/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:
 active(fst(0(),Z)) -> mark(nil())
 active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(add(0(),X)) -> mark(X)
 active(add(s(X),Y)) -> mark(s(add(X,Y)))
 active(len(nil())) -> mark(0())
 active(len(cons(X,Z))) -> mark(s(len(Z)))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(fst(X1,X2)) -> fst(active(X1),X2)
 active(fst(X1,X2)) -> fst(X1,active(X2))
 active(from(X)) -> from(active(X))
 active(add(X1,X2)) -> add(active(X1),X2)
 active(add(X1,X2)) -> add(X1,active(X2))
 active(len(X)) -> len(active(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 fst(mark(X1),X2) -> mark(fst(X1,X2))
 fst(X1,mark(X2)) -> mark(fst(X1,X2))
 from(mark(X)) -> mark(from(X))
 add(mark(X1),X2) -> mark(add(X1,X2))
 add(X1,mark(X2)) -> mark(add(X1,X2))
 len(mark(X)) -> mark(len(X))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(nil()) -> ok(nil())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 proper(add(X1,X2)) -> add(proper(X1),proper(X2))
 proper(len(X)) -> len(proper(X))
 s(ok(X)) -> ok(s(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
 from(ok(X)) -> ok(from(X))
 add(ok(X1),ok(X2)) -> ok(add(X1,X2))
 len(ok(X)) -> ok(len(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
               [2 1]  
   [top](x0) = [0 0]x0,
   
              [2 0]  
   [ok](x0) = [0 1]x0,
   
                    
   [proper](x0) = x0,
   
               [2 0]     [0]
   [len](x0) = [0 1]x0 + [2],
   
                   [1 0]          [0]
   [add](x0, x1) = [0 2]x0 + x1 + [2],
   
                [2 0]     [0]
   [from](x0) = [0 1]x0 + [2],
   
                         [1 0]  
   [cons](x0, x1) = x0 + [0 0]x1,
   
             [1 0]  
   [s](x0) = [0 0]x0,
   
                     [0]
   [mark](x0) = x0 + [1],
   
           [0]
   [nil] = [0],
   
                  [2 0]  
   [active](x0) = [0 1]x0,
   
                   [2 0]          [0]
   [fst](x0, x1) = [0 2]x0 + x1 + [2],
   
         [0]
   [0] = [0]
  orientation:
                        [2 0]    [0]    [0]              
   active(fst(0(),Z)) = [0 1]Z + [2] >= [1] = mark(nil())
   
                                 [4 0]    [2 0]    [2 0]    [0]    [2 0]        [1 0]    [0]                         
   active(fst(s(X),cons(Y,Z))) = [0 0]X + [0 1]Y + [0 0]Z + [2] >= [0 0]X + Y + [0 0]Z + [1] = mark(cons(Y,fst(X,Z)))
   
                     [4 0]    [0]    [3 0]    [0]                           
   active(from(X)) = [0 1]X + [2] >= [0 1]X + [1] = mark(cons(X,from(s(X))))
   
                        [2 0]    [0]        [0]          
   active(add(0(),X)) = [0 1]X + [2] >= X + [1] = mark(X)
   
                         [2 0]    [2 0]    [0]    [1 0]    [1 0]    [0]                    
   active(add(s(X),Y)) = [0 0]X + [0 1]Y + [2] >= [0 0]X + [0 0]Y + [1] = mark(s(add(X,Y)))
   
                        [0]    [0]            
   active(len(nil())) = [2] >= [1] = mark(0())
   
                            [4 0]    [4 0]    [0]    [2 0]    [0]                  
   active(len(cons(X,Z))) = [0 1]X + [0 0]Z + [2] >= [0 0]Z + [1] = mark(s(len(Z)))
   
                         [2 0]     [2 0]      [2 0]     [1 0]                        
   active(cons(X1,X2)) = [0 1]X1 + [0 0]X2 >= [0 1]X1 + [0 0]X2 = cons(active(X1),X2)
   
