YES 142.038 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ CR

mainModule FiniteMap
  ((elemFM :: Float  ->  FiniteMap Float a  ->  Bool) :: Float  ->  FiniteMap Float a  ->  Bool)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
  elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool
elemFM key fm = 
case lookupFM fm key of
  Nothing-> False
  Just elt-> True

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Case Reductions:
The following Case expression
case lookupFM fm key of
 Nothing → False
 Just elt → True

is transformed to
elemFM0 Nothing = False
elemFM0 (Just elt) = True



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR

mainModule FiniteMap
  ((elemFM :: Float  ->  FiniteMap Float a  ->  Bool) :: Float  ->  FiniteMap Float a  ->  Bool)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) 
  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
  elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool
elemFM key fm = elemFM0 (lookupFM fm key)

  
elemFM0 Nothing = False
elemFM0 (Just elt) = True

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt _ fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR

mainModule FiniteMap
  ((elemFM :: Float  ->  FiniteMap Float a  ->  Bool) :: Float  ->  FiniteMap Float a  ->  Bool)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
  elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool
elemFM key fm = elemFM0 (lookupFM fm key)

  
elemFM0 Nothing = False
elemFM0 (Just elt) = True

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt vw fm_l fm_r) key_to_find 
 | key_to_find < key = 
lookupFM fm_l key_to_find
 | key_to_find > key = 
lookupFM fm_r key_to_find
 | otherwise = 
Just elt


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Cond Reductions:
The following Function with conditions
lookupFM EmptyFM key = Nothing
lookupFM (Branch key elt vw fm_l fm_r) key_to_find
 | key_to_find < key
 = lookupFM fm_l key_to_find
 | key_to_find > key
 = lookupFM fm_r key_to_find
 | otherwise
 = Just elt

is transformed to
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt vw fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find

lookupFM0 key elt vw fm_l fm_r key_to_find True = Just elt

lookupFM2 key elt vw fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt vw fm_l fm_r key_to_find False = lookupFM1 key elt vw fm_l fm_r key_to_find (key_to_find > key)

lookupFM1 key elt vw fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt vw fm_l fm_r key_to_find False = lookupFM0 key elt vw fm_l fm_r key_to_find otherwise

lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find = lookupFM2 key elt vw fm_l fm_r key_to_find (key_to_find < key)

lookupFM4 EmptyFM key = Nothing
lookupFM4 wv ww = lookupFM3 wv ww

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow

mainModule FiniteMap
  (elemFM :: Float  ->  FiniteMap Float a  ->  Bool)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
  elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool
elemFM key fm = elemFM0 (lookupFM fm key)

  
elemFM0 Nothing = False
elemFM0 (Just elt) = True

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key = lookupFM4 EmptyFM key
lookupFM (Branch key elt vw fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find

  
lookupFM0 key elt vw fm_l fm_r key_to_find True = Just elt

  
lookupFM1 key elt vw fm_l fm_r key_to_find True = lookupFM fm_r key_to_find
lookupFM1 key elt vw fm_l fm_r key_to_find False = lookupFM0 key elt vw fm_l fm_r key_to_find otherwise

  
lookupFM2 key elt vw fm_l fm_r key_to_find True = lookupFM fm_l key_to_find
lookupFM2 key elt vw fm_l fm_r key_to_find False = lookupFM1 key elt vw fm_l fm_r key_to_find (key_to_find > key)

  
lookupFM3 (Branch key elt vw fm_l fm_r) key_to_find = lookupFM2 key elt vw fm_l fm_r key_to_find (key_to_find < key)

