 4x0,
    
    [s](x0) = 7x0 + 4,
    
    [-](x0, x1) = x0 + x1,
    
    [0] = 0
   orientation:
    -(x,0()) = x >= x = x
    
    f(0()) = 0 >= 0 = 0()
    
    f(s(x)) = 28x + 16 >= 23x + 8 = -(s(x),g(f(x)))
    
    g(0()) = 4 >= 4 = s(0())
    
    g(s(x)) = 28x + 20 >= 23x + 20 = -(s(x),f(g(x)))
   problem:
    -(x,0()) -> x
    f(0()) -> 0()
    g(0()) -> s(0())
    g(s(x)) -> -(s(x),f(g(x)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0) = 2x0 + 4,
     
     [f](x0) = x0,
     
     [s](x0) = 2x0 + 4,
     
     [-](x0, x1) = x0 + x1 + 4,
     
     [0] = 1
    orientation:
     -(x,0()) = x + 5 >= x = x
     
     f(0()) = 1 >= 1 = 0()
     
     g(0()) = 6 >= 6 = s(0())
     
     g(s(x)) = 4x + 12 >= 4x + 12 = -(s(x),f(g(x)))
    problem:
     f(0()) -> 0()
     g(0()) -> s(0())
     g(s(x)) -> -(s(x),f(g(x)))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [g](x0) = 4x0 + 3,
      
      [f](x0) = 2x0,
      
      [s](x0) = 3x0 + 4,
      
      [-](x0, x1) = x0 + x1 + 4,
      
      [0] = 3
     orientation:
      f(0()) = 6 >= 3 = 0()
      
      g(0()) = 15 >= 13 = s(0())
      
      g(s(x)) = 12x + 19 >= 11x + 14 = -(s(x),f(g(x)))
     problem:
      
     Qed