                        [4 0]     [2 0]     [0]    [4 0]          [0]                     
   active(fst(X1,X2)) = [0 2]X1 + [0 1]X2 + [2] >= [0 2]X1 + X2 + [2] = fst(active(X1),X2)
   
                        [4 0]     [2 0]     [0]    [2 0]     [2 0]     [0]                     
   active(fst(X1,X2)) = [0 2]X1 + [0 1]X2 + [2] >= [0 2]X1 + [0 1]X2 + [2] = fst(X1,active(X2))
   
                     [4 0]    [0]    [4 0]    [0]                  
   active(from(X)) = [0 1]X + [2] >= [0 1]X + [2] = from(active(X))
   
                        [2 0]     [2 0]     [0]    [2 0]          [0]                     
   active(add(X1,X2)) = [0 2]X1 + [0 1]X2 + [2] >= [0 2]X1 + X2 + [2] = add(active(X1),X2)
   
                        [2 0]     [2 0]     [0]    [1 0]     [2 0]     [0]                     
   active(add(X1,X2)) = [0 2]X1 + [0 1]X2 + [2] >= [0 2]X1 + [0 1]X2 + [2] = add(X1,active(X2))
   
                    [4 0]    [0]    [4 0]    [0]                 
   active(len(X)) = [0 1]X + [2] >= [0 1]X + [2] = len(active(X))
   
                            [1 0]     [0]         [1 0]     [0]                    
   cons(mark(X1),X2) = X1 + [0 0]X2 + [1] >= X1 + [0 0]X2 + [1] = mark(cons(X1,X2))
   
                      [2 0]          [0]    [2 0]          [0]                   
   fst(mark(X1),X2) = [0 2]X1 + X2 + [4] >= [0 2]X1 + X2 + [3] = mark(fst(X1,X2))
   
                      [2 0]          [0]    [2 0]          [0]                   
   fst(X1,mark(X2)) = [0 2]X1 + X2 + [3] >= [0 2]X1 + X2 + [3] = mark(fst(X1,X2))
   
                   [2 0]    [0]    [2 0]    [0]                
   from(mark(X)) = [0 1]X + [3] >= [0 1]X + [3] = mark(from(X))
   
                      [1 0]          [0]    [1 0]          [0]                   
   add(mark(X1),X2) = [0 2]X1 + X2 + [4] >= [0 2]X1 + X2 + [3] = mark(add(X1,X2))
   
                      [1 0]          [0]    [1 0]          [0]                   
   add(X1,mark(X2)) = [0 2]X1 + X2 + [3] >= [0 2]X1 + X2 + [3] = mark(add(X1,X2))
   
                  [2 0]    [0]    [2 0]    [0]               
   len(mark(X)) = [0 1]X + [3] >= [0 1]X + [3] = mark(len(X))
   
                 [0]    [0]          
   proper(0()) = [0] >= [0] = ok(0())
   
                  [1 0]     [1 0]                
   proper(s(X)) = [0 0]X >= [0 0]X = s(proper(X))
   
                   [0]    [0]            
   proper(nil()) = [0] >= [0] = ok(nil())
   
                              [1 0]           [1 0]                                
   proper(cons(X1,X2)) = X1 + [0 0]X2 >= X1 + [0 0]X2 = cons(proper(X1),proper(X2))
   
                        [2 0]          [0]    [2 0]          [0]                             
   proper(fst(X1,X2)) = [0 2]X1 + X2 + [2] >= [0 2]X1 + X2 + [2] = fst(proper(X1),proper(X2))
   
                     [2 0]    [0]    [2 0]    [0]                  
   proper(from(X)) = [0 1]X + [2] >= [0 1]X + [2] = from(proper(X))
   
                        [1 0]          [0]    [1 0]          [0]                             
   proper(add(X1,X2)) = [0 2]X1 + X2 + [2] >= [0 2]X1 + X2 + [2] = add(proper(X1),proper(X2))
   
                    [2 0]    [0]    [2 0]    [0]                 
   proper(len(X)) = [0 1]X + [2] >= [0 1]X + [2] = len(proper(X))
   