  
lookupFM4 EmptyFM key = Nothing
lookupFM4 wv ww = lookupFM3 wv ww


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                    ↳ QDPSizeChangeProof
                  ↳ QDP
                  ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_primPlusNat(Succ(wx8000), Succ(wx400000)) → new_primPlusNat(wx8000, wx400000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                    ↳ QDPSizeChangeProof
                  ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_primMulNat(Succ(wx30000), wx40000) → new_primMulNat(wx30000, wx40000)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM2195(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM240(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2130(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Pos(Zero)), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM227(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM243(wx39, Pos(wx400), wx41, wx42, wx43, wx44, wx45, Pos(wx460), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(wx460)), bd)
new_lookupFM269(wx58, Pos(wx590), wx60, wx61, wx62, wx63, wx64, Pos(wx650), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(wx650)), bf)
new_lookupFM148(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6060), ba) → new_lookupFM1313(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6060, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2146(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM274(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2730), ba) → new_lookupFM2178(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM1326(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx88600)), ba) → new_lookupFM1329(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx78000), Succ(wx60600), ba) → new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, wx78000, wx60600, ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Succ(wx38400)), bh) → new_lookupFM2203(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1278(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8040), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1309(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx87800)), ba) → new_lookupFM1312(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Zero, bd) → new_lookupFM2141(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1173(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54100), Succ(Succ(wx75600)), be) → new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx75600, wx54100, be)
new_lookupFM155(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7250), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20400), Zero, bd) → new_lookupFM2139(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Zero, ba) → new_lookupFM1169(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1413(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1394(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2154(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Zero, ba) → new_lookupFM1430(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM119(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM241(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1162(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Succ(Zero), be) → new_lookupFM1182(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), wx31), ba) → new_lookupFM2(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat1(new_primMulNat0(wx3000, wx40000), wx40000), ba)
new_lookupFM1131(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6610, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, Succ(wx58700), Succ(wx47400), ba) → new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, wx58700, wx47400, ba)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Zero, bf) → new_lookupFM2160(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM2217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6840), ba) → new_lookupFM1235(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6840, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM1359(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Succ(Zero), bh) → new_lookupFM1361(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM149(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1318(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1210(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx76400)), ba) → new_lookupFM1213(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2116(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2163(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2910), bf) → new_lookupFM2175(wx58, Succ(wx5900), wx60, wx61, wx62, wx63, wx64, Succ(wx6500), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM235(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69200), Zero, bf) → new_lookupFM1265(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM140(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Zero, bf) → new_lookupFM2173(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1245(wx40100, wx41, wx42, wx43, wx44, Succ(wx7690), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1340(wx40100, wx41, wx42, wx43, wx44, Succ(wx71300), Succ(Succ(wx89000)), ba) → new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, wx89000, wx71300, ba)
new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Succ(wx83000), ba) → new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx66000, wx83000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM148(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77400), Zero, bf) → new_lookupFM1261(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM249(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1880), ba) → new_lookupFM2151(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1127(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6600, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2223(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM126(wx40100, wx41, wx42, wx43, wx44, Succ(wx6660), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM110(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx5340), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Zero)), ba)
new_lookupFM117(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4590), ba) → new_lookupFM1109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4590, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1414(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM264(wx40100, wx41, wx42, wx43, wx44, Succ(wx2420), ba) → new_lookupFM2155(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1223(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx68200), Succ(Succ(wx86000)), ba) → new_lookupFM186(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, wx310000, wx86000, wx68200, ba)
new_lookupFM1417(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx9070), ba) → new_lookupFM1418(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1214(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx58500)), ba) → new_lookupFM1217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM13(wx30, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1377(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx76400), Succ(wx58400), ba) → new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, wx76400, wx58400, ba)
new_lookupFM111(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx6530), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM259(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2260), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Zero, be) → new_lookupFM1179(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, new_primMulNat0(wx2810, wx23), be)
new_lookupFM290(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3330), ba) → new_lookupFM2186(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Succ(wx72400), bh) → new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, wx53200, wx72400, bh)
new_lookupFM258(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2240), ba) → new_lookupFM2153(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1184(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Succ(Succ(wx75400)), bd) → new_lookupFM1187(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, Succ(wx7130), ba) → new_lookupFM1340(wx40100, wx41, wx42, wx43, wx44, wx7130, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM289(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM127(wx40100, wx41, wx42, wx43, wx44, Succ(wx5370), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM1290(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5640, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM233(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1126(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM282(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1244(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx76800)), ba) → new_lookupFM1247(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM146(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM27(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1344(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx78400)), ba) → new_lookupFM1347(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1404(wx40000, wx41, wx42, wx43, wx44, wx4980, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM27(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1050), h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM1259(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx7750), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM1424(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Succ(Succ(wx91000)), ba) → new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73600, wx91000, ba)
new_lookupFM225(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx990), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7070), ba) → new_lookupFM1309(wx40000, wx40100, wx41, wx42, wx43, wx44, wx7070, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), wx31), ba) → new_lookupFM294(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat0(new_primMulNat0(wx3000, wx40000), Succ(wx40000)), ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM2197(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM258(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Succ(Succ(wx78600)), bh) → new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx61700, wx78600, bh)
new_lookupFM1401(wx40000, wx41, wx42, wx43, wx44, wx4960, wx626, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Succ(wx57200), ba) → new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, wx46500, wx57200, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM290(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1348(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), Zero, bh) → new_lookupFM1179(wx67, wx6800, wx69, wx70, wx71, wx72, Succ(wx73), Succ(wx7400), new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM2103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3880), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1189(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx6750), bd) → new_lookupFM(wx44, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM189(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6550, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1173(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Zero, Succ(Succ(wx75600)), be) → new_lookupFM1176(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM1249(wx58, wx60, wx61, wx62, wx63, wx64, Zero, bf) → new_lookupFM1267(wx58, wx60, wx61, wx62, wx63, wx64, new_primMulNat1, bf)
new_lookupFM2120(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM175(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1169(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1247(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2129(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1406(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM232(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1171(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Zero, be) → new_lookupFM1174(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, new_primMulNat0(wx2810, wx23), be)
new_lookupFM2177(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1279(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1111(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM287(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM2221(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Zero, bd) → new_lookupFM2134(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM1140(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6620), ba) → new_lookupFM1141(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6620, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Zero)), bd)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1341(wx40100, wx41, wx42, wx43, wx44, Succ(wx8910), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Zero, bf) → new_lookupFM2163(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20400)), Succ(wx16500), bd) → new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20400, wx16500, bd)
new_lookupFM2108(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1115(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM2200(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM1304(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx70600), Succ(Succ(wx87600)), ba) → new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87600, wx70600, ba)
new_lookupFM1371(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8130), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1288(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8750), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(wx3100))), ba) → new_lookupFM168(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1238(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM252(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2133(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx1960), bd) → new_lookupFM2137(wx39, Succ(wx4000), wx41, wx42, wx43, wx44, wx45, Succ(wx4600), bd)
new_lookupFM189(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Succ(Zero), ba) → new_lookupFM191(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2105(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3940), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1277(wx58, wx60, wx61, wx62, wx63, wx64, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM1206(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx67900), Succ(Succ(wx85400)), ba) → new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, wx85400, wx67900, ba)
new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx76400), Zero, ba) → new_lookupFM1213(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM294(wx67, Neg(wx680), wx69, wx70, wx71, wx72, wx73, Pos(wx740), Succ(wx3450), bh) → new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM161(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Zero, ba) → new_lookupFM1380(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(wx3100))), ba) → new_lookupFM165(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1113(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6580, wx826, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM282(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1417(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1149(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1330(wx40100, wx41, wx42, wx43, wx44, Succ(wx61500), Succ(Succ(wx78200)), ba) → new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, wx78200, wx61500, ba)
new_lookupFM240(wx40100, wx41, wx42, wx43, wx44, Succ(wx1570), ba) → new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Succ(wx810), h) → new_lookupFM26(Float(Pos(Succ(wx30)), Neg(Succ(wx3100))), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1345(wx40100, wx41, wx42, wx43, wx44, Succ(wx7850), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM29(wx30, Zero, wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM1179(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx7620), be) → new_lookupFM(wx27, Float(Neg(wx2800), Pos(wx2810)), be)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1426(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM268(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM28(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM29(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM2152(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM221(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM148(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1314(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1206(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx85400)), ba) → new_lookupFM1209(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Succ(wx810), h) → new_lookupFM26(Float(Pos(Succ(wx30)), Neg(Zero)), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1244(wx40100, wx41, wx42, wx43, wx44, Succ(wx59200), Succ(Succ(wx76800)), ba) → new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, wx76800, wx59200, ba)
new_lookupFM18(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM1248(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Zero, bf) → new_lookupFM1263(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, new_primMulNat0(Zero, wx5900), bf)
new_lookupFM1331(wx40100, wx41, wx42, wx43, wx44, Succ(wx7830), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1279(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8050), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Zero, bf) → new_lookupFM2173(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM115(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1299(wx40000, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx60400)), ba) → new_lookupFM1302(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Zero, ba) → new_lookupFM191(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1170(wx39, wx41, wx42, wx43, wx44, wx45, Zero, bd) → new_lookupFM1189(wx39, wx41, wx42, wx43, wx44, wx45, new_primMulNat1, bd)
new_lookupFM2126(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM152(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1159(wx40100, wx41, wx42, wx43, wx44, wx6680, wx842, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1349(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), Zero, bh) → new_lookupFM1365(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM231(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1290), ba) → new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx58500), Zero, ba) → new_lookupFM1217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Succ(wx62800), ba) → new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, wx49800, wx62800, ba)
new_lookupFM1378(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Succ(Succ(wx61800)), ba) → new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, wx49000, wx61800, ba)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Zero, bh) → new_lookupFM2204(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM299(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1317(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx60700)), ba) → new_lookupFM1320(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM192(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Succ(Zero), ba) → new_lookupFM194(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM215(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM218(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Succ(wx11300)), h) → new_lookupFM216(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM280(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM162(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4920), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(wx3100))), ba)
new_lookupFM2139(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Zero, bh) → new_lookupFM2209(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2105(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1215(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5860), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx85400), Zero, ba) → new_lookupFM1209(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2213(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1371(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1227(wx40100, wx41, wx42, wx43, wx44, Succ(wx8630), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM255(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2180), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1199(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM249(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1195(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM244(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM121(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1250(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Zero, bf) → new_lookupFM1271(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, new_primMulNat0(Zero, wx5900), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM114(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Succ(wx11300)), h) → new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11300, h)
new_lookupFM1404(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Succ(Zero), ba) → new_lookupFM1406(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM2175(wx58, wx590, wx60, wx61, wx62, wx63, wx64, wx650, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(wx650)), bf)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Succ(wx3450), bh) → new_lookupFM2190(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx39)), Neg(Succ(wx4000))), wx41, wx42, wx43, wx44, wx45, bd)
new_lookupFM192(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4560, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM1156(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8410), ba) → new_lookupFM1157(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, Succ(wx78200), Succ(wx61500), ba) → new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, wx78200, wx61500, ba)
new_lookupFM1362(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Succ(Succ(wx72200)), bh) → new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, wx53000, wx72200, bh)
new_lookupFM2199(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM280(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3030), ba) → new_lookupFM2180(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM128(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM147(wx40000, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1300(wx40000, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1233(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM223(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM210(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM211(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM1431(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx5060, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Zero)), h)
new_lookupFM146(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4810), ba) → new_lookupFM1295(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4810, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM211(wx30, Zero, wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM1350(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx5280), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Zero, bh) → new_lookupFM1369(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM296(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1224(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8610), ba) → new_lookupFM185(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, wx310000, wx8610, Zero, ba)
new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6590), ba) → new_lookupFM1117(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6590, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1430(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM12(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx5060), h) → new_lookupFM1431(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx5060, new_primMulNat0(Zero, wx3100), h)
new_lookupFM276(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2790), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1404(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Succ(Succ(wx62800)), ba) → new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, wx49800, wx62800, ba)
new_lookupFM1397(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1241(wx40100, wx41, wx42, wx43, wx44, Succ(wx8670), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx58, Neg(Zero), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM274(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69800), Succ(wx52400), bf) → new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, wx69800, wx52400, bf)
new_lookupFM1285(wx500100, wx501, wx502, wx503, wx504, Succ(wx9490), bg) → new_lookupFM(wx504, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM1226(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx86200)), ba) → new_lookupFM1229(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1362(wx67, wx69, wx70, wx71, wx72, wx73, wx5300, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Zero)), bh)
new_lookupFM13(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx5070), h) → new_lookupFM1434(wx30, wx32, wx33, wx34, wx35, wx36, wx5070, new_primMulNat1, h)
new_lookupFM1253(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx59400), Succ(Succ(wx77200)), bf) → new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77200, wx59400, bf)
new_lookupFM151(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1331(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2156(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1424(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7360, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2189(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1350(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1418(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM135(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4730), ba) → new_lookupFM1214(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4730, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM163(wx40000, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1385(wx40000, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM242(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx86400), Zero, ba) → new_lookupFM1238(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM236(wx40100, wx41, wx42, wx43, wx44, Succ(wx1450), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM257(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2200), ba) → new_lookupFM2152(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1374(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7270), ba) → new_lookupFM1375(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx7270, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Succ(wx74800), h) → new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56400, wx74800, h)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Zero, bh) → new_lookupFM2202(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5640), h) → new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5640, new_primMulNat0(Succ(wx3700), wx3100), h)
new_lookupFM174(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7880), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM289(wx40100, wx41, wx42, wx43, wx44, Succ(wx3310), ba) → new_lookupFM2185(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM21(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM11(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM121(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4620), ba) → new_lookupFM1123(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4620, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Succ(Zero), h) → new_lookupFM18(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM291(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69200), Succ(wx52000), bf) → new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69200, wx52000, bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM225(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1177(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, wx760, be) → new_lookupFM1180(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM217(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1321(wx40000, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx60900)), ba) → new_lookupFM1324(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1166(wx40100, wx41, wx42, wx43, wx44, Succ(wx6710), ba) → new_lookupFM1167(wx40100, wx41, wx42, wx43, wx44, wx6710, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(wx3100))), ba) → new_lookupFM116(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM155(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1420(wx40100, wx41, wx42, wx43, wx44, wx7340, wx908, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), wx2560, bf)
new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60200), Zero, ba) → new_lookupFM1298(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, Succ(wx7340), ba) → new_lookupFM1420(wx40100, wx41, wx42, wx43, wx44, wx7340, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1326(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx71100), Succ(Succ(wx88600)), ba) → new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88600, wx71100, ba)
new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Zero, ba) → new_lookupFM1410(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60700), Succ(wx48400), ba) → new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60700, wx48400, ba)
new_lookupFM1282(Float(Pos(Succ(wx500000)), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1283(wx500000, wx500100, wx501, wx502, wx503, wx504, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM1375(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx7270, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2104(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Succ(Succ(wx74800)), h) → new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56400, wx74800, h)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Zero, bf) → new_lookupFM2168(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1209(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM153(wx40100, wx41, wx42, wx43, wx44, Succ(wx6160), ba) → new_lookupFM1344(wx40100, wx41, wx42, wx43, wx44, wx6160, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1254(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx85400), Succ(wx67900), ba) → new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, wx85400, wx67900, ba)
new_lookupFM2162(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM252(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2080), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, Succ(wx76600), Succ(wx59100), ba) → new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, wx76600, wx59100, ba)
new_lookupFM1258(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx59500), Succ(Succ(wx77400)), bf) → new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77400, wx59500, bf)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM170(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Zero)), ba) → new_lookupFM156(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2106(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2100(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3680), ba) → new_lookupFM1373(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM2198(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM1280(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8060), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM228(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1210), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Zero, bd) → new_lookupFM2135(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1156(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM269(wx58, Neg(wx590), wx60, wx61, wx62, wx63, wx64, Neg(wx650), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(wx650)), bf)
