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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [mark](x0) = 6x0,
   
   [f](x0, x1) = 3x0 + 2x1 + 4,
   
   [a__b] = 0,
   
   [b] = 0,
   
   [a] = 0,
   
   [a__f](x0, x1) = 3x0 + 4x1 + 4
  orientation:
   a__f(X,X) = 7X + 4 >= 4 = a__f(a(),b())
   
   a__b() = 0 >= 0 = a()
   
   mark(f(X1,X2)) = 18X1 + 12X2 + 24 >= 18X1 + 4X2 + 4 = a__f(mark(X1),X2)
   
   mark(b()) = 0 >= 0 = a__b()
   
   mark(a()) = 0 >= 0 = a()
   
   a__f(X1,X2) = 3X1 + 4X2 + 4 >= 3X1 + 2X2 + 4 = f(X1,X2)
   
   a__b() = 0 >= 0 = b()
  problem:
   a__f(X,X) -> a__f(a(),b())
   a__b() -> a()
   mark(b()) -> a__b()
   mark(a()) -> a()
   a__f(X1,X2) -> f(X1,X2)
   a__b() -> b()
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 1 0]     [1]
    [mark](x0) = [0 0 0]x0 + [1]
                 [0 0 0]     [0],
    
                  [1 0 0]     [1 0 0]  
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
             [1]
    [a__b] = [1]
             [0],
    
          [0]
    [b] = [1]
          [0],
    
          [0]
    [a] = [1]
          [0],
    
                     [1 0 0]     [1 0 0]     [1]
    [a__f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [0 0 0]     [0 0 0]     [0]
   orientation:
                [2 0 0]    [1]    [1]                
    a__f(X,X) = [0 0 0]X + [0] >= [0] = a__f(a(),b())
                [0 0 0]    [0]    [0]                
    
             [1]    [0]      
    a__b() = [1] >= [1] = a()
             [0]    [0]      
    
                [2]    [1]         
    mark(b()) = [1] >= [1] = a__b()
                [0]    [0]         
    
                [2]    [0]      
    mark(a()) = [1] >= [1] = a()
                [0]    [0]      
    
                  [1 0 0]     [1 0 0]     [1]    [1 0 0]     [1 0 0]             
    a__f(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = f(X1,X2)
                  [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]             
    
             [1]    [0]      
    a__b() = [1] >= [1] = b()
             [0]    [0]      
   problem:
    a__f(X,X) -> a__f(a(),b())
   DP Processor:
    DPs:
     a__f#(X,X) -> a__f#(a(),b())
    TRS:
     a__f(X,X) -> a__f(a(),b())
    EDG Processor:
     DPs:
      a__f#(X,X) -> a__f#(a(),b())
     TRS:
      a__f(X,X) -> a__f(a(),b())
     graph:
      
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 0/1