              [2 0]     [2 0]            
   s(ok(X)) = [0 0]X >= [0 0]X = ok(s(X))
   
                         [2 0]     [2 0]      [2 0]     [2 0]                    
   cons(ok(X1),ok(X2)) = [0 1]X1 + [0 0]X2 >= [0 1]X1 + [0 0]X2 = ok(cons(X1,X2))
   
                        [4 0]     [2 0]     [0]    [4 0]     [2 0]     [0]                 
   fst(ok(X1),ok(X2)) = [0 2]X1 + [0 1]X2 + [2] >= [0 2]X1 + [0 1]X2 + [2] = ok(fst(X1,X2))
   
                 [4 0]    [0]    [4 0]    [0]              
   from(ok(X)) = [0 1]X + [2] >= [0 1]X + [2] = ok(from(X))
   
                        [2 0]     [2 0]     [0]    [2 0]     [2 0]     [0]                 
   add(ok(X1),ok(X2)) = [0 2]X1 + [0 1]X2 + [2] >= [0 2]X1 + [0 1]X2 + [2] = ok(add(X1,X2))
   
                [4 0]    [0]    [4 0]    [0]             
   len(ok(X)) = [0 1]X + [2] >= [0 1]X + [2] = ok(len(X))
   
                  [2 1]    [1]    [2 1]                  
   top(mark(X)) = [0 0]X + [0] >= [0 0]X = top(proper(X))
   
                [4 1]     [4 1]                  
   top(ok(X)) = [0 0]X >= [0 0]X = top(active(X))
  problem:
   active(fst(0(),Z)) -> mark(nil())
   active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(add(0(),X)) -> mark(X)
   active(add(s(X),Y)) -> mark(s(add(X,Y)))
   active(len(nil())) -> mark(0())
   active(len(cons(X,Z))) -> mark(s(len(Z)))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(fst(X1,X2)) -> fst(active(X1),X2)
   active(fst(X1,X2)) -> fst(X1,active(X2))
   active(from(X)) -> from(active(X))
   active(add(X1,X2)) -> add(active(X1),X2)
   active(add(X1,X2)) -> add(X1,active(X2))
   active(len(X)) -> len(active(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   fst(mark(X1),X2) -> mark(fst(X1,X2))
   fst(X1,mark(X2)) -> mark(fst(X1,X2))
   from(mark(X)) -> mark(from(X))
   add(mark(X1),X2) -> mark(add(X1,X2))
   add(X1,mark(X2)) -> mark(add(X1,X2))
   len(mark(X)) -> mark(len(X))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   proper(nil()) -> ok(nil())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(add(X1,X2)) -> add(proper(X1),proper(X2))
   proper(len(X)) -> len(proper(X))
   s(ok(X)) -> ok(s(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
   from(ok(X)) -> ok(from(X))
   add(ok(X1),ok(X2)) -> ok(add(X1,X2))
   len(ok(X)) -> ok(len(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = x0,
    
    [ok](x0) = 2x0 + 1,
    
    [proper](x0) = 3x0,
    
    [len](x0) = 3x0 + 2,
    
    [add](x0, x1) = 5x0 + 5x1,
    
    [from](x0) = 4x0,
    
    [cons](x0, x1) = 4x0 + x1,
    
    [s](x0) = x0,
    
    [mark](x0) = x0,
    
    [nil] = 4,
    
    [active](x0) = 2x0,
    
    [fst](x0, x1) = x0 + 2x1 + 1,
    
    [0] = 1
   orientation:
    active(fst(0(),Z)) = 4Z + 4 >= 4 = mark(nil())
    
    active(fst(s(X),cons(Y,Z))) = 2X + 16Y + 4Z + 2 >= X + 4Y + 2Z + 1 = mark(cons(Y,fst(X,Z)))
    
    active(from(X)) = 8X >= 8X = mark(cons(X,from(s(X))))
    
    active(add(0(),X)) = 10X + 10 >= X = mark(X)
    
    active(add(s(X),Y)) = 10X + 10Y >= 5X + 5Y = mark(s(add(X,Y)))
    