new_lookupFM2127(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Neg(wx2810), Succ(wx5420), be) → new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, new_primMulNat0(wx2810, wx23), be)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM266(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Zero), bh) → new_lookupFM2209(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1219(wx40000, wx41, wx42, wx43, wx44, Succ(wx5880), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1167(wx40100, wx41, wx42, wx43, wx44, wx6710, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM145(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4060), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM216(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Succ(wx89600), ba) → new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx72700, wx89600, ba)
new_lookupFM213(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1283(wx500000, wx500100, wx501, wx502, wx503, wx504, Succ(wx9390), bg) → new_lookupFM(wx504, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(wx25600), bf) → new_lookupFM2172(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM221(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx870), ba) → new_lookupFM174(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM197(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM243(wx39, Neg(Zero), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Zero, bd) → new_lookupFM1170(wx39, wx41, wx42, wx43, wx44, wx45, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM288(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3270), ba) → new_lookupFM2184(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2116(wx40100, wx41, wx42, wx43, wx44, Succ(wx4280), ba) → new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx87800), Zero, ba) → new_lookupFM1312(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Zero), bh) → new_lookupFM2202(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1262(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx52000), Succ(Succ(wx69200)), bf) → new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69200, wx52000, bf)
new_lookupFM2187(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2169(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87400), Zero, ba) → new_lookupFM1290(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1352(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx5300), bh) → new_lookupFM1362(wx67, wx69, wx70, wx71, wx72, wx73, wx5300, new_primMulNat1, bh)
new_lookupFM1262(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Zero, Succ(Succ(wx69200)), bf) → new_lookupFM1265(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM166(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1399(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(wx11500), h) → new_lookupFM2226(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM10(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), Zero, h) → new_lookupFM182(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM2194(wx67, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM1354(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2186(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Succ(wx3450), bh) → new_lookupFM2191(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, Succ(wx86600), Zero, ba) → new_lookupFM1243(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1180(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be) → new_lookupFM(wx27, Float(Neg(wx2800), Pos(wx2810)), be)
new_lookupFM286(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3210), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx86400), Succ(wx68400), ba) → new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, wx86400, wx68400, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM234(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2207(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM133(wx40000, wx41, wx42, wx43, wx44, Succ(wx4710), ba) → new_lookupFM1196(wx40000, wx41, wx42, wx43, wx44, wx4710, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM249(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM227(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM183(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2113(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4180), ba) → new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1141(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6620, wx834, ba) → new_lookupFM185(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, wx310000, wx6620, wx834, ba)
new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Zero, h) → new_lookupFM18(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM273(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2710), ba) → new_lookupFM2177(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM139(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1245(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2171(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM2174(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2135(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM118(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1423(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7360), ba) → new_lookupFM1424(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7360, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM233(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1350), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx67400), Zero, bd) → new_lookupFM1191(wx39, wx41, wx42, wx43, wx44, wx45, bd)
new_lookupFM166(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4950), ba) → new_lookupFM1398(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4950, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM2100(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2215(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1378(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Succ(Zero), ba) → new_lookupFM1380(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1229(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6570, wx824, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1137(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Succ(Zero), ba) → new_lookupFM1139(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1428(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Succ(Succ(wx91200)), ba) → new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, wx73700, wx91200, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM231(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1187(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM(wx44, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM167(wx40000, wx41, wx42, wx43, wx44, Succ(wx4960), ba) → new_lookupFM1401(wx40000, wx41, wx42, wx43, wx44, wx4960, new_primMulNat1, ba)
new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Zero, ba) → new_lookupFM1426(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM125(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM163(wx40000, wx41, wx42, wx43, wx44, Succ(wx4930), ba) → new_lookupFM1384(wx40000, wx41, wx42, wx43, wx44, wx4930, new_primMulNat1, ba)
new_lookupFM1250(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx5230), bf) → new_lookupFM1270(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx5230, new_primMulNat0(Zero, wx5900), bf)
new_lookupFM1136(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1408(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Succ(Succ(wx90200)), ba) → new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73000, wx90200, ba)
new_lookupFM295(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3520), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM138(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM164(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1344(wx40100, wx41, wx42, wx43, wx44, Succ(wx61600), Succ(Succ(wx78400)), ba) → new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, wx78400, wx61600, ba)
new_lookupFM138(wx40100, wx41, wx42, wx43, wx44, Succ(wx5440), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM2161(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2870), bf) → new_lookupFM2169(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1307(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1362(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Succ(Zero), bh) → new_lookupFM1364(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Succ(wx16500), bd) → new_lookupFM2140(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Zero), Zero, bf) → new_lookupFM1248(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM2166(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM2169(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, Succ(wx58700), Zero, ba) → new_lookupFM1221(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1163(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Succ(Succ(wx84400)), ba) → new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, wx67000, wx84400, ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Neg(Succ(wx3100))), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM287(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1273(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM1292(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7790), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2107(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1145(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Zero), bh) → new_lookupFM2211(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1385(wx40000, wx41, wx42, wx43, wx44, Succ(wx6230), ba) → new_lookupFM1386(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7280), ba) → new_lookupFM1388(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx7280, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Succ(wx3450), bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM2115(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4240), ba) → new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1221(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1370(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8120), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM125(wx40000, wx41, wx42, wx43, wx44, Succ(wx4660), ba) → new_lookupFM1137(wx40000, wx41, wx42, wx43, wx44, wx4660, new_primMulNat1, ba)
new_lookupFM2108(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4040), ba) → new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2101(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1129(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM119(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5360), ba) → new_lookupFM1120(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5360, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1254(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx7730), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Succ(wx5420), be) → new_lookupFM1177(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, new_primMulNat0(wx2810, wx23), be)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM2203(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20600)), Zero, bd) → new_lookupFM2143(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20400), Succ(wx16500), bd) → new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20400, wx16500, bd)
new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Succ(wx78600), bh) → new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx61700, wx78600, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2115(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1270(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx52300), Succ(Succ(wx69600)), bf) → new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69600, wx52300, bf)
new_lookupFM1412(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7310, wx904, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM277(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29300)), Succ(wx25600), bf) → new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29300, wx25600, bf)
new_lookupFM11(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5050), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88800), Zero, ba) → new_lookupFM1338(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29500), Zero, bf) → new_lookupFM2171(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM23(wx30, wx32, wx33, wx34, wx35, wx36, h) → new_lookupFM13(wx30, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2191(wx67, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM1352(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2184(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2148(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1192(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2108(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1424(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Succ(Zero), ba) → new_lookupFM1426(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM19(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx6520), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM254(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1375(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Succ(Succ(wx89600)), ba) → new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx72700, wx89600, ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Succ(wx810), h) → new_lookupFM21(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1256(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM1333(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1226(wx40100, wx41, wx42, wx43, wx44, Succ(wx68300), Succ(Succ(wx86200)), ba) → new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, wx86200, wx68300, ba)
new_lookupFM273(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1279(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69600), Zero, bf) → new_lookupFM1273(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM1295(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx48100), Succ(Succ(wx60200)), ba) → new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60200, wx48100, ba)
new_lookupFM2228(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM298(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1223(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx86000)), ba) → new_lookupFM187(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM220(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2111(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1407(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, Succ(wx60400), Zero, ba) → new_lookupFM1302(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Succ(wx56600), ba) → new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, wx45600, wx56600, ba)
new_lookupFM1369(wx67, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM1352(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM29(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx75400), Zero, bd) → new_lookupFM1187(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM218(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM232(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1330), ba) → new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Succ(wx810), h) → new_lookupFM25(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2210(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM1433(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Zero)), h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(wx3100))), ba) → new_lookupFM120(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM285(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2119(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM174(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM228(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(wx38600), bh) → new_lookupFM2210(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM228(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM188(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2227(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Succ(Succ(wx75000)), h) → new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56500, wx75000, h)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM2199(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Succ(wx62000), ba) → new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, wx49100, wx62000, ba)
new_lookupFM1265(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM1367(wx67, wx69, wx70, wx71, wx72, wx73, wx5320, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM2102(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3740), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM168(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4970), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(wx3100))), ba)
new_lookupFM269(wx58, Neg(Zero), wx60, wx61, wx62, wx63, wx64, Pos(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM185(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Succ(Succ(wx92200)), bc) → new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, wx9210, wx92200, bc)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(wx3100))), ba) → new_lookupFM162(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), wx2560, bf)
new_lookupFM2150(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1194(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1201(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67800), Succ(Succ(wx85200)), ba) → new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx85200, wx67800, ba)
new_lookupFM149(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4840), ba) → new_lookupFM1317(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4840, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, Succ(wx60900), Succ(wx48500), ba) → new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, wx60900, wx48500, ba)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), wx1650, bd)
new_lookupFM1358(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM192(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Succ(Succ(wx56600)), ba) → new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, wx45600, wx56600, ba)
new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60700), Zero, ba) → new_lookupFM1320(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Zero)), ba) → new_lookupFM110(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, Succ(wx76800), Zero, ba) → new_lookupFM1247(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29300), Succ(wx25600), bf) → new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29300, wx25600, bf)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Succ(wx3450), bh) → new_lookupFM2194(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM132(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM281(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM238(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2128(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM213(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1309(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx70700), Succ(Succ(wx87800)), ba) → new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, wx87800, wx70700, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM163(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1282(Float(Neg(Succ(wx500000)), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1179(wx500000, wx500100, wx501, wx502, wx503, wx504, Zero, Succ(Succ(Zero)), new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM161(wx40000, wx41, wx42, wx43, wx44, Succ(wx4910), ba) → new_lookupFM1381(wx40000, wx41, wx42, wx43, wx44, wx4910, new_primMulNat1, ba)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, Succ(wx76600), Zero, ba) → new_lookupFM1233(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM229(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1230), ba) → new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1416(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7330, wx906, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(wx11300), h) → new_lookupFM216(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM273(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM113(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4560), ba) → new_lookupFM192(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4560, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Succ(wx11500)), h) → new_lookupFM2226(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM289(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6780), ba) → new_lookupFM1201(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6780, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1374(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1122(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1442(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM128(wx40100, wx41, wx42, wx43, wx44, Succ(wx6690), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM248(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM274(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1280(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM260(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx77800), Succ(wx60100), ba) → new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, wx77800, wx60100, ba)
new_lookupFM182(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx6460), h) → new_lookupFM181(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM224(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2122(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM2226(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM1170(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx5130), bd) → new_lookupFM1188(wx39, wx41, wx42, wx43, wx44, wx45, wx5130, new_primMulNat1, bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM154(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM248(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1194(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1143(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Succ(Succ(wx83500)), ba) → new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, wx66300, wx83500, ba)
new_lookupFM134(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1211(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Succ(Zero), bh) → new_lookupFM1358(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, Succ(wx86200), Zero, ba) → new_lookupFM1229(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM170(wx40100, wx41, wx42, wx43, wx44, Succ(wx7320), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1126(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6600), ba) → new_lookupFM1127(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6600, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM173(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM127(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM243(wx39, Neg(Zero), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, Succ(wx78400), Succ(wx61600), ba) → new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, wx78400, wx61600, ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Neg(Zero)), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM245(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM210(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1431(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Succ(Succ(wx64800)), h) → new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx50600, wx64800, h)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM2195(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM251(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1940), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx58, Pos(Zero), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM147(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2130(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2125(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1105(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1163(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Succ(Zero), ba) → new_lookupFM1165(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM229(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2123(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2167(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Succ(wx810), h) → new_lookupFM23(wx30, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM211(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2190(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM1351(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM135(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM280(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2112(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Zero, bd) → new_lookupFM2145(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM224(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM279(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2110(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4100), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM288(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2197(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1305(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8770), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1153(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Zero, bd) → new_lookupFM2136(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM290(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2118(wx40100, wx41, wx42, wx43, wx44, Succ(wx4340), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2198(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM2199(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM257(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM164(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5590), ba) → new_lookupFM1395(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5590, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69600), Succ(wx52300), bf) → new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69600, wx52300, bf)
new_lookupFM283(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3130), ba) → new_lookupFM2183(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2116(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2221(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM189(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Succ(Succ(wx82000)), ba) → new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, wx65500, wx82000, ba)
new_lookupFM2182(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2172(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM117(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1110(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Succ(wx11500)), h) → new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11500, h)
new_lookupFM165(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4940), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(wx3100))), ba)
new_lookupFM1143(wx40100, wx41, wx42, wx43, wx44, wx6630, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(wx3100))), ba) → new_lookupFM123(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1393(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2106(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1335(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx88800)), ba) → new_lookupFM1338(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM250(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM167(wx40000, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1402(wx40000, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM263(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Succ(wx38600)), bh) → new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38600, bh)
new_lookupFM298(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2213(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2104(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1389(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8990), ba) → new_lookupFM1390(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2222(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM242(wx40100, wx41, wx42, wx43, wx44, Succ(wx1630), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1152(wx40100, wx41, wx42, wx43, wx44, Succ(wx8390), ba) → new_lookupFM1153(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, wx2560, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Zero, h) → new_lookupFM2227(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1437(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx6430), h) → new_lookupFM1438(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM1304(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx87600)), ba) → new_lookupFM1307(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, Succ(wx4540), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(wx740)), bh)
new_lookupFM116(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4580), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(wx3100))), ba)
new_lookupFM144(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx5490), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Zero)), ba)
new_lookupFM129(wx40100, wx41, wx42, wx43, wx44, Succ(wx5380), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM2196(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM136(wx40000, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1219(wx40000, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx6170), bh) → new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx6170, new_primMulNat0(Succ(wx7400), wx6800), bh)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(wx11300), h) → new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11300, h)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Zero, h) → new_lookupFM2225(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2189(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1182(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be) → new_lookupFM(wx27, Float(Neg(wx2800), Neg(wx2810)), be)
new_lookupFM158(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx5570), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2110(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1365(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx7180), bh) → new_lookupFM1366(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM2196(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM2197(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, Succ(wx58200), Succ(wx47100), ba) → new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, wx58200, wx47100, ba)
new_lookupFM1388(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx7280, wx898, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM14(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1347(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM239(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2129(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM297(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, Zero, h) → new_lookupFM2228(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Zero, ba) → new_lookupFM1129(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77200), Zero, bf) → new_lookupFM1256(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM275(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2128(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1148(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2113(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2218(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM167(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Zero, bd) → new_lookupFM2133(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29500), Succ(wx25600), bf) → new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29500, wx25600, bf)
