/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

Problem:
 a__h(X) -> a__g(mark(X),X)
 a__g(a(),X) -> a__f(b(),X)
 a__f(X,X) -> a__h(a__a())
 a__a() -> b()
 mark(h(X)) -> a__h(mark(X))
 mark(g(X1,X2)) -> a__g(mark(X1),X2)
 mark(a()) -> a__a()
 mark(f(X1,X2)) -> a__f(mark(X1),X2)
 mark(b()) -> b()
 a__h(X) -> h(X)
 a__g(X1,X2) -> g(X1,X2)
 a__a() -> a()
 a__f(X1,X2) -> f(X1,X2)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b] = 0,
   
   [g](x0, x1) = 2x0 + x1 + 2,
   
   [mark](x0) = 3x0,
   
   [a] = 0,
   
   [a__f](x0, x1) = x0 + x1 + 4,
   
   [a__h](x0) = 7x0 + 4,
   
   [h](x0) = 7x0 + 4,
   
   [f](x0, x1) = x0 + x1 + 4,
   
   [a__a] = 0,
   
   [a__g](x0, x1) = 2x0 + x1 + 4
  orientation:
   a__h(X) = 7X + 4 >= 7X + 4 = a__g(mark(X),X)
   
   a__g(a(),X) = X + 4 >= X + 4 = a__f(b(),X)
   
   a__f(X,X) = 2X + 4 >= 4 = a__h(a__a())
   
   a__a() = 0 >= 0 = b()
   
   mark(h(X)) = 21X + 12 >= 21X + 4 = a__h(mark(X))
   
   mark(g(X1,X2)) = 6X1 + 3X2 + 6 >= 6X1 + X2 + 4 = a__g(mark(X1),X2)
   
   mark(a()) = 0 >= 0 = a__a()
   
   mark(f(X1,X2)) = 3X1 + 3X2 + 12 >= 3X1 + X2 + 4 = a__f(mark(X1),X2)
   
   mark(b()) = 0 >= 0 = b()
   
   a__h(X) = 7X + 4 >= 7X + 4 = h(X)
   
   a__g(X1,X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 2 = g(X1,X2)
   
   a__a() = 0 >= 0 = a()
   
   a__f(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 4 = f(X1,X2)
  problem:
   a__h(X) -> a__g(mark(X),X)
   a__g(a(),X) -> a__f(b(),X)
   a__f(X,X) -> a__h(a__a())
   a__a() -> b()
   mark(a()) -> a__a()
   mark(b()) -> b()
   a__h(X) -> h(X)
   a__a() -> a()
   a__f(X1,X2) -> f(X1,X2)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [b] = 0,
    
    [mark](x0) = x0,
    
    [a] = 0,
    
    [a__f](x0, x1) = 2x0 + x1 + 4,
    
    [a__h](x0) = 3x0 + 4,
    
    [h](x0) = 3x0 + 4,
    
    [f](x0, x1) = 2x0 + x1,
    
    [a__a] = 0,
    
    [a__g](x0, x1) = 2x0 + x1 + 4
   orientation:
    a__h(X) = 3X + 4 >= 3X + 4 = a__g(mark(X),X)
    
    a__g(a(),X) = X + 4 >= X + 4 = a__f(b(),X)
    
    a__f(X,X) = 3X + 4 >= 4 = a__h(a__a())
    
    a__a() = 0 >= 0 = b()
    
    mark(a()) = 0 >= 0 = a__a()
    
    mark(b()) = 0 >= 0 = b()
    
    a__h(X) = 3X + 4 >= 3X + 4 = h(X)
    
    a__a() = 0 >= 0 = a()
    
    a__f(X1,X2) = 2X1 + X2 + 4 >= 2X1 + X2 = f(X1,X2)
   problem:
    a__h(X) -> a__g(mark(X),X)
    a__g(a(),X) -> a__f(b(),X)
    a__f(X,X) -> a__h(a__a())
    a__a() -> b()
    mark(a()) -> a__a()
    mark(b()) -> b()
    a__h(X) -> h(X)
    a__a() -> a()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [b] = 0,
     
     [mark](x0) = x0,
     
     [a] = 0,
     
     [a__f](x0, x1) = 6x0 + x1 + 2,
     
     [a__h](x0) = 3x0 + 2,
     
     [h](x0) = 2x0,
     
     [a__a] = 0,
     
     [a__g](x0, x1) = x0 + 2x1 + 2
    orientation:
     a__h(X) = 3X + 2 >= 3X + 2 = a__g(mark(X),X)
     
     a__g(a(),X) = 2X + 2 >= X + 2 = a__f(b(),X)
     
     a__f(X,X) = 7X + 2 >= 2 = a__h(a__a())
     
     a__a() = 0 >= 0 = b()
     
     mark(a()) = 0 >= 0 = a__a()
     
     mark(b()) = 0 >= 0 = b()
     
     a__h(X) = 3X + 2 >= 2X = h(X)
     
     a__a() = 0 >= 0 = a()
    problem:
     a__h(X) -> a__g(mark(X),X)
     a__g(a(),X) -> a__f(b(),X)
     a__f(X,X) -> a__h(a__a())
     a__a() -> b()
     mark(a()) -> a__a()
     mark(b()) -> b()
     a__a() -> a()
    Unfolding Processor:
     loop length: 7
     terms:
      a__g(mark(a__a()),b())
      a__g(mark(a()),b())
      a__g(a__a(),b())
      a__g(a(),b())
      a__f(b(),b())
      a__h(a__a())
      a__g(mark(a__a()),a__a())
     context: []
     substitution:
      
     Qed