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


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YES

Problem:
 a__c() -> a__f(g(c()))
 a__f(g(X)) -> g(X)
 mark(c()) -> a__c()
 mark(f(X)) -> a__f(X)
 mark(g(X)) -> g(X)
 a__c() -> c()
 a__f(X) -> f(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [mark](x0) = x0 + 6,
   
   [c] = 0,
   
   [a__f](x0) = x0,
   
   [f](x0) = x0,
   
   [a__c] = 6,
   
   [g](x0) = 4x0 + 6
  orientation:
   a__c() = 6 >= 6 = a__f(g(c()))
   
   a__f(g(X)) = 4X + 6 >= 4X + 6 = g(X)
   
   mark(c()) = 6 >= 6 = a__c()
   
   mark(f(X)) = X + 6 >= X = a__f(X)
   
   mark(g(X)) = 4X + 12 >= 4X + 6 = g(X)
   
   a__c() = 6 >= 0 = c()
   
   a__f(X) = X >= X = f(X)
  problem:
   a__c() -> a__f(g(c()))
   a__f(g(X)) -> g(X)
   mark(c()) -> a__c()
   a__f(X) -> f(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]     [1]
    [mark](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
          [0]
    [c] = [0]
          [0],
    
                 [1 1 0]  
    [a__f](x0) = [0 0 1]x0
                 [0 0 1]  ,
    
              [1 0 0]  
    [f](x0) = [0 0 1]x0
              [0 0 1]  ,
    
             [1]
    [a__c] = [0]
             [0],
    
              [1 0 0]  
    [g](x0) = [0 0 1]x0
              [0 0 1]  
   orientation:
             [1]    [0]               
    a__c() = [0] >= [0] = a__f(g(c()))
             [0]    [0]               
    
                 [1 0 1]     [1 0 0]        
    a__f(g(X)) = [0 0 1]X >= [0 0 1]X = g(X)
                 [0 0 1]     [0 0 1]        
    
                [1]    [1]         
    mark(c()) = [0] >= [0] = a__c()
                [0]    [0]         
    
              [1 1 0]     [1 0 0]        
    a__f(X) = [0 0 1]X >= [0 0 1]X = f(X)
              [0 0 1]     [0 0 1]        
   problem:
    a__f(g(X)) -> g(X)
    mark(c()) -> a__c()
    a__f(X) -> f(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 0 0]     [1]
     [mark](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0],
     
           [0]
     [c] = [0]
           [0],
     
                  [1 0 0]     [1]
     [a__f](x0) = [0 1 0]x0 + [0]
                  [0 0 0]     [0],
     
               [1 0 0]  
     [f](x0) = [0 1 0]x0
               [0 0 0]  ,
     
              [0]
     [a__c] = [0]
              [0],
     
               [1 0 0]  
     [g](x0) = [0 0 1]x0
               [0 0 0]  
    orientation:
                  [1 0 0]    [1]    [1 0 0]        
     a__f(g(X)) = [0 0 1]X + [0] >= [0 0 1]X = g(X)
                  [0 0 0]    [0]    [0 0 0]        
     
                 [1]    [0]         
     mark(c()) = [0] >= [0] = a__c()
                 [0]    [0]         
     
               [1 0 0]    [1]    [1 0 0]        
     a__f(X) = [0 1 0]X + [0] >= [0 1 0]X = f(X)
               [0 0 0]    [0]    [0 0 0]        
    problem:
     
    Qed