new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Zero, h) → new_lookupFM1436(wx30, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM287(wx40100, wx41, wx42, wx43, wx44, Succ(wx3250), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM120(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4610), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(wx3100))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1114(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8270), ba) → new_lookupFM1115(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM213(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1110), h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM277(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2830), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1381(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Succ(Zero), ba) → new_lookupFM1383(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM220(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx850), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1378(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4900, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1395(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5590, wx746, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1298(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5650), h) → new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5650, new_primMulNat0(Succ(wx3700), wx3100), h)
new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7330), ba) → new_lookupFM1416(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7330, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM257(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM137(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1155(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6670, wx840, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1131(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Succ(Succ(wx83200)), ba) → new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, wx66100, wx83200, ba)
new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1114(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, Succ(wx76800), Succ(wx59200), ba) → new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, wx76800, wx59200, ba)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29500)), Zero, bf) → new_lookupFM2171(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29300)), Zero, bf) → new_lookupFM2166(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM169(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6640), ba) → new_lookupFM1147(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6640, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM262(wx40100, wx41, wx42, wx43, wx44, Succ(wx2360), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1403(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2111(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4120), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, Succ(wx6830), ba) → new_lookupFM1226(wx40100, wx41, wx42, wx43, wx44, wx6830, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1438(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(wx370)), h)
new_lookupFM1194(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7980), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1139(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1295(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx60200)), ba) → new_lookupFM1298(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2147(wx39, wx400, wx41, wx42, wx43, wx44, wx45, wx460, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(wx460)), bd)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Zero), bh) → new_lookupFM2204(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM236(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1142(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM224(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx970), ba) → new_lookupFM177(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM122(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx75600), Zero, be) → new_lookupFM1176(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM1335(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx71200), Succ(Succ(wx88800)), ba) → new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88800, wx71200, ba)
new_lookupFM1108(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Succ(wx38600)), bh) → new_lookupFM2210(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1322(wx40000, wx41, wx42, wx43, wx44, Succ(wx6100), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM253(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1372(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8140), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2206(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Zero, bd) → new_lookupFM2141(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM26(Float(Pos(Succ(wx15000)), wx151), wx16, wx17, wx18, wx19, wx20, bb) → new_lookupFM178(wx15000, wx151, wx16, wx17, wx18, wx19, wx20, new_primPlusNat0(new_primMulNat0(wx20, wx15000), Succ(wx15000)), bb)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM144(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM247(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1193(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2178(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1280(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87400), Succ(wx70500), ba) → new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87400, wx70500, ba)
new_lookupFM119(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1121(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, Succ(wx89000), Zero, ba) → new_lookupFM1343(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1312(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Zero, ba) → new_lookupFM1139(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM2173(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM272(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2670), ba) → new_lookupFM2176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM133(wx40000, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1197(wx40000, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM265(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM188(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6550), ba) → new_lookupFM189(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6550, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1240(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx86600)), ba) → new_lookupFM1243(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Zero, ba) → new_lookupFM1383(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM296(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3560), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM239(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Succ(wx810), h) → new_lookupFM22(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1421(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1351(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx5290), bh) → new_lookupFM1359(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx5290, new_primMulNat0(Zero, wx6800), bh)
new_lookupFM1336(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8890), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM282(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3090), ba) → new_lookupFM2182(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM141(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1218(wx40000, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx58700)), ba) → new_lookupFM1221(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1227(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Zero, bh) → new_lookupFM1364(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM2162(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2890), bf) → new_lookupFM2174(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2135(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx2000), bd) → new_lookupFM2146(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Zero, ba) → new_lookupFM1377(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM283(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1259(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Succ(wx91200), ba) → new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, wx73700, wx91200, ba)
new_lookupFM266(wx40100, wx41, wx42, wx43, wx44, Succ(wx2480), ba) → new_lookupFM2157(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM29(wx30, Zero, wx32, wx33, wx34, wx35, wx36, Zero, h)
new_lookupFM1195(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7990), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM259(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1133(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1117(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6590, wx828, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM244(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1720), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM221(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2119(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM151(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Zero, be) → new_lookupFM1182(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Zero, ba) → new_lookupFM194(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1167(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Succ(Zero), ba) → new_lookupFM1169(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1383(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1359(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx5290, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Zero)), bh)
new_lookupFM2141(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29500)), Succ(wx25600), bf) → new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29500, wx25600, bf)
new_lookupFM2101(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3700), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, Succ(wx89000), Succ(wx71300), ba) → new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, wx89000, wx71300, ba)
new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, Succ(wx58200), Zero, ba) → new_lookupFM1199(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Zero)), ba) → new_lookupFM131(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Zero, bh) → new_lookupFM1361(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM1160(wx40100, wx41, wx42, wx43, wx44, Succ(wx8430), ba) → new_lookupFM1161(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM261(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM265(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1165(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1317(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx48400), Succ(Succ(wx60700)), ba) → new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60700, wx48400, ba)
new_lookupFM130(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7420), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM2198(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3800), bh) → new_lookupFM2207(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM146(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1296(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Zero, h) → new_lookupFM217(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6560), ba) → new_lookupFM199(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6560, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1163(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6700, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM28(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM1185(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx4600), wx4000), bd)
new_lookupFM156(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx5560), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Zero)), ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM2197(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM1275(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx6990), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, Zero, h) → new_lookupFM218(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2145(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM1373(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8150), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69800), Zero, bf) → new_lookupFM1277(wx58, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM227(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1170), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2200(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3820), bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM11(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1184(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx57600), Succ(Succ(wx75400)), bd) → new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx75400, wx57600, bd)
new_lookupFM2112(wx40100, wx41, wx42, wx43, wx44, Succ(wx4160), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM153(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1345(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM160(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM22(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h) → new_lookupFM12(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM152(wx40100, wx41, wx42, wx43, wx44, Succ(wx5520), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1134(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Succ(Succ(wx57200)), ba) → new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, wx46500, wx57200, ba)
new_lookupFM177(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7910), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Succ(wx38400)), bh) → new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38400, bh)
new_lookupFM281(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3070), ba) → new_lookupFM2181(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM158(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Succ(wx16500), bd) → new_lookupFM2140(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM2104(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3920), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1211(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7650), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1287(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx87400)), ba) → new_lookupFM1290(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, Succ(wx86200), Succ(wx68300), ba) → new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, wx86200, wx68300, ba)
new_lookupFM299(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3640), ba) → new_lookupFM1372(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1336(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM264(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1235(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx86400)), ba) → new_lookupFM1238(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1353(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx5310), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM243(wx39, Pos(Zero), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Zero)), bd)
new_lookupFM1119(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, Succ(wx78200), Zero, ba) → new_lookupFM1333(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1396(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7470), ba) → new_lookupFM1397(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM265(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2440), ba) → new_lookupFM2156(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Succ(wx90200), ba) → new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73000, wx90200, ba)
new_lookupFM1393(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx9010), ba) → new_lookupFM1394(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1348(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Zero, Zero, bh) → new_lookupFM1179(wx67, wx6800, wx69, wx70, wx71, wx72, Succ(wx73), Zero, Zero, bh)
new_lookupFM122(wx40000, wx41, wx42, wx43, wx44, Succ(wx4630), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), wx1650, bd)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM233(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM191(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1118(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM134(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Succ(wx16500), bd) → new_lookupFM2144(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM172(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1398(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4950, wx624, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2140(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM2179(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1281(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Zero), Zero, bf) → new_lookupFM1250(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM246(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1780), ba) → new_lookupFM2148(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(wx38600), bh) → new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38600, bh)
new_lookupFM270(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2610), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Zero, ba) → new_lookupFM1165(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1366(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(wx740)), bh)
new_lookupFM275(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1281(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1197(wx40000, wx41, wx42, wx43, wx44, Succ(wx5830), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM246(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1192(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Zero), h) → new_lookupFM2227(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Zero, bh) → new_lookupFM1358(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1210(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx58400), Succ(Succ(wx76400)), ba) → new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, wx76400, wx58400, ba)
new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1241(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7110), ba) → new_lookupFM1326(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7110, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1202(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1267(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx6950), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69400), Zero, bf) → new_lookupFM1269(wx58, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx75400), Succ(wx57600), bd) → new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx75400, wx57600, bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM241(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1152(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM259(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM134(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5840), ba) → new_lookupFM1210(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5840, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1235(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx68400), Succ(Succ(wx86400)), ba) → new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, wx86400, wx68400, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2105(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1236(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1224(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2113(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM279(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM297(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2212(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM1201(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, Succ(Succ(wx85200)), ba) → new_lookupFM1204(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM278(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2970), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM145(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6010), ba) → new_lookupFM1291(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6010, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1266(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx52100), Succ(Succ(wx69400)), bf) → new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, wx69400, wx52100, bf)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Succ(wx25600), bf) → new_lookupFM2167(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1271(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx6970), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM1313(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx78000)), ba) → new_lookupFM1316(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM181(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(wx370)), h)
new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, Succ(wx6850), ba) → new_lookupFM1240(wx40100, wx41, wx42, wx43, wx44, wx6850, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2225(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM2228(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6820), ba) → new_lookupFM1223(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6820, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1110(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5690), ba) → new_lookupFM1111(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1123(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4620, wx570, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1207(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8550), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM250(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1900), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM149(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM236(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1266(wx58, wx60, wx61, wx62, wx63, wx64, Zero, Succ(Succ(wx69400)), bf) → new_lookupFM1269(wx58, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), wx31), ba) → new_lookupFM243(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat0(new_primMulNat0(wx3000, wx40000), Succ(wx40000)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM130(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM271(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2650), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM2199(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM2110(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM283(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Zero, bf) → new_lookupFM2161(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2107(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM12(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, Succ(wx86600), Succ(wx68500), ba) → new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, wx86600, wx68500, ba)
new_lookupFM1121(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7410), ba) → new_lookupFM1122(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM269(wx58, Neg(Zero), wx60, wx61, wx62, wx63, wx64, Pos(Zero), Zero, bf) → new_lookupFM1249(wx58, wx60, wx61, wx62, wx63, wx64, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM195(wx40000, wx41, wx42, wx43, wx44, wx4570, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM178(wx15000, Pos(wx1510), wx16, wx17, wx18, wx19, wx20, Succ(wx6300), bb) → new_lookupFM179(wx15000, wx1510, wx16, wx17, wx18, wx19, wx20, Zero, wx6300, bb)
new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6570), ba) → new_lookupFM1103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6570, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, Succ(wx60400), Succ(wx48200), ba) → new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, wx60400, wx48200, ba)
new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Succ(wx63400), ba) → new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, wx45700, wx63400, ba)
new_lookupFM219(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx820), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2121(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, Zero, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7290), ba) → new_lookupFM1392(wx40000, wx40100, wx41, wx42, wx43, wx44, wx7290, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2(wx30, Neg(wx310), wx32, wx33, wx34, wx35, wx36, Pos(wx370), Succ(wx810), h) → new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1130(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6610), ba) → new_lookupFM1131(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6610, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1407(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7300), ba) → new_lookupFM1408(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7300, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1134(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Succ(Zero), ba) → new_lookupFM1136(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2136(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx2020), bd) → new_lookupFM2147(wx39, Succ(wx4000), wx41, wx42, wx43, wx44, wx45, Succ(wx4600), bd)
new_lookupFM1384(wx40000, wx41, wx42, wx43, wx44, wx4930, wx622, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1390(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM230(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1270), ba) → new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Pos(Zero)), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM2157(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM219(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM230(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2124(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM114(wx40000, wx41, wx42, wx43, wx44, Succ(wx4570), ba) → new_lookupFM195(wx40000, wx41, wx42, wx43, wx44, wx4570, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2117(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1196(wx40000, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx58200)), ba) → new_lookupFM1199(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM247(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1820), ba) → new_lookupFM2149(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77400), Succ(wx59500), bf) → new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77400, wx59500, bf)
new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, Succ(wx4510), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(wx370)), h)
new_lookupFM234(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1130(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Succ(wx65000), h) → new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, wx50700, wx65000, h)
new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1341(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1310(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8790), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2117(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1423(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1434(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Succ(Zero), h) → new_lookupFM1436(wx30, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1127(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Succ(Succ(wx83000)), ba) → new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx66000, wx83000, ba)
new_lookupFM1386(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM237(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2127(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1270(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Zero, Succ(Succ(wx69600)), bf) → new_lookupFM1273(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Succ(Zero), h) → new_lookupFM1442(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM278(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29300), Zero, bf) → new_lookupFM2166(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1243(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1202(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8530), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1399(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6250), ba) → new_lookupFM1400(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1191(wx39, wx41, wx42, wx43, wx44, wx45, bd) → new_lookupFM(wx44, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM1324(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM124(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4650), ba) → new_lookupFM1134(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4650, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1367(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Succ(Zero), bh) → new_lookupFM1369(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1470), ba) → new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM150(wx40000, wx41, wx42, wx43, wx44, Succ(wx4850), ba) → new_lookupFM1321(wx40000, wx41, wx42, wx43, wx44, wx4850, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Zero)), ba) → new_lookupFM142(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM254(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1258(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(Succ(wx77400)), bf) → new_lookupFM1261(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, wx2560, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM1236(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8650), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1381(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Succ(Succ(wx62000)), ba) → new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, wx49100, wx62000, ba)
new_lookupFM137(wx40100, wx41, wx42, wx43, wx44, Succ(wx5910), ba) → new_lookupFM1230(wx40100, wx41, wx42, wx43, wx44, wx5910, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM243(wx39, Pos(Zero), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx39)), Pos(Zero)), wx41, wx42, wx43, wx44, wx45, bd)
new_lookupFM194(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM1100(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8230), ba) → new_lookupFM1101(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2160(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2850), bf) → new_lookupFM2164(wx58, Succ(wx5900), wx60, wx61, wx62, wx63, wx64, Succ(wx6500), bf)
new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, Succ(wx4520), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(wx370)), h)