    active(len(nil())) = 28 >= 1 = mark(0())
    
    active(len(cons(X,Z))) = 24X + 6Z + 4 >= 3Z + 2 = mark(s(len(Z)))
    
    active(cons(X1,X2)) = 8X1 + 2X2 >= 8X1 + X2 = cons(active(X1),X2)
    
    active(fst(X1,X2)) = 2X1 + 4X2 + 2 >= 2X1 + 2X2 + 1 = fst(active(X1),X2)
    
    active(fst(X1,X2)) = 2X1 + 4X2 + 2 >= X1 + 4X2 + 1 = fst(X1,active(X2))
    
    active(from(X)) = 8X >= 8X = from(active(X))
    
    active(add(X1,X2)) = 10X1 + 10X2 >= 10X1 + 5X2 = add(active(X1),X2)
    
    active(add(X1,X2)) = 10X1 + 10X2 >= 5X1 + 10X2 = add(X1,active(X2))
    
    active(len(X)) = 6X + 4 >= 6X + 2 = len(active(X))
    
    cons(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(cons(X1,X2))
    
    fst(mark(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = mark(fst(X1,X2))
    
    fst(X1,mark(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = mark(fst(X1,X2))
    
    from(mark(X)) = 4X >= 4X = mark(from(X))
    
    add(mark(X1),X2) = 5X1 + 5X2 >= 5X1 + 5X2 = mark(add(X1,X2))
    
    add(X1,mark(X2)) = 5X1 + 5X2 >= 5X1 + 5X2 = mark(add(X1,X2))
    
    len(mark(X)) = 3X + 2 >= 3X + 2 = mark(len(X))
    
    proper(0()) = 3 >= 3 = ok(0())
    
    proper(s(X)) = 3X >= 3X = s(proper(X))
    
    proper(nil()) = 12 >= 9 = ok(nil())
    
    proper(cons(X1,X2)) = 12X1 + 3X2 >= 12X1 + 3X2 = cons(proper(X1),proper(X2))
    
    proper(fst(X1,X2)) = 3X1 + 6X2 + 3 >= 3X1 + 6X2 + 1 = fst(proper(X1),proper(X2))
    
    proper(from(X)) = 12X >= 12X = from(proper(X))
    
    proper(add(X1,X2)) = 15X1 + 15X2 >= 15X1 + 15X2 = add(proper(X1),proper(X2))
    
    proper(len(X)) = 9X + 6 >= 9X + 2 = len(proper(X))
    
    s(ok(X)) = 2X + 1 >= 2X + 1 = ok(s(X))
    
    cons(ok(X1),ok(X2)) = 8X1 + 2X2 + 5 >= 8X1 + 2X2 + 1 = ok(cons(X1,X2))
    
    fst(ok(X1),ok(X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 3 = ok(fst(X1,X2))
    
    from(ok(X)) = 8X + 4 >= 8X + 1 = ok(from(X))
    
    add(ok(X1),ok(X2)) = 10X1 + 10X2 + 10 >= 10X1 + 10X2 + 1 = ok(add(X1,X2))
    
    len(ok(X)) = 6X + 5 >= 6X + 5 = ok(len(X))
    
    top(ok(X)) = 2X + 1 >= 2X = top(active(X))
   problem:
    active(fst(0(),Z)) -> mark(nil())
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(add(s(X),Y)) -> mark(s(add(X,Y)))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(from(X)) -> from(active(X))
    active(add(X1,X2)) -> add(active(X1),X2)
    active(add(X1,X2)) -> add(X1,active(X2))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    fst(mark(X1),X2) -> mark(fst(X1,X2))
    fst(X1,mark(X2)) -> mark(fst(X1,X2))
    from(mark(X)) -> mark(from(X))
    add(mark(X1),X2) -> mark(add(X1,X2))
    add(X1,mark(X2)) -> mark(add(X1,X2))
    len(mark(X)) -> mark(len(X))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    proper(add(X1,X2)) -> add(proper(X1),proper(X2))
    s(ok(X)) -> ok(s(X))
    len(ok(X)) -> ok(len(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [ok](x0) = x0,
     
