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


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YES

Problem:
 f(s(X),X) -> f(X,a(X))
 f(X,c(X)) -> f(s(X),X)
 f(X,X) -> c(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0, x1) = 2x0 + 2x1 + 3,
   
   [c](x0) = 4x0,
   
   [s](x0) = 4x0,
   
   [a](x0) = 4x0
  orientation:
   f(s(X),X) = 10X + 3 >= 10X + 3 = f(X,a(X))
   
   f(X,c(X)) = 10X + 3 >= 10X + 3 = f(s(X),X)
   
   f(X,X) = 4X + 3 >= 4X = c(X)
  problem:
   f(s(X),X) -> f(X,a(X))
   f(X,c(X)) -> f(s(X),X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0, x1) = x0 + x1 + 4,
    
    [c](x0) = 7x0 + 1,
    
    [s](x0) = 7x0,
    
    [a](x0) = 7x0
   orientation:
    f(s(X),X) = 8X + 4 >= 8X + 4 = f(X,a(X))
    
    f(X,c(X)) = 8X + 5 >= 8X + 4 = f(s(X),X)
   problem:
    f(s(X),X) -> f(X,a(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 1 0]     [1 1 0]     [0]
     [f](x0, x1) = [1 1 0]x0 + [1 1 0]x1 + [0]
                   [1 0 1]     [0 0 1]     [1],
     
               [1 0 0]     [1]
     [s](x0) = [1 0 0]x0 + [0]
               [1 0 0]     [0],
     
               [1 0 0]     [0]
     [a](x0) = [1 0 0]x0 + [0]
               [1 0 0]     [1]
    orientation:
                 [3 1 0]    [1]    [3 1 0]    [0]            
     f(s(X),X) = [3 1 0]X + [1] >= [3 1 0]X + [0] = f(X,a(X))
                 [2 0 1]    [2]    [2 0 1]    [2]            
    problem:
     
    Qed