new_lookupFM140(wx40100, wx41, wx42, wx43, wx44, Succ(wx5450), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM297(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3580), ba) → new_lookupFM1370(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Zero, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM112(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4550), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(wx3100))), ba)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(wx38400), bh) → new_lookupFM2203(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM298(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3620), ba) → new_lookupFM1371(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM129(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1253(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(Succ(wx77200)), bf) → new_lookupFM1256(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2115(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2220(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1287(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx70500), Succ(Succ(wx87400)), ba) → new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87400, wx70500, ba)
new_lookupFM226(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1030), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM28(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1070), h) → new_lookupFM2222(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM248(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1840), ba) → new_lookupFM2150(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Zero, ba) → new_lookupFM1406(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1381(wx40000, wx41, wx42, wx43, wx44, wx4910, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx85200), Zero, ba) → new_lookupFM1204(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1434(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Succ(Succ(wx65000)), h) → new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, wx50700, wx65000, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM262(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7120), ba) → new_lookupFM1335(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7120, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM269(wx58, Pos(Zero), wx60, wx61, wx62, wx63, wx64, Neg(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM230(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2136(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Zero, bf) → new_lookupFM2168(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1354(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx5320), bh) → new_lookupFM1367(wx67, wx69, wx70, wx71, wx72, wx73, wx5320, new_primMulNat1, bh)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM19(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1124(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5710), ba) → new_lookupFM1125(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM272(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1278(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM269(wx58, Pos(Zero), wx60, wx61, wx62, wx63, wx64, Neg(Zero), Zero, bf) → new_lookupFM1251(wx58, wx60, wx61, wx62, wx63, wx64, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM260(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2300), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1125(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM285(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3190), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1151(wx40100, wx41, wx42, wx43, wx44, wx6650, wx838, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1299(wx40000, wx41, wx42, wx43, wx44, Succ(wx48200), Succ(Succ(wx60400)), ba) → new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, wx60400, wx48200, ba)
new_lookupFM2134(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM1340(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx89000)), ba) → new_lookupFM1343(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM157(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM195(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Succ(Succ(wx63400)), ba) → new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, wx45700, wx63400, ba)
new_lookupFM1127(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Succ(Zero), ba) → new_lookupFM1129(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Succ(wx91000), ba) → new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73600, wx91000, ba)
new_lookupFM14(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5080), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Succ(wx84400), ba) → new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, wx67000, wx84400, ba)
new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1327(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Succ(wx76100), be) → new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx54200, wx76100, be)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM111(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Succ(wx61800), ba) → new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, wx49000, wx61800, ba)
new_lookupFM2164(wx58, wx590, wx60, wx61, wx62, wx63, wx64, wx650, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(wx650)), bf)
new_lookupFM1(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), Zero, h) → new_lookupFM1437(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM243(wx39, Neg(Zero), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM1428(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Succ(Zero), ba) → new_lookupFM1430(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM132(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7430), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM1137(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Succ(Succ(wx63500)), ba) → new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, wx46600, wx63500, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Neg(Zero)), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM243(wx39, Neg(wx400), wx41, wx42, wx43, wx44, wx45, Neg(wx460), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(wx460)), bd)
new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx6170, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2112(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1375(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Succ(Zero), ba) → new_lookupFM1377(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM1353(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM241(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1590), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1213(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Succ(wx75000), h) → new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56500, wx75000, h)
new_lookupFM173(wx40100, wx41, wx42, wx43, wx44, Succ(wx5620), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2180(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM160(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4900), ba) → new_lookupFM1378(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4900, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM2122(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM177(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1147(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6640, wx836, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1134(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4650, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Zero, ba) → new_lookupFM1145(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2212(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1370(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM142(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx5480), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Zero)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM286(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20400)), Zero, bd) → new_lookupFM2139(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM235(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1140(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1118(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8290), ba) → new_lookupFM1119(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM115(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1107(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM143(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7450), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM281(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx58500), Succ(wx47300), ba) → new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx58500, wx47300, ba)
new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, wx69400, wx52100, bf)
new_lookupFM2202(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM2205(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM266(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, Zero, bh) → new_lookupFM2205(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Zero, ba) → new_lookupFM1133(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM178(wx15000, Neg(Zero), wx16, wx17, wx18, wx19, wx20, Succ(wx6300), bb) → new_lookupFM(wx19, Float(Pos(Succ(wx20)), Neg(Zero)), bb)
new_lookupFM2123(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM242(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1166(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(wx3100))), ba) → new_lookupFM159(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1302(wx40000, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM1350(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1330(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx78200)), ba) → new_lookupFM1333(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1408(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Succ(Zero), ba) → new_lookupFM1410(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2193(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1353(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Zero, h) → new_lookupFM1433(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(wx3100))), ba) → new_lookupFM112(wx40000, wx41, wx42, wx43, wx44, wx3100, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1305(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1100(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1107(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7390), ba) → new_lookupFM1108(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1240(wx40100, wx41, wx42, wx43, wx44, Succ(wx68500), Succ(Succ(wx86600)), ba) → new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, wx86600, wx68500, ba)
new_lookupFM1313(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60600), Succ(Succ(wx78000)), ba) → new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, wx78000, wx60600, ba)
new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7050), ba) → new_lookupFM1287(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx7050, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Zero, bf) → new_lookupFM2162(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM1188(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx51300), Succ(Succ(wx67400)), bd) → new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, wx67400, wx51300, bd)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Succ(wx16500), bd) → new_lookupFM2144(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7060), ba) → new_lookupFM1304(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx7060, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM115(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx5350), ba) → new_lookupFM1106(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5350, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, Succ(wx6680), ba) → new_lookupFM1159(wx40100, wx41, wx42, wx43, wx44, wx6680, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM195(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Succ(Zero), ba) → new_lookupFM197(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM2211(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Zero), h) → new_lookupFM217(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM27(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, wx1650, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM294(wx67, Pos(wx680), wx69, wx70, wx71, wx72, wx73, Neg(wx740), Succ(wx3450), bh) → new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Zero, h) → new_lookupFM215(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6790), ba) → new_lookupFM1206(wx40000, wx40100, wx41, wx42, wx43, wx44, wx6790, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM293(wx40100, wx41, wx42, wx43, wx44, Succ(wx3430), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM240(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2151(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1195(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM175(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7890), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1294(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1413(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx9050), ba) → new_lookupFM1414(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM268(wx40100, wx41, wx42, wx43, wx44, Succ(wx2540), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1284(wx500100, wx501, wx502, wx503, wx504, Succ(wx9430), bg) → new_lookupFM(wx504, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM2155(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2118(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx5760), bd) → new_lookupFM1184(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx5760, new_primMulNat0(Succ(wx4600), wx4000), bd)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(wx25600), bf) → new_lookupFM2167(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1161(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx39)), Pos(Succ(wx4000))), wx41, wx42, wx43, wx44, wx45, bd)
new_lookupFM1400(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1364(wx67, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Zero)), bh)
new_lookupFM1316(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx75600), Succ(wx54100), be) → new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx75600, wx54100, be)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2193(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1436(wx30, wx32, wx33, wx34, wx35, wx36, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Zero)), h)
new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Zero, ba) → new_lookupFM197(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM2124(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1320(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM166(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM178(wx15000, Pos(wx1510), wx16, wx17, wx18, wx19, wx20, Zero, bb) → new_lookupFM180(wx15000, wx1510, wx16, wx17, wx18, wx19, wx20, Zero, bb)
new_lookupFM25(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM14(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1231(wx40100, wx41, wx42, wx43, wx44, Succ(wx7670), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1101(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1251(wx58, wx60, wx61, wx62, wx63, wx64, Zero, bf) → new_lookupFM1275(wx58, wx60, wx61, wx62, wx63, wx64, new_primMulNat1, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), wx31), ba) → new_lookupFM269(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat0(new_primMulNat0(wx3000, wx40000), Succ(wx40000)), ba)
new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1310(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1367(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Succ(Succ(wx72400)), bh) → new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, wx53200, wx72400, bh)
new_lookupFM1431(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Succ(Zero), h) → new_lookupFM1433(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, Zero, be) → new_lookupFM(wx27, Float(Neg(wx2800), Neg(wx2810)), be)
new_lookupFM2220(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2106(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3980), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx77800), Zero, ba) → new_lookupFM1294(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2215(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1373(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM253(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2120), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1296(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6030), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM2195(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3760), bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM2219(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM1291(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60100), Succ(Succ(wx77800)), ba) → new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, wx77800, wx60100, ba)
new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx78000), Zero, ba) → new_lookupFM1316(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM223(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx930), ba) → new_lookupFM176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2209(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM247(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1321(wx40000, wx41, wx42, wx43, wx44, Succ(wx48500), Succ(Succ(wx60900)), ba) → new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, wx60900, wx48500, ba)
new_lookupFM1157(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2181(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1282(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM226(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM232(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2126(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM180(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h) → new_lookupFM182(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1230(wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx76600)), ba) → new_lookupFM1233(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM136(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1421(wx40100, wx41, wx42, wx43, wx44, Succ(wx9090), ba) → new_lookupFM1422(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2204(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM1351(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1171(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Succ(wx5410), be) → new_lookupFM1173(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5410, new_primMulNat0(wx2810, wx23), be)
new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx5950), bf) → new_lookupFM1258(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx5950, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM164(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1396(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1142(wx40100, wx41, wx42, wx43, wx44, Succ(wx6630), ba) → new_lookupFM1143(wx40100, wx41, wx42, wx43, wx44, wx6630, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Succ(wx810), h) → new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM299(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2214(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM113(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1167(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Succ(Succ(wx84600)), ba) → new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, wx67100, wx84600, ba)
new_lookupFM1338(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1380(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1410(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1300(wx40000, wx41, wx42, wx43, wx44, Succ(wx6050), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1329(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM255(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM139(wx40100, wx41, wx42, wx43, wx44, Succ(wx5920), ba) → new_lookupFM1244(wx40100, wx41, wx42, wx43, wx44, wx5920, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7900), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Zero), h) → new_lookupFM2225(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1192(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7960), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM29(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Zero, h)
new_lookupFM1131(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Succ(Zero), ba) → new_lookupFM1133(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM172(wx40100, wx41, wx42, wx43, wx44, Succ(wx7350), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM121(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1124(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM258(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Succ(wx72000), bh) → new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx52900, wx72000, bh)
new_lookupFM185(wx915, wx916, wx917, wx918, wx919, wx920, wx921, Zero, bc) → new_lookupFM(wx919, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx920))))), bc)
new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5650, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM1120(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5360, wx740, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2205(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2100(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1196(wx40000, wx41, wx42, wx43, wx44, Succ(wx47100), Succ(Succ(wx58200)), ba) → new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, wx58200, wx47100, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM251(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1285(wx500100, wx501, wx502, wx503, wx504, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Succ(wx82000), ba) → new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, wx65500, wx82000, ba)
new_lookupFM118(wx40000, wx41, wx42, wx43, wx44, Succ(wx4600), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM2161(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM123(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4640), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(wx3100))), ba)
new_lookupFM184(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6540, wx818, ba) → new_lookupFM185(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, wx310000, wx6540, wx818, ba)
new_lookupFM1204(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM263(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2380), ba) → new_lookupFM2154(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM237(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Succ(wx83500), ba) → new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, wx66300, wx83500, ba)
new_lookupFM231(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2125(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1389(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM2197(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6670), ba) → new_lookupFM1155(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6670, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM239(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1530), ba) → new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, wx1650, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM139(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1278(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2111(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1174(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx7580), be) → new_lookupFM(wx27, Float(Pos(wx2800), Pos(wx2810)), be)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM238(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM141(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7440), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM292(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3390), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, Succ(wx6650), ba) → new_lookupFM1151(wx40100, wx41, wx42, wx43, wx44, wx6650, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM288(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Zero, bh) → new_lookupFM2211(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2214(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1372(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM234(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1390), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, wx53000, wx72200, bh)
new_lookupFM1402(wx40000, wx41, wx42, wx43, wx44, Succ(wx6270), ba) → new_lookupFM1403(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM2117(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4300), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM137(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1231(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2118(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1427(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2114(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM187(wx915, wx916, wx917, wx918, wx919, wx920, bc) → new_lookupFM(wx919, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx920))))), bc)
new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88600), Zero, ba) → new_lookupFM1329(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1176(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be) → new_lookupFM(wx27, Float(Pos(wx2800), Pos(wx2810)), be)
new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx7310), ba) → new_lookupFM1412(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7310, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1160(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM222(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2120(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Zero), h) → new_lookupFM215(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1281(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8070), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx87800), Succ(wx70700), ba) → new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, wx87800, wx70700, ba)
new_lookupFM2143(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM2146(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM256(wx22, wx23, wx24, wx25, wx26, wx27, Float(Neg(wx2800), wx281), be) → new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx281, new_primMulNat0(wx2800, wx22), be)
new_lookupFM1162(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6700), ba) → new_lookupFM1163(wx40100, wx41, wx42, wx43, wx44, wx310000, wx6700, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1185(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx7550), bd) → new_lookupFM(wx44, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM147(wx40000, wx41, wx42, wx43, wx44, Succ(wx4820), ba) → new_lookupFM1299(wx40000, wx41, wx42, wx43, wx44, wx4820, new_primMulNat1, ba)
new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88800), Succ(wx71200), ba) → new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88800, wx71200, ba)
new_lookupFM1428(wx40100, wx41, wx42, wx43, wx44, wx7370, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM261(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2320), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1314(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7810), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1327(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8870), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM271(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM210(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1090), h) → new_lookupFM2223(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM246(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM2199(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM1354(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM159(wx40000, wx41, wx42, wx43, wx44, wx3100, Succ(wx4890), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(wx3100))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM295(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM264(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(wx11500), h) → new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11500, h)
new_lookupFM223(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2121(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM267(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2500), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1104(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Pos(Zero)), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Neg(Zero)), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM291(wx40100, wx41, wx42, wx43, wx44, Succ(wx3370), ba) → new_lookupFM2187(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM267(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM185(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Succ(Zero), bc) → new_lookupFM187(wx915, wx916, wx917, wx918, wx919, wx920, bc)
new_lookupFM1361(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Zero)), bh)
new_lookupFM263(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM238(wx40100, wx41, wx42, wx43, wx44, Succ(wx1510), ba) → new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM284(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3150), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1214(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx47300), Succ(Succ(wx58500)), ba) → new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx58500, wx47300, ba)
new_lookupFM199(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6560, wx822, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1106(wx40000, wx40100, wx41, wx42, wx43, wx44, wx5350, wx738, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM291(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Zero, bd) → new_lookupFM2145(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20600)), Succ(wx16500), bd) → new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20600, wx16500, bd)
new_lookupFM2114(wx40100, wx41, wx42, wx43, wx44, Succ(wx4220), ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM2153(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60200), Succ(wx48100), ba) → new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60200, wx48100, ba)
new_lookupFM254(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2140), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1193(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7970), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1284(wx500100, wx501, wx502, wx503, wx504, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87600), Zero, ba) → new_lookupFM1307(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1148(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8370), ba) → new_lookupFM1149(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM284(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM235(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1410), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Succ(wx83200), ba) → new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, wx66100, wx83200, ba)
new_lookupFM1269(wx58, wx60, wx61, wx62, wx63, wx64, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Zero, h) → new_lookupFM1442(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1251(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx5240), bf) → new_lookupFM1274(wx58, wx60, wx61, wx62, wx63, wx64, wx5240, new_primMulNat1, bf)
new_lookupFM243(wx39, Neg(Zero), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx39)), Neg(Zero)), wx41, wx42, wx43, wx44, wx45, bd)
new_lookupFM1143(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Succ(Zero), ba) → new_lookupFM1145(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2137(wx39, wx400, wx41, wx42, wx43, wx44, wx45, wx460, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(wx460)), bd)
