/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:
 f(x,empty()) -> x
 f(empty(),cons(a,k)) -> f(cons(a,k),k)
 f(cons(a,k),y) -> f(y,k)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [cons](x0, x1) = x0 + 4x1,
   
   [f](x0, x1) = x0 + 4x1 + 7,
   
   [empty] = 4
  orientation:
   f(x,empty()) = x + 23 >= x = x
   
   f(empty(),cons(a,k)) = 4a + 16k + 11 >= a + 8k + 7 = f(cons(a,k),k)
   
   f(cons(a,k),y) = a + 4k + 4y + 7 >= 4k + y + 7 = f(y,k)
  problem:
   f(cons(a,k),y) -> f(y,k)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]     [1 0 0]     [1]
    [cons](x0, x1) = [0 0 1]x0 + [0 1 0]x1 + [0]
                     [0 0 0]     [0 0 0]     [0],
    
                  [1 0 0]     [1 0 0]  
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 1 0]     [0 1 0]  
   orientation:
                     [1 0 0]    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]          
    f(cons(a,k),y) = [0 0 0]a + [0 0 0]k + [0 0 0]y + [0] >= [0 0 0]k + [0 0 0]y = f(y,k)
                     [0 0 1]    [0 1 0]    [0 1 0]    [0]    [0 1 0]    [0 1 0]          
   problem:
    
   Qed