/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(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
 active(__(X,nil())) -> mark(X)
 active(__(nil(),X)) -> mark(X)
 active(and(tt(),X)) -> mark(X)
 active(isNePal(__(I,__(P,I)))) -> mark(tt())
 mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
 mark(nil()) -> active(nil())
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(isNePal(X)) -> active(isNePal(mark(X)))
 __(mark(X1),X2) -> __(X1,X2)
 __(X1,mark(X2)) -> __(X1,X2)
 __(active(X1),X2) -> __(X1,X2)
 __(X1,active(X2)) -> __(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 isNePal(mark(X)) -> isNePal(X)
 isNePal(active(X)) -> isNePal(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [tt] = 2,
   
   [active](x0) = x0,
   
   [nil] = 3,
   
   [and](x0, x1) = 4x0 + x1 + 4,
   
   [__](x0, x1) = x0 + x1 + 1,
   
   [isNePal](x0) = x0,
   
   [mark](x0) = x0
  orientation:
   active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = mark(__(X,__(Y,Z)))
   
   active(__(X,nil())) = X + 4 >= X = mark(X)
   
   active(__(nil(),X)) = X + 4 >= X = mark(X)
   
   active(and(tt(),X)) = X + 12 >= X = mark(X)
   
   active(isNePal(__(I,__(P,I)))) = 2I + P + 2 >= 2 = mark(tt())
   
   mark(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(__(mark(X1),mark(X2)))
   
   mark(nil()) = 3 >= 3 = active(nil())
   
   mark(and(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = active(and(mark(X1),X2))
   
   mark(tt()) = 2 >= 2 = active(tt())
   
   mark(isNePal(X)) = X >= X = active(isNePal(mark(X)))
   
   __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2)
   
   __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2)
   
   __(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2)
   
   __(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,X2)
   
   and(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = and(X1,X2)
   
   and(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = and(X1,X2)
   
   and(active(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = and(X1,X2)
   
   and(X1,active(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = and(X1,X2)
   
   isNePal(mark(X)) = X >= X = isNePal(X)
   
   isNePal(active(X)) = X >= X = isNePal(X)
  problem:
   active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
   active(isNePal(__(I,__(P,I)))) -> mark(tt())
   mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
   mark(nil()) -> active(nil())
   mark(and(X1,X2)) -> active(and(mark(X1),X2))
   mark(tt()) -> active(tt())
   mark(isNePal(X)) -> active(isNePal(mark(X)))
   __(mark(X1),X2) -> __(X1,X2)
   __(X1,mark(X2)) -> __(X1,X2)
   __(active(X1),X2) -> __(X1,X2)
   __(X1,active(X2)) -> __(X1,X2)
   and(mark(X1),X2) -> and(X1,X2)
   and(X1,mark(X2)) -> and(X1,X2)
   and(active(X1),X2) -> and(X1,X2)
   and(X1,active(X2)) -> and(X1,X2)
   isNePal(mark(X)) -> isNePal(X)
   isNePal(active(X)) -> isNePal(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [tt] = 0,
    
    [active](x0) = x0,
    
    [nil] = 0,
    
    [and](x0, x1) = 4x0 + 4x1,
    
    [__](x0, x1) = 2x0 + x1 + 1,
    
    [isNePal](x0) = 2x0 + 4,
    
    [mark](x0) = x0
   orientation:
    active(__(__(X,Y),Z)) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = mark(__(X,__(Y,Z)))
    
    active(isNePal(__(I,__(P,I)))) = 6I + 4P + 8 >= 0 = mark(tt())
    
    mark(__(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = active(__(mark(X1),mark(X2)))
    
    mark(nil()) = 0 >= 0 = active(nil())
    
    mark(and(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = active(and(mark(X1),X2))
    
    mark(tt()) = 0 >= 0 = active(tt())
    
    mark(isNePal(X)) = 2X + 4 >= 2X + 4 = active(isNePal(mark(X)))
    