     [proper](x0) = x0,
     
     [len](x0) = x0 + 2,
     
     [add](x0, x1) = 4x0 + x1 + 2,
     
     [from](x0) = x0,
     
     [cons](x0, x1) = x0 + 2x1,
     
     [s](x0) = x0 + 1,
     
     [mark](x0) = x0,
     
     [nil] = 1,
     
     [active](x0) = 4x0 + 2,
     
     [fst](x0, x1) = 2x0 + 3x1 + 4,
     
     [0] = 0
    orientation:
     active(fst(0(),Z)) = 12Z + 18 >= 1 = mark(nil())
     
     active(from(X)) = 4X + 2 >= 3X + 2 = mark(cons(X,from(s(X))))
     
     active(add(s(X),Y)) = 16X + 4Y + 26 >= 4X + Y + 3 = mark(s(add(X,Y)))
     
     active(cons(X1,X2)) = 4X1 + 8X2 + 2 >= 4X1 + 2X2 + 2 = cons(active(X1),X2)
     
     active(from(X)) = 4X + 2 >= 4X + 2 = from(active(X))
     
     active(add(X1,X2)) = 16X1 + 4X2 + 10 >= 16X1 + X2 + 10 = add(active(X1),X2)
     
     active(add(X1,X2)) = 16X1 + 4X2 + 10 >= 4X1 + 4X2 + 4 = add(X1,active(X2))
     
     cons(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = mark(cons(X1,X2))
     
     fst(mark(X1),X2) = 2X1 + 3X2 + 4 >= 2X1 + 3X2 + 4 = mark(fst(X1,X2))
     
     fst(X1,mark(X2)) = 2X1 + 3X2 + 4 >= 2X1 + 3X2 + 4 = mark(fst(X1,X2))
     
     from(mark(X)) = X >= X = mark(from(X))
     
     add(mark(X1),X2) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = mark(add(X1,X2))
     
     add(X1,mark(X2)) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = mark(add(X1,X2))
     
     len(mark(X)) = X + 2 >= X + 2 = mark(len(X))
     
     proper(0()) = 0 >= 0 = ok(0())
     
     proper(s(X)) = X + 1 >= X + 1 = s(proper(X))
     
     proper(cons(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = cons(proper(X1),proper(X2))
     
     proper(from(X)) = X >= X = from(proper(X))
     
     proper(add(X1,X2)) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = add(proper(X1),proper(X2))
     
     s(ok(X)) = X + 1 >= X + 1 = ok(s(X))
     
     len(ok(X)) = X + 2 >= X + 2 = ok(len(X))
    problem:
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(add(X1,X2)) -> add(active(X1),X2)
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     fst(mark(X1),X2) -> mark(fst(X1,X2))
     fst(X1,mark(X2)) -> mark(fst(X1,X2))
     from(mark(X)) -> mark(from(X))
     add(mark(X1),X2) -> mark(add(X1,X2))
     add(X1,mark(X2)) -> mark(add(X1,X2))
     len(mark(X)) -> mark(len(X))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(add(X1,X2)) -> add(proper(X1),proper(X2))
     s(ok(X)) -> ok(s(X))
     len(ok(X)) -> ok(len(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [ok](x0) = x0,
      
      [proper](x0) = x0,
      
      [len](x0) = x0,
      
      [add](x0, x1) = 4x0 + x1 + 2,
      
      [from](x0) = x0 + 6,
      
      [cons](x0, x1) = x0 + x1,
      
      [s](x0) = 4x0,
      
      [mark](x0) = x0,
      
      [active](x0) = 5x0 + 1,
      
      [fst](x0, x1) = x0 + x1 + 4,
      
      [0] = 0
     orientation:
      active(from(X)) = 5X + 31 >= 5X + 6 = mark(cons(X,from(s(X))))
      
      active(cons(X1,X2)) = 5X1 + 5X2 + 1 >= 5X1 + X2 + 1 = cons(active(X1),X2)
      