new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, Succ(wx60900), Zero, ba) → new_lookupFM1324(wx40000, wx41, wx42, wx43, wx44, ba)
new_lookupFM1434(wx30, wx32, wx33, wx34, wx35, wx36, wx5070, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Zero)), h)
new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, Succ(wx4530), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(wx740)), bh)
new_lookupFM1109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx4590, wx568, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM117(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Zero, ba) → new_lookupFM1136(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, Succ(wx78400), Zero, ba) → new_lookupFM1347(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM243(wx39, Pos(Zero), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM279(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3010), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2168(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2185(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2102(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1291(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, Succ(Succ(wx77800)), ba) → new_lookupFM1294(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM293(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1343(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1274(wx58, wx60, wx61, wx62, wx63, wx64, Zero, Succ(Succ(wx69800)), bf) → new_lookupFM1277(wx58, wx60, wx61, wx62, wx63, wx64, bf)
new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1288(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77200), Succ(wx59400), bf) → new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77200, wx59400, bf)
new_lookupFM260(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2144(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM153(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM135(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1215(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM1218(wx40000, wx41, wx42, wx43, wx44, Succ(wx47400), Succ(Succ(wx58700)), ba) → new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, wx58700, wx47400, ba)
new_lookupFM145(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1292(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM171(wx40100, wx41, wx42, wx43, wx44, Succ(wx5610), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM151(wx40100, wx41, wx42, wx43, wx44, Succ(wx6150), ba) → new_lookupFM1330(wx40100, wx41, wx42, wx43, wx44, wx6150, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Succ(wx63500), ba) → new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, wx46600, wx63500, ba)
new_lookupFM1263(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx6930), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM124(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1249(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx5210), bf) → new_lookupFM1266(wx58, wx60, wx61, wx62, wx63, wx64, wx5210, new_primMulNat1, bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM212(Float(Pos(Succ(wx15000)), wx151), wx16, wx17, wx18, wx19, wx20, bb) → new_lookupFM178(wx15000, wx151, wx16, wx17, wx18, wx19, wx20, new_primPlusNat0(new_primMulNat0(wx20, wx15000), Succ(wx15000)), bb)
new_lookupFM178(wx15000, Neg(Succ(wx15100)), wx16, wx17, wx18, wx19, wx20, Succ(wx6300), bb) → new_lookupFM(wx19, Float(Pos(Succ(wx20)), Neg(Zero)), bb)
new_lookupFM183(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6540), ba) → new_lookupFM184(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6540, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1318(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx6080), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1422(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM229(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM256(wx22, wx23, wx24, wx25, wx26, wx27, Float(Pos(wx2800), wx281), be) → new_lookupFM1171(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx281, new_primMulNat0(wx2800, wx22), be)
new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Succ(wx92200), bc) → new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, wx9210, wx92200, bc)
new_lookupFM2174(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM1392(wx40000, wx40100, wx41, wx42, wx43, wx44, wx7290, wx900, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2218(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1427(wx40100, wx41, wx42, wx43, wx44, Succ(wx7370), ba) → new_lookupFM1428(wx40100, wx41, wx42, wx43, wx44, wx7370, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM154(wx40100, wx41, wx42, wx43, wx44, Succ(wx5530), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Succ(wx64800), h) → new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx50600, wx64800, h)
new_lookupFM1248(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx5200), bf) → new_lookupFM1262(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx5200, new_primMulNat0(Zero, wx5900), bf)
new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Zero, bc) → new_lookupFM187(wx915, wx916, wx917, wx918, wx919, wx920, bc)
new_lookupFM2200(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20600), Zero, bd) → new_lookupFM2143(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM157(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7260), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM270(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2134(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx1980), bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM276(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1274(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx52400), Succ(Succ(wx69800)), bf) → new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, wx69800, wx52400, bf)
new_lookupFM2183(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM150(wx40000, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1322(wx40000, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM136(wx40000, wx41, wx42, wx43, wx44, Succ(wx4740), ba) → new_lookupFM1218(wx40000, wx41, wx42, wx43, wx44, wx4740, new_primMulNat1, ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Succ(wx810), h) → new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20600), Succ(wx16500), bd) → new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20600, wx16500, bd)
new_lookupFM1104(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8250), ba) → new_lookupFM1105(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM222(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM292(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1359(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Succ(Succ(wx72000)), bh) → new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx52900, wx72000, bh)
new_lookupFM2114(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2219(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM171(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM272(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM255(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM126(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1137(wx40000, wx41, wx42, wx43, wx44, wx4660, Zero, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(wx38400), bh) → new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38400, bh)
new_lookupFM1230(wx40100, wx41, wx42, wx43, wx44, Succ(wx59100), Succ(Succ(wx76600)), ba) → new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, wx76600, wx59100, ba)
new_lookupFM222(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx910), ba) → new_lookupFM175(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Succ(wx25600), bf) → new_lookupFM2172(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM131(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx5400), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Zero)), ba)
new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Succ(Succ(wx76100)), be) → new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx54200, wx76100, be)
new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx67400), Succ(wx51300), bd) → new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, wx67400, wx51300, bd)
new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Succ(wx84600), ba) → new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, wx67100, wx84600, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM143(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx85200), Succ(wx67800), ba) → new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx85200, wx67800, ba)
new_lookupFM1261(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM2196(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3780), bh) → new_lookupFM2206(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Zero)), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM133(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87600), Succ(wx70600), ba) → new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87600, wx70600, ba)
new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx6580), ba) → new_lookupFM1113(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx6580, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM275(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2770), ba) → new_lookupFM2179(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx5940), bf) → new_lookupFM1253(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx5940, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Pos(Succ(wx3100))), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM2149(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1193(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM179(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, wx4520, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(wx370)), h)
new_lookupFM1408(wx40100, wx41, wx42, wx43, wx44, wx310000, wx7300, Zero, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Pos(wx310), wx32, wx33, wx34, wx35, wx36, Neg(wx370), Succ(wx810), h) → new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Zero)), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM150(wx40000, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1207(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2107(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4000), ba) → new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88600), Succ(wx71100), ba) → new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88600, wx71100, ba)
new_lookupFM169(wx40000, wx41, wx42, wx43, wx44, Succ(wx4980), ba) → new_lookupFM1404(wx40000, wx41, wx42, wx43, wx44, wx4980, new_primMulNat1, ba)
new_lookupFM245(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1760), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1188(wx39, wx41, wx42, wx43, wx44, wx45, Zero, Succ(Succ(wx67400)), bd) → new_lookupFM1191(wx39, wx41, wx42, wx43, wx44, wx45, bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 59 SCCs with 471 less nodes.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM148(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1314(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM172(wx40100, wx41, wx42, wx43, wx44, Succ(wx7350), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM164(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1397(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM153(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1345(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1396(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7470), ba) → new_lookupFM1397(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM148(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM164(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1396(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1314(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7810), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1345(wx40100, wx41, wx42, wx43, wx44, Succ(wx7850), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM172(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM153(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, Succ(wx78400), Succ(wx61600), ba) → new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, wx78400, wx61600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, Succ(wx78400), Succ(wx61600), ba) → new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, wx78400, wx61600, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, Succ(wx78400), Succ(wx61600), ba) → new_lookupFM1346(wx40100, wx41, wx42, wx43, wx44, wx78400, wx61600, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1121(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7410), ba) → new_lookupFM1122(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM119(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1245(wx40100, wx41, wx42, wx43, wx44, Succ(wx7690), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM128(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM119(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1121(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM139(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1245(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM134(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1211(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM139(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1122(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM134(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1211(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7650), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM128(wx40100, wx41, wx42, wx43, wx44, Succ(wx6690), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Zero))), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx76400), Succ(wx58400), ba) → new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, wx76400, wx58400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx76400), Succ(wx58400), ba) → new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, wx76400, wx58400, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx76400), Succ(wx58400), ba) → new_lookupFM1212(wx40000, wx40100, wx41, wx42, wx43, wx44, wx76400, wx58400, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, Succ(wx76800), Succ(wx59200), ba) → new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, wx76800, wx59200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, Succ(wx76800), Succ(wx59200), ba) → new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, wx76800, wx59200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, Succ(wx76800), Succ(wx59200), ba) → new_lookupFM1246(wx40100, wx41, wx42, wx43, wx44, wx76800, wx59200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx78000), Succ(wx60600), ba) → new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, wx78000, wx60600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx78000), Succ(wx60600), ba) → new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, wx78000, wx60600, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx78000), Succ(wx60600), ba) → new_lookupFM1315(wx40000, wx40100, wx41, wx42, wx43, wx44, wx78000, wx60600, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM213(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Pos(Zero)), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM221(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx870), ba) → new_lookupFM174(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM262(wx40100, wx41, wx42, wx43, wx44, Succ(wx2360), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM227(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM243(wx39, Pos(wx400), wx41, wx42, wx43, wx44, wx45, Pos(wx460), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(wx460)), bd)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20400)), Zero, bd) → new_lookupFM2139(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM2146(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM1438(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(wx370)), h)
new_lookupFM1194(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7980), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM115(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1107(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2147(wx39, wx400, wx41, wx42, wx43, wx44, wx45, wx460, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(wx460)), bd)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(wx11500), h) → new_lookupFM2226(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx75600), Zero, be) → new_lookupFM1176(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM224(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx970), ba) → new_lookupFM177(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1108(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Zero, bd) → new_lookupFM2141(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM10(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), Zero, h) → new_lookupFM182(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1173(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54100), Succ(Succ(wx75600)), be) → new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx75600, wx54100, be)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20400), Zero, bd) → new_lookupFM2139(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM178(wx15000, Neg(Zero), wx16, wx17, wx18, wx19, wx20, Succ(wx6300), bb) → new_lookupFM(wx19, Float(Pos(Succ(wx20)), Neg(Zero)), bb)
new_lookupFM2123(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM253(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2154(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM249(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Zero, bd) → new_lookupFM2141(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1100(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), wx31), ba) → new_lookupFM2(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat1(new_primMulNat0(wx3000, wx40000), wx40000), ba)
new_lookupFM26(Float(Pos(Succ(wx15000)), wx151), wx16, wx17, wx18, wx19, wx20, bb) → new_lookupFM178(wx15000, wx151, wx16, wx17, wx18, wx19, wx20, new_primPlusNat0(new_primMulNat0(wx20, wx15000), Succ(wx15000)), bb)
new_lookupFM247(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1193(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1107(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7390), ba) → new_lookupFM1108(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Zero, h) → new_lookupFM18(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Succ(wx16500), bd) → new_lookupFM2144(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM2135(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM235(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Succ(wx810), h) → new_lookupFM22(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Zero), h) → new_lookupFM217(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM27(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1227(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, wx1650, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM1187(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM(wx44, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM2135(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx2000), bd) → new_lookupFM2146(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Zero, h) → new_lookupFM215(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM249(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1880), ba) → new_lookupFM2151(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM2223(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM29(wx30, Zero, wx32, wx33, wx34, wx35, wx36, Zero, h)
new_lookupFM126(wx40100, wx41, wx42, wx43, wx44, Succ(wx6660), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2151(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1195(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1195(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7990), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM175(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7890), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM244(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1720), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM264(wx40100, wx41, wx42, wx43, wx44, Succ(wx2420), ba) → new_lookupFM2155(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM221(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2119(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM2155(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM13(wx30, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx5760), bd) → new_lookupFM1184(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx5760, new_primMulNat0(Succ(wx4600), wx4000), bd)
new_lookupFM111(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx6530), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx75600), Succ(wx54100), be) → new_lookupFM1175(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx75600, wx54100, be)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Succ(wx16500), bd) → new_lookupFM2140(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1184(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Succ(Succ(wx75400)), bd) → new_lookupFM1187(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM2141(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM2124(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM261(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM25(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM14(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5640, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM1231(wx40100, wx41, wx42, wx43, wx44, Succ(wx7670), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Neg(Succ(wx3100))), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1101(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM130(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7420), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM27(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1050), h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM27(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Zero, h) → new_lookupFM217(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM28(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM1185(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx4600), wx4000), bd)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, Zero, h) → new_lookupFM218(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2145(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM1183(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primMulNat0(Succ(wx45), wx39), bd)
new_lookupFM225(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx990), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM227(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1170), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM11(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1184(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx57600), Succ(Succ(wx75400)), bd) → new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx75400, wx57600, bd)
new_lookupFM253(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2120), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM223(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx930), ba) → new_lookupFM176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM22(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, h) → new_lookupFM12(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM247(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM226(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM177(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7910), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Succ(wx16500), bd) → new_lookupFM2140(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20600)), Zero, bd) → new_lookupFM2143(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1173(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Zero, Succ(Succ(wx75600)), be) → new_lookupFM1176(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20400), Succ(wx16500), bd) → new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20400, wx16500, bd)
new_lookupFM2120(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM175(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM264(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1171(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Succ(wx5410), be) → new_lookupFM1173(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5410, new_primMulNat0(wx2810, wx23), be)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM11(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5050), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM243(wx39, Pos(Zero), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Zero)), bd)
new_lookupFM23(wx30, wx32, wx33, wx34, wx35, wx36, h) → new_lookupFM13(wx30, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2148(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1192(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1171(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Zero, be) → new_lookupFM1174(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, new_primMulNat0(wx2810, wx23), be)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Succ(wx810), h) → new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), wx1650, bd)
new_lookupFM19(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx6520), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM254(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Succ(wx810), h) → new_lookupFM21(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM255(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Succ(wx16500), bd) → new_lookupFM2144(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7900), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Zero), h) → new_lookupFM2225(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1192(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7960), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM29(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Zero, h)
new_lookupFM2140(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM246(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1780), ba) → new_lookupFM2148(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM2228(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Zero, bd) → new_lookupFM2134(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Zero)), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM220(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM185(wx915, wx916, wx917, wx918, wx919, wx920, wx921, Zero, bc) → new_lookupFM(wx919, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx920))))), bc)
new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5650, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20400)), Succ(wx16500), bd) → new_lookupFM2138(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20400, wx16500, bd)
new_lookupFM29(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx75400), Zero, bd) → new_lookupFM1187(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM218(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM246(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1192(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Zero), h) → new_lookupFM2227(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Succ(wx810), h) → new_lookupFM25(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2133(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx1960), bd) → new_lookupFM2137(wx39, Succ(wx4000), wx41, wx42, wx43, wx44, wx45, Succ(wx4600), bd)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM252(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM251(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM228(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2119(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM174(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2227(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Succ(Succ(wx75000)), h) → new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56500, wx75000, h)
new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx75400), Succ(wx57600), bd) → new_lookupFM1186(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx75400, wx57600, bd)
new_lookupFM263(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2380), ba) → new_lookupFM2154(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM237(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1152(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM2150(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1194(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1149(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1224(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, wx1650, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Succ(wx810), h) → new_lookupFM26(Float(Pos(Succ(wx30)), Neg(Succ(wx3100))), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM2131(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), wx1650, bd)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Succ(wx3700)), Zero, h) → new_lookupFM29(wx30, Zero, wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM1174(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx7580), be) → new_lookupFM(wx27, Float(Pos(wx2800), Pos(wx2810)), be)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM238(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM28(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM29(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM221(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM132(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM238(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2128(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM213(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM229(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1230), ba) → new_lookupFM198(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM181(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(wx370)), h)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Succ(wx810), h) → new_lookupFM26(Float(Pos(Succ(wx30)), Neg(Zero)), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(wx11300), h) → new_lookupFM216(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2225(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM2228(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM18(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM137(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1231(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Succ(wx11500)), h) → new_lookupFM2226(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM250(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1900), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM115(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM236(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1442(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), wx31), ba) → new_lookupFM243(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat0(new_primMulNat0(wx3000, wx40000), Succ(wx40000)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM130(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM248(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1176(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be) → new_lookupFM(wx27, Float(Pos(wx2800), Pos(wx2810)), be)
