/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /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,
   
   [s](x0) = x0,
   
   [g](x0, x1) = 3x0 + 4x1 + 4,
   
   [h](x0, x1) = 5x0 + 4x1,
   
   [f](x0, x1, x2) = 4x0 + x1 + 4x2
  orientation:
   h(X,Z) = 5X + 4Z >= 5X + 4Z = f(X,s(X),Z)
   
   f(X,Y,g(X,Y)) = 16X + 17Y + 16 >= 12X + 16Y + 16 = h(0(),g(X,Y))
   
   g(0(),Y) = 4Y + 4 >= 0 = 0()
   
   g(X,s(Y)) = 3X + 4Y + 4 >= 3X + 4Y + 4 = 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],
    
              [1 1]     [0]
    [s](x0) = [0 1]x0 + [3],
    
                  [2 0]     [1 1]     [0]
    [g](x0, x1) = [0 0]x0 + [0 0]x1 + [2],
    
                  [3 2]     [2 0]  
    [h](x0, x1) = [2 0]x0 + [0 2]x1,
    
                      [1 0]     [2 0]     [2 0]  
    [f](x0, x1, x2) = [1 0]x0 + [0 0]x1 + [0 2]x2
   orientation:
             [3 2]    [2 0]     [3 2]    [2 0]               
    h(X,Z) = [2 0]X + [0 2]Z >= [1 0]X + [0 2]Z = f(X,s(X),Z)
    
                    [5 0]    [4 2]    [0]    [4 0]    [2 2]    [0]                
    f(X,Y,g(X,Y)) = [1 0]X + [0 0]Y + [4] >= [0 0]X + [0 0]Y + [4] = h(0(),g(X,Y))
    
                [2 0]    [1 2]    [3]    [2 0]    [1 1]    [0]         
    g(X,s(Y)) = [0 0]X + [0 0]Y + [2] >= [0 0]X + [0 0]Y + [2] = 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