      active(from(X)) = 5X + 31 >= 5X + 7 = from(active(X))
      
      active(add(X1,X2)) = 20X1 + 5X2 + 11 >= 20X1 + X2 + 6 = add(active(X1),X2)
      
      cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(cons(X1,X2))
      
      fst(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(fst(X1,X2))
      
      fst(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(fst(X1,X2))
      
      from(mark(X)) = X + 6 >= X + 6 = mark(from(X))
      
      add(mark(X1),X2) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = mark(add(X1,X2))
      
      add(X1,mark(X2)) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = mark(add(X1,X2))
      
      len(mark(X)) = X >= X = mark(len(X))
      
      proper(0()) = 0 >= 0 = ok(0())
      
      proper(s(X)) = 4X >= 4X = s(proper(X))
      
      proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = X + 6 >= X + 6 = from(proper(X))
      
      proper(add(X1,X2)) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = add(proper(X1),proper(X2))
      
      s(ok(X)) = 4X >= 4X = ok(s(X))
      
      len(ok(X)) = X >= X = ok(len(X))
     problem:
      active(cons(X1,X2)) -> cons(active(X1),X2)
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      fst(mark(X1),X2) -> mark(fst(X1,X2))
      fst(X1,mark(X2)) -> mark(fst(X1,X2))
      from(mark(X)) -> mark(from(X))
      add(mark(X1),X2) -> mark(add(X1,X2))
      add(X1,mark(X2)) -> mark(add(X1,X2))
      len(mark(X)) -> mark(len(X))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(from(X)) -> from(proper(X))
      proper(add(X1,X2)) -> add(proper(X1),proper(X2))
      s(ok(X)) -> ok(s(X))
      len(ok(X)) -> ok(len(X))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [ok](x0) = 2x0 + 4,
       
       [proper](x0) = 4x0,
       
       [len](x0) = 4x0 + 2,
       
       [add](x0, x1) = 2x0 + 4x1 + 4,
       
       [from](x0) = x0 + 3,
       
       [cons](x0, x1) = 2x0 + 2x1 + 4,
       
       [s](x0) = 4x0,
       
       [mark](x0) = x0,
       
       [active](x0) = x0,
       
       [fst](x0, x1) = 2x0 + x1 + 2,
       
       [0] = 5
      orientation:
       active(cons(X1,X2)) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = cons(active(X1),X2)
       
       cons(mark(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = mark(cons(X1,X2))
       
       fst(mark(X1),X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = mark(fst(X1,X2))
       
       fst(X1,mark(X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = mark(fst(X1,X2))
       
       from(mark(X)) = X + 3 >= X + 3 = mark(from(X))
       
       add(mark(X1),X2) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = mark(add(X1,X2))
       
       add(X1,mark(X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = mark(add(X1,X2))
       
       len(mark(X)) = 4X + 2 >= 4X + 2 = mark(len(X))
       
       proper(0()) = 20 >= 14 = ok(0())
       
       proper(s(X)) = 16X >= 16X = s(proper(X))
       
       proper(cons(X1,X2)) = 8X1 + 8X2 + 16 >= 8X1 + 8X2 + 4 = cons(proper(X1),proper(X2))
       
       proper(from(X)) = 4X + 12 >= 4X + 3 = from(proper(X))
       
       proper(add(X1,X2)) = 8X1 + 16X2 + 16 >= 8X1 + 16X2 + 4 = add(proper(X1),proper(X2))
       
       s(ok(X)) = 8X + 16 >= 8X + 4 = ok(s(X))
       
       len(ok(X)) = 8X + 18 >= 8X + 8 = ok(len(X))
      problem:
       active(cons(X1,X2)) -> cons(active(X1),X2)
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       fst(mark(X1),X2) -> mark(fst(X1,X2))
       fst(X1,mark(X2)) -> mark(fst(X1,X2))
       from(mark(X)) -> mark(from(X))
       add(mark(X1),X2) -> mark(add(X1,X2))
       add(X1,mark(X2)) -> mark(add(X1,X2))
       len(mark(X)) -> mark(len(X))
       proper(s(X)) -> s(proper(X))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
                       [1 0 0]     [0]
        [proper](x0) = [0 0 0]x0 + [0]
                       [0 0 0]     [1],
        