new_lookupFM182(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx6460), h) → new_lookupFM181(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM222(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2120(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Zero), h) → new_lookupFM215(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM224(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2122(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM2226(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM248(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1194(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2143(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM2146(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM1185(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx7550), bd) → new_lookupFM(wx44, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM261(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2320), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Zero, h) → new_lookupFM12(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM210(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1090), h) → new_lookupFM2223(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM243(wx39, Neg(Zero), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM246(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Neg(Zero)), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM245(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM210(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM215(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM218(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(wx11500), h) → new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11500, h)
new_lookupFM264(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1225(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM223(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2121(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1104(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM251(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1940), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Succ(Succ(wx11300)), h) → new_lookupFM216(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2139(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM263(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1222(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM178(wx15000, Pos(wx1510), wx16, wx17, wx18, wx19, wx20, Succ(wx6300), bb) → new_lookupFM179(wx15000, wx1510, wx16, wx17, wx18, wx19, wx20, Zero, wx6300, bb)
new_lookupFM238(wx40100, wx41, wx42, wx43, wx44, Succ(wx1510), ba) → new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Zero), Zero, bd) → new_lookupFM2145(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM2132(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(Succ(wx20600)), Succ(wx16500), bd) → new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20600, wx16500, bd)
new_lookupFM1105(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1227(wx40100, wx41, wx42, wx43, wx44, Succ(wx8630), ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM229(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2123(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM254(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2140), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM219(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx820), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1193(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7970), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2121(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM255(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2180), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1148(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8370), ba) → new_lookupFM1149(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2(wx30, Neg(wx310), wx32, wx33, wx34, wx35, wx36, Pos(wx370), Succ(wx810), h) → new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM235(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1410), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM249(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1195(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Pos(Zero), Succ(wx810), h) → new_lookupFM23(wx30, wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Zero, h) → new_lookupFM1442(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM244(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM211(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2136(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx2020), bd) → new_lookupFM2147(wx39, Succ(wx4000), wx41, wx42, wx43, wx44, wx45, Succ(wx4600), bd)
new_lookupFM230(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1270), ba) → new_lookupFM1102(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM20(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Succ(wx11300)), h) → new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11300, h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM219(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM230(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2124(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2137(wx39, wx400, wx41, wx42, wx43, wx44, wx45, wx460, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(wx460)), bd)
new_lookupFM1434(wx30, wx32, wx33, wx34, wx35, wx36, wx5070, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Zero)), h)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, Zero, bd) → new_lookupFM2145(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM247(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1820), ba) → new_lookupFM2149(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, Succ(wx4510), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(wx370)), h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM224(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1153(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Zero, bd) → new_lookupFM2136(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM243(wx39, Pos(Zero), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM210(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, h) → new_lookupFM211(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM223(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1431(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx5060, Zero, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Pos(Zero)), h)
new_lookupFM237(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2127(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Succ(Zero), h) → new_lookupFM1442(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM2(wx30, Pos(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM211(wx30, Zero, wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM2144(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM1224(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8610), ba) → new_lookupFM185(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, wx310000, wx8610, Zero, ba)
new_lookupFM12(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx5060), h) → new_lookupFM1431(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx5060, new_primMulNat0(Zero, wx3100), h)
new_lookupFM237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1470), ba) → new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM254(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(Succ(wx11500)), h) → new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11500, h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM250(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM212(Float(Pos(Succ(wx15000)), wx151), wx16, wx17, wx18, wx19, wx20, bb) → new_lookupFM178(wx15000, wx151, wx16, wx17, wx18, wx19, wx20, new_primPlusNat0(new_primMulNat0(wx20, wx15000), Succ(wx15000)), bb)
new_lookupFM178(wx15000, Neg(Succ(wx15100)), wx16, wx17, wx18, wx19, wx20, Succ(wx6300), bb) → new_lookupFM(wx19, Float(Pos(Succ(wx20)), Neg(Zero)), bb)
new_lookupFM13(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx5070), h) → new_lookupFM1434(wx30, wx32, wx33, wx34, wx35, wx36, wx5070, new_primMulNat1, h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM263(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM229(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM256(wx22, wx23, wx24, wx25, wx26, wx27, Float(Pos(wx2800), wx281), be) → new_lookupFM1171(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx281, new_primMulNat0(wx2800, wx22), be)
new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, Succ(wx4520), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(wx370)), h)
new_lookupFM1100(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8230), ba) → new_lookupFM1101(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2222(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, h) → new_lookupFM1(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM243(wx39, Neg(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Zero, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM1152(wx40100, wx41, wx42, wx43, wx44, Succ(wx8390), ba) → new_lookupFM1153(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM236(wx40100, wx41, wx42, wx43, wx44, Succ(wx1450), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Zero, Zero, h) → new_lookupFM2227(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM1437(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx6430), h) → new_lookupFM1438(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Succ(wx74800), h) → new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56400, wx74800, h)
new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5640), h) → new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5640, new_primMulNat0(Succ(wx3700), wx3100), h)
new_lookupFM174(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx7880), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM21(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM11(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20600), Zero, bd) → new_lookupFM2143(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, bd)
new_lookupFM226(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1030), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM28(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1070), h) → new_lookupFM2222(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), h)
new_lookupFM248(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx1840), ba) → new_lookupFM2150(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Succ(Zero), h) → new_lookupFM18(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM262(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Succ(wx11300), h) → new_lookupFM214(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx8100, wx11300, h)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM230(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2134(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx1980), bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM225(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2224(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx8100), Zero, h) → new_lookupFM2225(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM217(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM15(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM2136(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Neg(Succ(wx4600))), bd)
new_lookupFM2(wx30, Neg(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Succ(wx810), h) → new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Succ(wx20600), Succ(wx16500), bd) → new_lookupFM2142(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, wx20600, wx16500, bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM19(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1104(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8250), ba) → new_lookupFM1105(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2(wx30, Neg(Zero), wx32, wx33, wx34, wx35, wx36, Neg(Succ(wx3700)), Zero, h) → new_lookupFM14(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM222(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM24(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx810, Zero, h) → new_lookupFM2228(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM126(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM255(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM16(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56400), Succ(Succ(wx74800)), h) → new_lookupFM17(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56400, wx74800, h)
new_lookupFM2134(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, Zero, bd) → new_lookupFM256(wx39, wx4000, wx41, wx42, wx43, wx44, Float(Pos(Succ(wx45)), Pos(Succ(wx4600))), bd)
new_lookupFM14(wx30, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5080), h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM222(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx910), ba) → new_lookupFM175(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2128(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1150(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM111(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1148(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Pos(Succ(wx4600)), Zero, bd) → new_lookupFM2133(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM252(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2080), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1(wx30, Succ(wx3100), wx32, wx33, wx34, wx35, wx36, Succ(wx3700), Zero, h) → new_lookupFM1437(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, new_primPlusNat0(new_primMulNat0(wx3700, wx3100), Succ(wx3100)), h)
new_lookupFM243(wx39, Neg(Zero), wx41, wx42, wx43, wx44, wx45, Pos(Zero), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Pos(Zero)), bd)
new_lookupFM132(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7430), ba) → new_lookupFM(wx44, Float(Pos(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM243(wx39, Neg(wx400), wx41, wx42, wx43, wx44, wx45, Neg(wx460), Succ(wx1650), bd) → new_lookupFM(wx43, Float(Pos(Succ(wx45)), Neg(wx460)), bd)
new_lookupFM2(wx30, Pos(Succ(wx3100)), wx32, wx33, wx34, wx35, wx36, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx30)), Pos(Succ(wx3100))), wx32, wx33, wx34, wx35, wx36, h)
new_lookupFM213(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx1110), h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Neg(Succ(wx3700))), h)
new_lookupFM2149(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1193(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM179(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, wx4520, h) → new_lookupFM(wx35, Float(Pos(Succ(wx36)), Neg(wx370)), h)
new_lookupFM228(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1210), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM220(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx850), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx39, Pos(Succ(wx4000)), wx41, wx42, wx43, wx44, wx45, Neg(Succ(wx4600)), Zero, bd) → new_lookupFM2135(wx39, wx4000, wx41, wx42, wx43, wx44, wx45, wx4600, new_primPlusNat0(new_primMulNat0(wx4600, wx4000), Succ(wx4000)), bd)
new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx56500), Succ(wx75000), h) → new_lookupFM1441(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx56500, wx75000, h)
new_lookupFM2127(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1146(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2(wx30, Pos(wx310), wx32, wx33, wx34, wx35, wx36, Neg(wx370), Succ(wx810), h) → new_lookupFM10(wx30, wx310, wx32, wx33, wx34, wx35, wx36, wx370, new_primMulNat0(Succ(wx36), wx30), h)
new_lookupFM1439(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, Succ(wx5650), h) → new_lookupFM1440(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, wx5650, new_primMulNat0(Succ(wx3700), wx3100), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM137(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM245(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx1760), ba) → new_lookupFM(wx43, Float(Pos(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM216(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx3700, h) → new_lookupFM(wx34, Float(Pos(Succ(wx36)), Pos(Succ(wx3700))), h)
new_lookupFM2122(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM177(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Succ(wx65000), h) → new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, wx50700, wx65000, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Succ(wx65000), h) → new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, wx50700, wx65000, h)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, Succ(wx50700), Succ(wx65000), h) → new_lookupFM1435(wx30, wx32, wx33, wx34, wx35, wx36, wx50700, wx65000, h)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx67400), Succ(wx51300), bd) → new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, wx67400, wx51300, bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx67400), Succ(wx51300), bd) → new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, wx67400, wx51300, bd)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, Succ(wx67400), Succ(wx51300), bd) → new_lookupFM1190(wx39, wx41, wx42, wx43, wx44, wx45, wx67400, wx51300, bd)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Succ(wx64800), h) → new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx50600, wx64800, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Succ(wx64800), h) → new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx50600, wx64800, h)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, Succ(wx50600), Succ(wx64800), h) → new_lookupFM1432(wx30, wx3100, wx32, wx33, wx34, wx35, wx36, wx50600, wx64800, h)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, Succ(wx76600), Succ(wx59100), ba) → new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, wx76600, wx59100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, Succ(wx76600), Succ(wx59100), ba) → new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, wx76600, wx59100, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, Succ(wx76600), Succ(wx59100), ba) → new_lookupFM1232(wx40100, wx41, wx42, wx43, wx44, wx76600, wx59100, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx58500), Succ(wx47300), ba) → new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx58500, wx47300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx58500), Succ(wx47300), ba) → new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx58500, wx47300, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx58500), Succ(wx47300), ba) → new_lookupFM1216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx58500, wx47300, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Succ(wx63500), ba) → new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, wx46600, wx63500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Succ(wx63500), ba) → new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, wx46600, wx63500, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, Succ(wx46600), Succ(wx63500), ba) → new_lookupFM1138(wx40000, wx41, wx42, wx43, wx44, wx46600, wx63500, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, Succ(wx58700), Succ(wx47400), ba) → new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, wx58700, wx47400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, Succ(wx58700), Succ(wx47400), ba) → new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, wx58700, wx47400, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, Succ(wx58700), Succ(wx47400), ba) → new_lookupFM1220(wx40000, wx41, wx42, wx43, wx44, wx58700, wx47400, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Succ(wx57200), ba) → new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, wx46500, wx57200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Succ(wx57200), ba) → new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, wx46500, wx57200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx46500), Succ(wx57200), ba) → new_lookupFM1135(wx40000, wx40100, wx41, wx42, wx43, wx44, wx46500, wx57200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1202(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8530), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM233(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1350), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM267(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2500), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM239(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM267(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM239(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2129(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2125(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1236(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8650), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM231(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1115(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1157(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2156(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1202(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM257(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2200), ba) → new_lookupFM2152(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1156(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8410), ba) → new_lookupFM1157(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM241(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM259(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2260), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM231(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2125(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM259(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM231(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1290), ba) → new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1114(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8270), ba) → new_lookupFM1115(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1236(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2129(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM241(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1590), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM265(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2440), ba) → new_lookupFM2156(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM239(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx1530), ba) → new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM265(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1234(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM1154(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1156(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM257(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM257(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM233(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1112(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1114(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM265(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2152(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1200(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx85200), Succ(wx67800), ba) → new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx85200, wx67800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx85200), Succ(wx67800), ba) → new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx85200, wx67800, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx85200), Succ(wx67800), ba) → new_lookupFM1203(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx85200, wx67800, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Succ(wx84400), ba) → new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, wx67000, wx84400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Succ(wx84400), ba) → new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, wx67000, wx84400, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx67000), Succ(wx84400), ba) → new_lookupFM1164(wx40100, wx41, wx42, wx43, wx44, wx310000, wx67000, wx84400, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Succ(wx83000), ba) → new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx66000, wx83000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Succ(wx83000), ba) → new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx66000, wx83000, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx66000), Succ(wx83000), ba) → new_lookupFM1128(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx66000, wx83000, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx86400), Succ(wx68400), ba) → new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, wx86400, wx68400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx86400), Succ(wx68400), ba) → new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, wx86400, wx68400, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx86400), Succ(wx68400), ba) → new_lookupFM1237(wx40100, wx41, wx42, wx43, wx44, wx310000, wx86400, wx68400, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Succ(wx56600), ba) → new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, wx45600, wx56600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Succ(wx56600), ba) → new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, wx45600, wx56600, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx45600), Succ(wx56600), ba) → new_lookupFM193(wx40000, wx40100, wx41, wx42, wx43, wx44, wx45600, wx56600, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Succ(wx63400), ba) → new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, wx45700, wx63400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Succ(wx63400), ba) → new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, wx45700, wx63400, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, Succ(wx45700), Succ(wx63400), ba) → new_lookupFM196(wx40000, wx41, wx42, wx43, wx44, wx45700, wx63400, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, Succ(wx58200), Succ(wx47100), ba) → new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, wx58200, wx47100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, Succ(wx58200), Succ(wx47100), ba) → new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, wx58200, wx47100, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, Succ(wx58200), Succ(wx47100), ba) → new_lookupFM1198(wx40000, wx41, wx42, wx43, wx44, wx58200, wx47100, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Succ(wx92200), bc) → new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, wx9210, wx92200, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Succ(wx92200), bc) → new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, wx9210, wx92200, bc)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, Succ(wx9210), Succ(wx92200), bc) → new_lookupFM186(wx915, wx916, wx917, wx918, wx919, wx920, wx9210, wx92200, bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Succ(wx82000), ba) → new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, wx65500, wx82000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Succ(wx82000), ba) → new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, wx65500, wx82000, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx65500), Succ(wx82000), ba) → new_lookupFM190(wx40000, wx40100, wx41, wx42, wx43, wx44, wx65500, wx82000, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Succ(wx83500), ba) → new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, wx66300, wx83500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Succ(wx83500), ba) → new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, wx66300, wx83500, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, Succ(wx66300), Succ(wx83500), ba) → new_lookupFM1144(wx40100, wx41, wx42, wx43, wx44, wx66300, wx83500, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, Succ(wx86200), Succ(wx68300), ba) → new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, wx86200, wx68300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, Succ(wx86200), Succ(wx68300), ba) → new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, wx86200, wx68300, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, Succ(wx86200), Succ(wx68300), ba) → new_lookupFM1228(wx40100, wx41, wx42, wx43, wx44, wx86200, wx68300, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM240(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2130(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2130(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM258(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1241(wx40100, wx41, wx42, wx43, wx44, Succ(wx8670), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM260(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2300), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2153(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1118(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8290), ba) → new_lookupFM1119(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM258(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM232(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1330), ba) → new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM234(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx1390), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1207(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8550), ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM240(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM266(wx40100, wx41, wx42, wx43, wx44, Succ(wx2480), ba) → new_lookupFM2157(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM232(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2126(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM266(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM268(wx40100, wx41, wx42, wx43, wx44, Succ(wx2540), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1241(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2157(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1239(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM242(wx40100, wx41, wx42, wx43, wx44, Succ(wx1630), ba) → new_lookupFM(wx43, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM260(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2126(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM242(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM234(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1161(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1160(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM258(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx2240), ba) → new_lookupFM2153(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1119(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1160(wx40100, wx41, wx42, wx43, wx44, Succ(wx8430), ba) → new_lookupFM1161(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM240(wx40100, wx41, wx42, wx43, wx44, Succ(wx1570), ba) → new_lookupFM1158(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM232(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM266(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1205(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1207(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM268(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1116(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1118(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, Succ(wx86600), Succ(wx68500), ba) → new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, wx86600, wx68500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, Succ(wx86600), Succ(wx68500), ba) → new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, wx86600, wx68500, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, Succ(wx86600), Succ(wx68500), ba) → new_lookupFM1242(wx40100, wx41, wx42, wx43, wx44, wx86600, wx68500, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Succ(wx83200), ba) → new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, wx66100, wx83200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Succ(wx83200), ba) → new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, wx66100, wx83200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx66100), Succ(wx83200), ba) → new_lookupFM1132(wx40000, wx40100, wx41, wx42, wx43, wx44, wx66100, wx83200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx85400), Succ(wx67900), ba) → new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, wx85400, wx67900, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx85400), Succ(wx67900), ba) → new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, wx85400, wx67900, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx85400), Succ(wx67900), ba) → new_lookupFM1208(wx40000, wx40100, wx41, wx42, wx43, wx44, wx85400, wx67900, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Succ(wx84600), ba) → new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, wx67100, wx84600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Succ(wx84600), ba) → new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, wx67100, wx84600, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, Succ(wx67100), Succ(wx84600), ba) → new_lookupFM1168(wx40100, wx41, wx42, wx43, wx44, wx67100, wx84600, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM2195(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29300)), Zero, bf) → new_lookupFM2166(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1283(wx500000, wx500100, wx501, wx502, wx503, wx504, Succ(wx9390), bg) → new_lookupFM(wx504, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(wx25600), bf) → new_lookupFM2172(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2212(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1370(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2116(wx40100, wx41, wx42, wx43, wx44, Succ(wx4280), ba) → new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM288(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3270), ba) → new_lookupFM2184(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM286(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM269(wx58, Pos(wx590), wx60, wx61, wx62, wx63, wx64, Pos(wx650), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(wx650)), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Zero), bh) → new_lookupFM2202(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM274(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2730), ba) → new_lookupFM2178(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM2111(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4120), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Succ(wx38400)), bh) → new_lookupFM2203(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2187(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM1352(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx5300), bh) → new_lookupFM1362(wx67, wx69, wx70, wx71, wx72, wx73, wx5300, new_primMulNat1, bh)
