/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:
 concat(leaf(),Y) -> Y
 concat(cons(U,V),Y) -> cons(U,concat(V,Y))
 lessleaves(X,leaf()) -> false()
 lessleaves(leaf(),cons(W,Z)) -> true()
 lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
            [0]
   [true] = [0]
            [0],
   
             [1]
   [false] = [0]
             [0],
   
                          [1 0 1]     [1 1 0]  
   [lessleaves](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                          [0 0 0]     [0 0 0]  ,
   
                    [1 1 0]          [0]
   [cons](x0, x1) = [0 0 0]x0 + x1 + [0]
                    [0 0 1]          [1],
   
                      [1 1 0]          [0]
   [concat](x0, x1) = [0 0 0]x0 + x1 + [1]
                      [0 0 1]          [0],
   
            [0]
   [leaf] = [1]
            [0]
  orientation:
                          [1]         
   concat(leaf(),Y) = Y + [1] >= Y = Y
                          [0]         
   
                         [1 1 0]    [1 1 0]        [0]    [1 1 0]    [1 1 0]        [0]                      
   concat(cons(U,V),Y) = [0 0 0]U + [0 0 0]V + Y + [1] >= [0 0 0]U + [0 0 0]V + Y + [1] = cons(U,concat(V,Y))
                         [0 0 1]    [0 0 1]        [1]    [0 0 1]    [0 0 1]        [1]                      
   
                          [1 0 1]    [1]    [1]          
   lessleaves(X,leaf()) = [0 0 0]X + [0] >= [0] = false()
                          [0 0 0]    [0]    [0]          
   
                                  [1 1 0]    [1 1 0]     [0]         
   lessleaves(leaf(),cons(W,Z)) = [0 0 0]W + [0 0 0]Z >= [0] = true()
                                  [0 0 0]    [0 0 0]     [0]         
   
                                     [1 1 1]    [1 0 1]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 0 1]    [1 1 0]    [1 1 0]    [1]                                      
   lessleaves(cons(U,V),cons(W,Z)) = [0 0 0]U + [0 0 0]V + [0 0 0]W + [0 0 0]Z + [0] >= [0 0 0]U + [0 0 0]V + [0 0 0]W + [0 0 0]Z + [0] = lessleaves(concat(U,V),concat(W,Z))
                                     [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                                      
  problem:
   concat(cons(U,V),Y) -> cons(U,concat(V,Y))
   lessleaves(X,leaf()) -> false()
   lessleaves(leaf(),cons(W,Z)) -> true()
   lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [true] = 0,
    
    [false] = 0,
    
    [lessleaves](x0, x1) = 2x0 + 2x1 + 4,
    
    [cons](x0, x1) = 4x0 + x1 + 4,
    
    [concat](x0, x1) = 4x0 + x1 + 1,
    
    [leaf] = 0
   orientation:
    concat(cons(U,V),Y) = 16U + 4V + Y + 17 >= 4U + 4V + Y + 5 = cons(U,concat(V,Y))
    
    lessleaves(X,leaf()) = 2X + 4 >= 0 = false()
    
    lessleaves(leaf(),cons(W,Z)) = 8W + 2Z + 12 >= 0 = true()
    
    lessleaves(cons(U,V),cons(W,Z)) = 8U + 2V + 8W + 2Z + 20 >= 8U + 2V + 8W + 2Z + 8 = lessleaves(concat(U,V),concat(W,Z))
   problem:
    
   Qed