                    [1 0 0]  
        [len](x0) = [1 0 0]x0
                    [0 0 1]  ,
        
                        [1 0 0]     [1 0 0]  
        [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                        [0 0 1]     [0 0 1]  ,
        
                     [1 0 0]     [1]
        [from](x0) = [0 0 0]x0 + [0]
                     [0 1 1]     [0],
        
                         [1 0 1]     [1 0 0]     [0]
        [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1]
                         [0 0 1]     [0 0 0]     [0],
        
                  [1 0 0]  
        [s](x0) = [0 0 0]x0
                  [0 0 1]  ,
        
                          [0]
        [mark](x0) = x0 + [0]
                          [1],
        
                       [1 1 0]  
        [active](x0) = [0 1 0]x0
                       [0 0 1]  ,
        
                        [1 0 1]     [1 0 0]  
        [fst](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                        [0 0 1]     [0 0 1]  
       orientation:
                              [1 1 1]     [1 0 0]     [1]    [1 1 1]     [1 0 0]     [0]                      
        active(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = cons(active(X1),X2)
                              [0 0 1]     [0 0 0]     [0]    [0 0 1]     [0 0 0]     [0]                      
        
                            [1 0 1]     [1 0 0]     [1]    [1 0 1]     [1 0 0]     [0]                    
        cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = mark(cons(X1,X2))
                            [0 0 1]     [0 0 0]     [1]    [0 0 1]     [0 0 0]     [1]                    
        
                           [1 0 1]     [1 0 0]     [1]    [1 0 1]     [1 0 0]     [0]                   
        fst(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(fst(X1,X2))
                           [0 0 1]     [0 0 1]     [1]    [0 0 1]     [0 0 1]     [1]                   
        
                           [1 0 1]     [1 0 0]     [0]    [1 0 1]     [1 0 0]     [0]                   
        fst(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(fst(X1,X2))
                           [0 0 1]     [0 0 1]     [1]    [0 0 1]     [0 0 1]     [1]                   
        
                        [1 0 0]    [1]    [1 0 0]    [1]                
        from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(from(X))
                        [0 1 1]    [1]    [0 1 1]    [1]                
        
                           [1 0 0]     [1 0 0]     [0]    [1 0 0]     [1 0 0]     [0]                   
        add(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(add(X1,X2))
                           [0 0 1]     [0 0 1]     [1]    [0 0 1]     [0 0 1]     [1]                   
        
                           [1 0 0]     [1 0 0]     [0]    [1 0 0]     [1 0 0]     [0]                   
        add(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(add(X1,X2))
                           [0 0 1]     [0 0 1]     [1]    [0 0 1]     [0 0 1]     [1]                   
        
                       [1 0 0]    [0]    [1 0 0]    [0]               
        len(mark(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = mark(len(X))
                       [0 0 1]    [1]    [0 0 1]    [1]               
        
                       [1 0 0]    [0]    [1 0 0]    [0]               
        proper(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(proper(X))
                       [0 0 0]    [1]    [0 0 0]    [1]               
       problem:
        fst(X1,mark(X2)) -> mark(fst(X1,X2))
        from(mark(X)) -> mark(from(X))
        add(mark(X1),X2) -> mark(add(X1,X2))
        add(X1,mark(X2)) -> mark(add(X1,X2))
        len(mark(X)) -> mark(len(X))
        proper(s(X)) -> s(proper(X))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [proper](x0) = 4x0 + 3,
         
