/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /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:
   [top](x0) = 2x0 + 2,
   
   [ok](x0) = 6x0 + 4,
   
   [proper](x0) = x0,
   
   [mark](x0) = x0,
   
   [active](x0) = 6x0 + 4,
   
   [f](x0, x1) = 2x0 + 4x1 + 4,
   
   [g](x0) = x0
  orientation:
   active(f(g(X),Y)) = 12X + 24Y + 28 >= 10X + 16Y + 20 = mark(f(X,f(g(X),Y)))
   
   active(f(X1,X2)) = 12X1 + 24X2 + 28 >= 12X1 + 4X2 + 12 = f(active(X1),X2)
   
   active(g(X)) = 6X + 4 >= 6X + 4 = g(active(X))
   
   f(mark(X1),X2) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = mark(f(X1,X2))
   
   g(mark(X)) = X >= X = mark(g(X))
   
   proper(f(X1,X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = f(proper(X1),proper(X2))
   
   proper(g(X)) = X >= X = g(proper(X))
   
   f(ok(X1),ok(X2)) = 12X1 + 24X2 + 28 >= 12X1 + 24X2 + 28 = ok(f(X1,X2))
   
   g(ok(X)) = 6X + 4 >= 6X + 4 = ok(g(X))
   
   top(mark(X)) = 2X + 2 >= 2X + 2 = top(proper(X))
   
   top(ok(X)) = 12X + 10 >= 12X + 10 = top(active(X))
  problem:
   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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = 2x0 + 3,
    
    [ok](x0) = 4x0 + 2,
    
    [proper](x0) = x0,
    
    [mark](x0) = x0 + 4,
    
    [active](x0) = 2x0,
    
    [f](x0, x1) = 4x0 + 4x1,
    
    [g](x0) = 4x0
   orientation:
    active(g(X)) = 8X >= 8X = g(active(X))
    
    f(mark(X1),X2) = 4X1 + 4X2 + 16 >= 4X1 + 4X2 + 4 = mark(f(X1,X2))
    
    g(mark(X)) = 4X + 16 >= 4X + 4 = mark(g(X))
    
    proper(f(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = f(proper(X1),proper(X2))
    
    proper(g(X)) = 4X >= 4X = g(proper(X))
    
    f(ok(X1),ok(X2)) = 16X1 + 16X2 + 16 >= 16X1 + 16X2 + 2 = ok(f(X1,X2))
    
    g(ok(X)) = 16X + 8 >= 16X + 2 = ok(g(X))
    
    top(mark(X)) = 2X + 11 >= 2X + 3 = top(proper(X))
    
    top(ok(X)) = 8X + 7 >= 4X + 3 = top(active(X))
   problem:
    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=1
    
    interpretation:
     [proper](x0) = 2x0 + 1,
     
     [active](x0) = 5x0 + 5,
     
     [f](x0, x1) = x0 + x1 + 1,
     
     [g](x0) = 5x0 + 5
    orientation:
     active(g(X)) = 25X + 30 >= 25X + 30 = g(active(X))
     
     proper(f(X1,X2)) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 3 = f(proper(X1),proper(X2))
     
     proper(g(X)) = 10X + 11 >= 10X + 10 = g(proper(X))
    problem:
     active(g(X)) -> g(active(X))
     proper(f(X1,X2)) -> f(proper(X1),proper(X2))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [proper](x0) = 2x0,
      
      [active](x0) = x0,
      
      [f](x0, x1) = 4x0 + 4x1 + 4,
      
      [g](x0) = x0 + 2
     orientation:
      active(g(X)) = X + 2 >= X + 2 = g(active(X))
      
      proper(f(X1,X2)) = 8X1 + 8X2 + 8 >= 8X1 + 8X2 + 4 = f(proper(X1),proper(X2))
     problem:
      active(g(X)) -> g(active(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                      [1 0 1]  
       [active](x0) = [0 0 0]x0
                      [0 0 1]  ,
       
                 [1 0 0]     [0]
       [g](x0) = [0 0 0]x0 + [0]
                 [0 0 1]     [1]
      orientation:
                      [1 0 1]    [1]    [1 0 1]    [0]               
       active(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(active(X))
                      [0 0 1]    [1]    [0 0 1]    [1]               
      problem:
       
      Qed