/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:
 active(f(g(X),Y)) -> mark(f(X,f(g(X),Y)))
 active(f(X1,X2)) -> f(active(X1),X2)
 active(g(X)) -> g(active(X))
 f(mark(X1),X2) -> mark(f(X1,X2))
 g(mark(X)) -> mark(g(X))
 proper(f(X1,X2)) -> f(proper(X1),proper(X2))
 proper(g(X)) -> g(proper(X))
 f(ok(X1),ok(X2)) -> ok(f(X1,X2))
 g(ok(X)) -> ok(g(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [proper](x0) = x0,
   
   [f](x0, x1) = 4x0 + x1 + 3,
   
   [mark](x0) = x0 + 3,
   
   [ok](x0) = 3x0 + 4,
   
   [g](x0) = 2x0 + 1,
   
   [top](x0) = x0 + 4,
   
   [active](x0) = 2x0 + 1
  orientation:
   active(f(g(X),Y)) = 16X + 2Y + 15 >= 12X + Y + 13 = mark(f(X,f(g(X),Y)))
   
   active(f(X1,X2)) = 8X1 + 2X2 + 7 >= 8X1 + X2 + 7 = f(active(X1),X2)
   
   active(g(X)) = 4X + 3 >= 4X + 3 = g(active(X))
   
   f(mark(X1),X2) = 4X1 + X2 + 15 >= 4X1 + X2 + 6 = mark(f(X1,X2))
   
   g(mark(X)) = 2X + 7 >= 2X + 4 = mark(g(X))
   
   proper(f(X1,X2)) = 4X1 + X2 + 3 >= 4X1 + X2 + 3 = f(proper(X1),proper(X2))
   
   proper(g(X)) = 2X + 1 >= 2X + 1 = g(proper(X))
   
   f(ok(X1),ok(X2)) = 12X1 + 3X2 + 23 >= 12X1 + 3X2 + 13 = ok(f(X1,X2))
   
   g(ok(X)) = 6X + 9 >= 6X + 7 = ok(g(X))
   
   top(mark(X)) = X + 7 >= X + 4 = top(proper(X))
   
   top(ok(X)) = 3X + 8 >= 2X + 5 = top(active(X))
  problem:
   active(f(X1,X2)) -> f(active(X1),X2)
   active(g(X)) -> g(active(X))
   proper(f(X1,X2)) -> f(proper(X1),proper(X2))
   proper(g(X)) -> g(proper(X))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                   [1 0 1]  
    [proper](x0) = [0 1 0]x0
                   [0 0 1]  ,
    
                  [1 0 0]     [1 0 0]     [0]
    [f](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1]
                  [0 1 1]     [0 0 1]     [1],
    
              [1 0 0]     [0]
    [g](x0) = [0 1 0]x0 + [1]
              [0 1 1]     [0],
    
                   [1 1 0]  
    [active](x0) = [0 1 0]x0
                   [0 0 1]  
   orientation:
                       [1 1 0]     [1 0 0]     [1]    [1 1 0]     [1 0 0]     [0]                   
    active(f(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = f(active(X1),X2)
                       [0 1 1]     [0 0 1]     [1]    [0 1 1]     [0 0 1]     [1]                   
    
                   [1 1 0]    [1]    [1 1 0]    [0]               
    active(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(active(X))
                   [0 1 1]    [0]    [0 1 1]    [0]               
    
                       [1 1 1]     [1 0 1]     [1]    [1 0 1]     [1 0 1]     [0]                           
    proper(f(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = f(proper(X1),proper(X2))
                       [0 1 1]     [0 0 1]     [1]    [0 1 1]     [0 0 1]     [1]                           
    
                   [1 1 1]    [0]    [1 0 1]    [0]               
    proper(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(proper(X))
                   [0 1 1]    [0]    [0 1 1]    [0]               
   problem:
    proper(g(X)) -> g(proper(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                    [1 1 0]  
     [proper](x0) = [0 1 0]x0
                    [0 0 0]  ,
     
               [1 0 0]     [0]
     [g](x0) = [0 1 0]x0 + [1]
               [0 0 0]     [0]
    orientation:
                    [1 1 0]    [1]    [1 1 0]    [0]               
     proper(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(proper(X))
                    [0 0 0]    [0]    [0 0 0]    [0]               
    problem:
     
    Qed