         [len](x0) = x0,
         
         [add](x0, x1) = 2x0 + x1,
         
         [from](x0) = 4x0 + 2,
         
         [s](x0) = 4x0 + 6,
         
         [mark](x0) = x0,
         
         [fst](x0, x1) = 2x0 + 2x1 + 7
        orientation:
         fst(X1,mark(X2)) = 2X1 + 2X2 + 7 >= 2X1 + 2X2 + 7 = mark(fst(X1,X2))
         
         from(mark(X)) = 4X + 2 >= 4X + 2 = mark(from(X))
         
         add(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(add(X1,X2))
         
         add(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = mark(add(X1,X2))
         
         len(mark(X)) = X >= X = mark(len(X))
         
         proper(s(X)) = 16X + 27 >= 16X + 18 = s(proper(X))
        problem:
         fst(X1,mark(X2)) -> mark(fst(X1,X2))
         from(mark(X)) -> mark(from(X))
         add(mark(X1),X2) -> mark(add(X1,X2))
         add(X1,mark(X2)) -> mark(add(X1,X2))
         len(mark(X)) -> mark(len(X))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [len](x0) = x0,
          
          [add](x0, x1) = x0 + 2x1 + 3,
          
          [from](x0) = 4x0 + 6,
          
          [mark](x0) = x0 + 4,
          
          [fst](x0, x1) = 4x0 + x1 + 4
         orientation:
          fst(X1,mark(X2)) = 4X1 + X2 + 8 >= 4X1 + X2 + 8 = mark(fst(X1,X2))
          
          from(mark(X)) = 4X + 22 >= 4X + 10 = mark(from(X))
          
          add(mark(X1),X2) = X1 + 2X2 + 7 >= X1 + 2X2 + 7 = mark(add(X1,X2))
          
          add(X1,mark(X2)) = X1 + 2X2 + 11 >= X1 + 2X2 + 7 = mark(add(X1,X2))
          
          len(mark(X)) = X + 4 >= X + 4 = mark(len(X))
         problem:
          fst(X1,mark(X2)) -> mark(fst(X1,X2))
          add(mark(X1),X2) -> mark(add(X1,X2))
          len(mark(X)) -> mark(len(X))
         Matrix Interpretation Processor: dim=1
          
          interpretation:
           [len](x0) = 6x0 + 1,
           
           [add](x0, x1) = x0 + x1 + 3,
           
           [mark](x0) = x0 + 5,
           
           [fst](x0, x1) = x0 + x1 + 4
          orientation:
           fst(X1,mark(X2)) = X1 + X2 + 9 >= X1 + X2 + 9 = mark(fst(X1,X2))
           
           add(mark(X1),X2) = X1 + X2 + 8 >= X1 + X2 + 8 = mark(add(X1,X2))
           
           len(mark(X)) = 6X + 31 >= 6X + 6 = mark(len(X))
          problem:
           fst(X1,mark(X2)) -> mark(fst(X1,X2))
           add(mark(X1),X2) -> mark(add(X1,X2))
          Matrix Interpretation Processor: dim=1
           
           interpretation:
            [add](x0, x1) = 2x0 + 2x1 + 1,
            
            [mark](x0) = x0 + 1,
            
            [fst](x0, x1) = x0 + x1 + 4
           orientation:
            fst(X1,mark(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = mark(fst(X1,X2))
            
            add(mark(X1),X2) = 2X1 + 2X2 + 3 >= 2X1 + 2X2 + 2 = mark(add(X1,X2))
           problem:
            fst(X1,mark(X2)) -> mark(fst(X1,X2))
           Matrix Interpretation Processor: dim=3
            
            interpretation:
                          [1 0 0]     [0]
             [mark](x0) = [0 0 1]x0 + [0]
                          [0 1 1]     [1],
             
                             [1 0 0]     [1 0 1]  
             [fst](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                             [0 0 0]     [0 0 1]  
            orientation:
                                [1 0 0]     [1 1 1]     [1]    [1 0 0]     [1 0 1]     [0]                   
             fst(X1,mark(X2)) = [0 0 0]X1 + [0 0 1]X2 + [0] >= [0 0 0]X1 + [0 0 1]X2 + [0] = mark(fst(X1,X2))
                                [0 0 0]     [0 1 1]     [1]    [0 0 0]     [0 1 1]     [1]                   
            problem:
             
            Qed