/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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NO

Problem:
 h(X,Z) -> f(X,s(X),Z)
 f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
 g(0(),Y) -> 0()
 g(X,s(Y)) -> g(X,Y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [0] = 0,
   
   [g](x0, x1) = 4x0 + 2x1 + 1,
   
   [f](x0, x1, x2) = x0 + 2x1 + 4x2,
   
   [s](x0) = 2x0,
   
   [h](x0, x1) = 5x0 + 4x1
  orientation:
   h(X,Z) = 5X + 4Z >= 5X + 4Z = f(X,s(X),Z)
   
   f(X,Y,g(X,Y)) = 17X + 10Y + 4 >= 16X + 8Y + 4 = h(0(),g(X,Y))
   
   g(0(),Y) = 2Y + 1 >= 0 = 0()
   
   g(X,s(Y)) = 4X + 4Y + 1 >= 4X + 2Y + 1 = g(X,Y)
  problem:
   h(X,Z) -> f(X,s(X),Z)
   f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
   g(X,s(Y)) -> g(X,Y)
  Matrix Interpretation Processor: dim=2
   
   interpretation:
          [0]
    [0] = [0],
    
                  [3 0]     [2 2]     [1]
    [g](x0, x1) = [1 0]x0 + [0 0]x1 + [3],
    
                      [1 0]     [1 0]     [2 0]  
    [f](x0, x1, x2) = [0 0]x0 + [0 0]x1 + [1 1]x2,
    
              [2 0]     [0]
    [s](x0) = [1 1]x0 + [1],
    
                  [3 0]     [2 0]  
    [h](x0, x1) = [0 0]x0 + [1 1]x1
   orientation:
             [3 0]    [2 0]     [3 0]    [2 0]               
    h(X,Z) = [0 0]X + [1 1]Z >= [0 0]X + [1 1]Z = f(X,s(X),Z)
    
                    [7 0]    [5 4]    [2]    [6 0]    [4 4]    [2]                
    f(X,Y,g(X,Y)) = [4 0]X + [2 2]Y + [4] >= [4 0]X + [2 2]Y + [4] = h(0(),g(X,Y))
    
                [3 0]    [6 2]    [3]    [3 0]    [2 2]    [1]         
    g(X,s(Y)) = [1 0]X + [0 0]Y + [3] >= [1 0]X + [0 0]Y + [3] = g(X,Y)
   problem:
    h(X,Z) -> f(X,s(X),Z)
    f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
   Unfolding Processor:
    loop length: 2
    terms:
     h(0(),g(0(),s(0())))
     f(0(),s(0()),g(0(),s(0())))
    context: []
    substitution:
     
    Qed