/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:
 a__f(a(),X,X) -> a__f(X,a__b(),b())
 a__b() -> a()
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
 mark(b()) -> a__b()
 mark(a()) -> a()
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 a__b() -> b()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [mark](x0) = 2x0,
   
   [f](x0, x1, x2) = 3x0 + 2x1 + 2x2 + 2,
   
   [b] = 0,
   
   [a__b] = 0,
   
   [a__f](x0, x1, x2) = 6x0 + 2x1 + 4x2 + 4,
   
   [a] = 0
  orientation:
   a__f(a(),X,X) = 6X + 4 >= 6X + 4 = a__f(X,a__b(),b())
   
   a__b() = 0 >= 0 = a()
   
   mark(f(X1,X2,X3)) = 6X1 + 4X2 + 4X3 + 4 >= 6X1 + 4X2 + 4X3 + 4 = a__f(X1,mark(X2),X3)
   
   mark(b()) = 0 >= 0 = a__b()
   
   mark(a()) = 0 >= 0 = a()
   
   a__f(X1,X2,X3) = 6X1 + 2X2 + 4X3 + 4 >= 3X1 + 2X2 + 2X3 + 2 = f(X1,X2,X3)
   
   a__b() = 0 >= 0 = b()
  problem:
   a__f(a(),X,X) -> a__f(X,a__b(),b())
   a__b() -> a()
   mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
   mark(b()) -> a__b()
   mark(a()) -> a()
   a__b() -> b()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark](x0) = 4x0 + 7,
    
    [f](x0, x1, x2) = 4x0 + 4x1 + 4x2 + 2,
    
    [b] = 0,
    
    [a__b] = 4,
    
    [a__f](x0, x1, x2) = 4x0 + 2x1 + 4x2,
    
    [a] = 4
   orientation:
    a__f(a(),X,X) = 6X + 16 >= 4X + 8 = a__f(X,a__b(),b())
    
    a__b() = 4 >= 4 = a()
    
    mark(f(X1,X2,X3)) = 16X1 + 16X2 + 16X3 + 15 >= 4X1 + 8X2 + 4X3 + 14 = a__f(X1,mark(X2),X3)
    
    mark(b()) = 7 >= 4 = a__b()
    
    mark(a()) = 23 >= 4 = a()
    
    a__b() = 4 >= 0 = b()
   problem:
    a__b() -> a()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
              [1]
     [a__b] = [0]
              [1],
     
           [0]
     [a] = [0]
           [0]
    orientation:
              [1]    [0]      
     a__b() = [0] >= [0] = a()
              [1]    [0]      
    problem:
     
    Qed