/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:
 rev(ls) -> r1(ls,empty())
 r1(empty(),a) -> a
 r1(cons(x,k),a) -> r1(k,cons(x,a))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                    [1 0 1]       
   [cons](x0, x1) = [0 0 1]x0 + x1
                    [0 0 0]       ,
   
                  [1 0 1]     [1 0 0]  
   [r1](x0, x1) = [0 1 0]x0 + [0 1 1]x1
                  [0 0 0]     [0 0 1]  ,
   
             [0]
   [empty] = [0]
             [1],
   
               [1 0 1]     [0]
   [rev](x0) = [1 1 0]x0 + [1]
               [0 0 0]     [1]
  orientation:
             [1 0 1]     [0]    [1 0 1]     [0]                 
   rev(ls) = [1 1 0]ls + [1] >= [0 1 0]ls + [1] = r1(ls,empty())
             [0 0 0]     [1]    [0 0 0]     [1]                 
   
                   [1 0 0]    [1]         
   r1(empty(),a) = [0 1 1]a + [0] >= a = a
                   [0 0 1]    [0]         
   
                     [1 0 0]    [1 0 1]    [1 0 1]     [1 0 0]    [1 0 1]    [1 0 1]                   
   r1(cons(x,k),a) = [0 1 1]a + [0 1 0]k + [0 0 1]x >= [0 1 1]a + [0 1 0]k + [0 0 1]x = r1(k,cons(x,a))
                     [0 0 1]    [0 0 0]    [0 0 0]     [0 0 1]    [0 0 0]    [0 0 0]                   
  problem:
   rev(ls) -> r1(ls,empty())
   r1(cons(x,k),a) -> r1(k,cons(x,a))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 0 0]     [1 0 0]     [0]
    [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [0 0 0]     [0 0 1]     [1],
    
                   [1 0 1]     [1 0 0]  
    [r1](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
    
              [0]
    [empty] = [0]
              [0],
    
                [1 0 1]     [0]
    [rev](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1]
   orientation:
              [1 0 1]     [0]    [1 0 1]                   
    rev(ls) = [0 0 0]ls + [1] >= [0 0 0]ls = r1(ls,empty())
              [0 0 0]     [1]    [0 0 0]                   
    
                      [1 0 0]    [1 0 1]    [1 0 0]    [1]    [1 0 0]    [1 0 1]    [1 0 0]                   
    r1(cons(x,k),a) = [0 0 0]a + [0 0 0]k + [0 0 0]x + [0] >= [0 0 0]a + [0 0 0]k + [0 0 0]x = r1(k,cons(x,a))
                      [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                   
   problem:
    rev(ls) -> r1(ls,empty())
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                    [1 0 0]     [1 0 0]  
     [r1](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
     
               [0]
     [empty] = [0]
               [0],
     
                 [1 0 0]     [1]
     [rev](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0]
    orientation:
               [1 0 0]     [1]    [1 0 0]                   
     rev(ls) = [0 0 0]ls + [0] >= [0 0 0]ls = r1(ls,empty())
               [0 0 0]     [0]    [0 0 0]                   
    problem:
     
    Qed