    __(mark(X1),X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2)
    
    __(X1,mark(X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2)
    
    __(active(X1),X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2)
    
    __(X1,active(X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2)
    
    and(mark(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
    
    and(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
    
    and(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
    
    and(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = and(X1,X2)
    
    isNePal(mark(X)) = 2X + 4 >= 2X + 4 = isNePal(X)
    
    isNePal(active(X)) = 2X + 4 >= 2X + 4 = isNePal(X)
   problem:
    mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
    mark(nil()) -> active(nil())
    mark(and(X1,X2)) -> active(and(mark(X1),X2))
    mark(tt()) -> active(tt())
    mark(isNePal(X)) -> active(isNePal(mark(X)))
    __(mark(X1),X2) -> __(X1,X2)
    __(X1,mark(X2)) -> __(X1,X2)
    __(active(X1),X2) -> __(X1,X2)
    __(X1,active(X2)) -> __(X1,X2)
    and(mark(X1),X2) -> and(X1,X2)
    and(X1,mark(X2)) -> and(X1,X2)
    and(active(X1),X2) -> and(X1,X2)
    and(X1,active(X2)) -> and(X1,X2)
    isNePal(mark(X)) -> isNePal(X)
    isNePal(active(X)) -> isNePal(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [tt] = 2,
     
     [active](x0) = x0 + 4,
     
     [nil] = 4,
     
     [and](x0, x1) = x0 + 4x1 + 4,
     
     [__](x0, x1) = 4x0 + 2x1 + 3,
     
     [isNePal](x0) = 2x0 + 4,
     
     [mark](x0) = 4x0 + 1
    orientation:
     mark(__(X1,X2)) = 16X1 + 8X2 + 13 >= 16X1 + 8X2 + 13 = active(__(mark(X1),mark(X2)))
     
     mark(nil()) = 17 >= 8 = active(nil())
     
     mark(and(X1,X2)) = 4X1 + 16X2 + 17 >= 4X1 + 4X2 + 9 = active(and(mark(X1),X2))
     
     mark(tt()) = 9 >= 6 = active(tt())
     
     mark(isNePal(X)) = 8X + 17 >= 8X + 10 = active(isNePal(mark(X)))
     
     __(mark(X1),X2) = 16X1 + 2X2 + 7 >= 4X1 + 2X2 + 3 = __(X1,X2)
     
     __(X1,mark(X2)) = 4X1 + 8X2 + 5 >= 4X1 + 2X2 + 3 = __(X1,X2)
     
     __(active(X1),X2) = 4X1 + 2X2 + 19 >= 4X1 + 2X2 + 3 = __(X1,X2)
     
     __(X1,active(X2)) = 4X1 + 2X2 + 11 >= 4X1 + 2X2 + 3 = __(X1,X2)
     
     and(mark(X1),X2) = 4X1 + 4X2 + 5 >= X1 + 4X2 + 4 = and(X1,X2)
     
     and(X1,mark(X2)) = X1 + 16X2 + 8 >= X1 + 4X2 + 4 = and(X1,X2)
     
     and(active(X1),X2) = X1 + 4X2 + 8 >= X1 + 4X2 + 4 = and(X1,X2)
     
     and(X1,active(X2)) = X1 + 4X2 + 20 >= X1 + 4X2 + 4 = and(X1,X2)
     
     isNePal(mark(X)) = 8X + 6 >= 2X + 4 = isNePal(X)
     
     isNePal(active(X)) = 2X + 12 >= 2X + 4 = isNePal(X)
    problem:
     mark(__(X1,X2)) -> active(__(mark(X1),mark(X2)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                     [1 0 0]  
      [active](x0) = [0 0 0]x0
                     [0 0 0]  ,
      
                          [1 0 0]     [0]
      [__](x0, x1) = x0 + [0 0 0]x1 + [0]
                          [0 0 1]     [1],
      
                   [1 0 1]  
      [mark](x0) = [0 1 0]x0
                   [0 0 0]  
     orientation:
                        [1 0 1]     [1 0 1]     [1]    [1 0 1]     [1 0 1]                                  
      mark(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = active(__(mark(X1),mark(X2)))
                        [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]                                  
     problem:
      
     Qed