/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__f(b(),X,c()) -> a__f(X,a__c(),X)
 a__c() -> b()
 mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
 mark(c()) -> a__c()
 mark(b()) -> b()
 a__f(X1,X2,X3) -> f(X1,X2,X3)
 a__c() -> c()

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                     [1 1]     [3 1]     [2 0]     [0]
   [f](x0, x1, x2) = [0 0]x0 + [0 3]x1 + [0 3]x2 + [1],
   
         [1]
   [c] = [0],
   
            [1]
   [a__c] = [0],
   
                [1 2]     [1]
   [mark](x0) = [0 1]x0 + [0],
   
         [1]
   [b] = [0],
   
                        [1 1]     [3 1]     [2 0]     [0]
   [a__f](x0, x1, x2) = [0 0]x0 + [0 3]x1 + [0 3]x2 + [1]
  orientation:
                     [3 1]    [3]    [3 1]    [3]                   
   a__f(b(),X,c()) = [0 3]X + [1] >= [0 3]X + [1] = a__f(X,a__c(),X)
   
            [1]    [1]      
   a__c() = [0] >= [0] = b()
   
                       [1 1]     [3 7]     [2 6]     [3]    [1 1]     [3 7]     [2 0]     [3]                       
   mark(f(X1,X2,X3)) = [0 0]X1 + [0 3]X2 + [0 3]X3 + [1] >= [0 0]X1 + [0 3]X2 + [0 3]X3 + [1] = a__f(X1,mark(X2),X3)
   
               [2]    [1]         
   mark(c()) = [0] >= [0] = a__c()
   
               [2]    [1]      
   mark(b()) = [0] >= [0] = b()
   
                    [1 1]     [3 1]     [2 0]     [0]    [1 1]     [3 1]     [2 0]     [0]              
   a__f(X1,X2,X3) = [0 0]X1 + [0 3]X2 + [0 3]X3 + [1] >= [0 0]X1 + [0 3]X2 + [0 3]X3 + [1] = f(X1,X2,X3)
   
            [1]    [1]      
   a__c() = [0] >= [0] = c()
  problem:
   a__f(b(),X,c()) -> a__f(X,a__c(),X)
   a__c() -> b()
   mark(f(X1,X2,X3)) -> a__f(X1,mark(X2),X3)
   a__f(X1,X2,X3) -> f(X1,X2,X3)
   a__c() -> c()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0, x1, x2) = x0 + 2x1 + x2 + 4,
    
    [c] = 5,
    
    [a__c] = 5,
    
    [mark](x0) = 4x0 + 1,
    
    [b] = 5,
    
    [a__f](x0, x1, x2) = x0 + 2x1 + x2 + 7
   orientation:
    a__f(b(),X,c()) = 2X + 17 >= 2X + 17 = a__f(X,a__c(),X)
    
    a__c() = 5 >= 5 = b()
    
    mark(f(X1,X2,X3)) = 4X1 + 8X2 + 4X3 + 17 >= X1 + 8X2 + X3 + 9 = a__f(X1,mark(X2),X3)
    
    a__f(X1,X2,X3) = X1 + 2X2 + X3 + 7 >= X1 + 2X2 + X3 + 4 = f(X1,X2,X3)
    
    a__c() = 5 >= 5 = c()
   problem:
    a__f(b(),X,c()) -> a__f(X,a__c(),X)
    a__c() -> b()
    a__c() -> c()
   Unfolding Processor:
    loop length: 3
    terms:
     a__f(a__c(),a__c(),a__c())
     a__f(a__c(),a__c(),c())
     a__f(b(),a__c(),c())
    context: []
    substitution:
     
    Qed