new_lookupFM2169(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM281(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM143(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7450), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Zero), bh) → new_lookupFM2204(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1278(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8040), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2194(wx67, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM1354(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2202(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM2205(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Succ(wx38600)), bh) → new_lookupFM2210(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2186(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Succ(wx3450), bh) → new_lookupFM2191(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM155(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7250), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, Zero, bh) → new_lookupFM2205(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1180(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be) → new_lookupFM(wx27, Float(Neg(wx2800), Pos(wx2810)), be)
new_lookupFM286(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3210), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1413(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1394(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM1350(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2207(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2193(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1353(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2206(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1372(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8140), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Succ(Zero), be) → new_lookupFM1182(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1305(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2113(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4180), ba) → new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2178(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1280(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM273(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2710), ba) → new_lookupFM2177(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Zero, bf) → new_lookupFM2160(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM2217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2171(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM2174(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Zero, bf) → new_lookupFM2162(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM2173(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM272(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2670), ba) → new_lookupFM2176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2116(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2163(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2910), bf) → new_lookupFM2175(wx58, Succ(wx5900), wx60, wx61, wx62, wx63, wx64, Succ(wx6500), bf)
new_lookupFM296(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3560), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2100(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2215(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1421(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Zero, bf) → new_lookupFM2173(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1351(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx5290), bh) → new_lookupFM1359(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx5290, new_primMulNat0(Zero, wx6800), bh)
new_lookupFM1336(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8890), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2211(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM282(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3090), ba) → new_lookupFM2182(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM141(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM294(wx67, Pos(wx680), wx69, wx70, wx71, wx72, wx73, Neg(wx740), Succ(wx3450), bh) → new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2162(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2890), bf) → new_lookupFM2174(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77400), Zero, bf) → new_lookupFM1261(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM283(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM293(wx40100, wx41, wx42, wx43, wx44, Succ(wx3430), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1259(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM1413(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx9050), ba) → new_lookupFM1414(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM295(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3520), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1414(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1417(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx9070), ba) → new_lookupFM1418(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1284(wx500100, wx501, wx502, wx503, wx504, Succ(wx9430), bg) → new_lookupFM(wx504, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2118(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM151(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(wx25600), bf) → new_lookupFM2167(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Zero, be) → new_lookupFM1182(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM2161(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2870), bf) → new_lookupFM2169(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Zero, be) → new_lookupFM1179(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, new_primMulNat0(wx2810, wx23), be)
new_lookupFM290(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3330), ba) → new_lookupFM2186(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2193(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1359(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx5290, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Zero)), bh)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29500)), Succ(wx25600), bf) → new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29500, wx25600, bf)
new_lookupFM2101(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3700), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM289(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2166(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM2169(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM282(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM287(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2198(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3800), bh) → new_lookupFM2207(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM1292(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx7790), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2107(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1310(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), wx31), ba) → new_lookupFM269(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat0(new_primMulNat0(wx3000, wx40000), Succ(wx40000)), ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM2197(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM1259(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx7750), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, Zero, be) → new_lookupFM(wx27, Float(Neg(wx2800), Neg(wx2810)), be)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(Zero), bh) → new_lookupFM2211(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2220(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2106(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3980), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1373(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8150), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Succ(wx3450), bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM2200(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3820), bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM2215(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1373(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2115(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4240), ba) → new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2195(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3760), bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM2219(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM2197(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), wx401), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), wx31), ba) → new_lookupFM294(wx40000, wx401, wx41, wx42, wx43, wx44, wx3000, wx31, new_primPlusNat0(new_primMulNat0(wx3000, wx40000), Succ(wx40000)), ba)
new_lookupFM2112(wx40100, wx41, wx42, wx43, wx44, Succ(wx4160), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1370(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8120), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2209(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM2108(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4040), ba) → new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Succ(Succ(wx78600)), bh) → new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx61700, wx78600, bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2101(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1348(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), Zero, bh) → new_lookupFM1179(wx67, wx6800, wx69, wx70, wx71, wx72, Succ(wx73), Succ(wx7400), new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM290(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1254(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx7730), bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM2181(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1282(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM2103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3880), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Pos(wx2810), Succ(wx5420), be) → new_lookupFM1177(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, new_primMulNat0(wx2810, wx23), be)
new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Succ(wx38400)), bh) → new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38400, bh)
new_lookupFM281(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3070), ba) → new_lookupFM2181(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2104(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3920), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2203(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM1421(wx40100, wx41, wx42, wx43, wx44, Succ(wx9090), ba) → new_lookupFM1422(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2115(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Succ(wx78600), bh) → new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx61700, wx78600, bh)
new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1336(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM299(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3640), ba) → new_lookupFM1372(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2204(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM1351(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM277(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29300)), Succ(wx25600), bf) → new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29300, wx25600, bf)
new_lookupFM1353(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx5310), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM2216(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29500), Zero, bf) → new_lookupFM2171(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx5950), bf) → new_lookupFM1258(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx5950, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM2191(wx67, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM1352(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM1393(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx9010), ba) → new_lookupFM1394(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2184(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM299(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2214(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2108(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2177(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1279(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM1256(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM273(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1279(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2179(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1281(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2221(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1419(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM298(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(wx38600), bh) → new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38600, bh)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM270(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2610), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1341(wx40100, wx41, wx42, wx43, wx44, Succ(wx8910), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM1352(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1366(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(wx740)), bh)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Zero, bf) → new_lookupFM2163(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM2205(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM275(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM1281(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2108(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2217(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2100(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM2200(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM1371(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8130), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1288(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8750), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1357(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Zero, bh) → new_lookupFM1358(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2210(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM(wx71, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM285(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1285(wx500100, wx501, wx502, wx503, wx504, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(wx38600), bh) → new_lookupFM2210(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2161(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM2105(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3940), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM2199(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM1367(wx67, wx69, wx70, wx71, wx72, wx73, wx5320, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(Zero)), bh)
new_lookupFM294(wx67, Neg(wx680), wx69, wx70, wx71, wx72, wx73, Pos(wx740), Succ(wx3450), bh) → new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM2102(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3740), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx58, Neg(Zero), wx60, wx61, wx62, wx63, wx64, Pos(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1389(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), wx2560, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM282(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1415(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1417(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Zero, bh) → new_lookupFM2197(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2105(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2113(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2176(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1278(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2111(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1179(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx7620), be) → new_lookupFM(wx27, Float(Neg(wx2800), Pos(wx2810)), be)
new_lookupFM297(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM2212(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba)
new_lookupFM278(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx2970), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2103(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1358(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29300), Succ(wx25600), bf) → new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29300, wx25600, bf)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Succ(wx3450), bh) → new_lookupFM2194(wx67, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM141(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7440), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM292(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3390), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Succ(wx25600), bf) → new_lookupFM2167(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM281(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM288(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Zero, bh) → new_lookupFM2211(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM273(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2214(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, ba) → new_lookupFM1372(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM1331(wx40100, wx41, wx42, wx43, wx44, Succ(wx7830), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1279(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8050), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2117(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4300), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM289(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2114(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Zero, bf) → new_lookupFM2173(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM274(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1280(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM2199(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM271(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2650), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2110(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1281(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx8070), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM283(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1349(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), Zero, bh) → new_lookupFM1365(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Zero, bf) → new_lookupFM2161(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba)
new_lookupFM256(wx22, wx23, wx24, wx25, wx26, wx27, Float(Neg(wx2800), wx281), be) → new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx281, new_primMulNat0(wx2800, wx22), be)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2107(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Zero, bh) → new_lookupFM2204(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx61700), Succ(Zero), bh) → new_lookupFM1358(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1327(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8870), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM299(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM170(wx40100, wx41, wx42, wx43, wx44, Succ(wx7320), ba) → new_lookupFM(wx44, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM271(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM2199(wx67, Zero, wx69, wx70, wx71, wx72, wx73, Zero, bh)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Zero), Zero, bh) → new_lookupFM1354(wx67, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM269(wx58, Neg(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Pos(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Zero)), bf)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM295(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM2195(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM269(wx58, Pos(Zero), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM280(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM291(wx40100, wx41, wx42, wx43, wx44, Succ(wx3370), ba) → new_lookupFM2187(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Zero, bh) → new_lookupFM2209(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM284(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3150), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM291(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, new_primMulNat1, ba)
new_lookupFM2105(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2213(wx40100, wx41, wx42, wx43, wx44, wx3000, ba) → new_lookupFM1371(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2114(wx40100, wx41, wx42, wx43, wx44, Succ(wx4220), ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1284(wx500100, wx501, wx502, wx503, wx504, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, Zero, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM284(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2167(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM1390(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2190(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh) → new_lookupFM1351(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Zero), Succ(wx3450), bh) → new_lookupFM2190(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, bh)
new_lookupFM2175(wx58, wx590, wx60, wx61, wx62, wx63, wx64, wx650, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(wx650)), bf)
new_lookupFM280(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2117(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, Succ(wx4530), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(wx740)), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM279(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77400), Succ(wx59500), bf) → new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77400, wx59500, bf)
new_lookupFM2110(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx4100), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM288(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2199(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM1339(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1341(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2197(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, bh) → new_lookupFM1348(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM280(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx3030), ba) → new_lookupFM2180(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM1305(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8770), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM1310(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx8790), ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM290(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1334(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM2198(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM2199(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM2118(wx40100, wx41, wx42, wx43, wx44, Succ(wx4340), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM279(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3010), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2185(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44, ba)
new_lookupFM2168(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2102(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM278(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM293(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1350(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx5280), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29300), Zero, bf) → new_lookupFM2166(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1288(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM283(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3130), ba) → new_lookupFM2183(wx40000, wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77200), Succ(wx59400), bf) → new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77200, wx59400, bf)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM296(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2116(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2221(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM276(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx2790), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM2182(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1303(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM145(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1292(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM274(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM269(wx58, Neg(Zero), wx60, wx61, wx62, wx63, wx64, Pos(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM1258(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(Succ(wx77400)), bf) → new_lookupFM1261(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2172(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, wx2560, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM1391(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1393(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2106(wx40000, wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM256(wx40000, wx40100, wx41, wx42, wx43, wx44, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1285(wx500100, wx501, wx502, wx503, wx504, Succ(wx9490), bg) → new_lookupFM(wx504, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM1362(wx67, wx69, wx70, wx71, wx72, wx73, wx5300, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Zero)), bh)
new_lookupFM1253(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx59400), Succ(Succ(wx77200)), bf) → new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77200, wx59400, bf)
new_lookupFM1422(wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM151(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM1331(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Succ(wx38600)), bh) → new_lookupFM2208(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38600, bh)
new_lookupFM298(wx40100, wx41, wx42, wx43, wx44, wx3000, Zero, ba) → new_lookupFM2213(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM2174(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM2218(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1411(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2104(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2160(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx2850), bf) → new_lookupFM2164(wx58, Succ(wx5900), wx60, wx61, wx62, wx63, wx64, Succ(wx6500), bf)
new_lookupFM1389(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx8990), ba) → new_lookupFM1390(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2189(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh) → new_lookupFM1350(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM297(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx3580), ba) → new_lookupFM1370(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, Succ(wx38400), bh) → new_lookupFM2203(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1418(wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM(wx44, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM298(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3620), ba) → new_lookupFM1371(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, wx2560, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(Succ(wx6500))), bf)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Zero, bh) → new_lookupFM2202(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM1253(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Succ(Succ(wx77200)), bf) → new_lookupFM1256(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2115(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2220(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM289(wx40100, wx41, wx42, wx43, wx44, Succ(wx3310), ba) → new_lookupFM2185(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM2200(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM256(wx67, wx6800, wx69, wx70, wx71, wx72, Float(Neg(Succ(wx73)), Neg(Succ(wx7400))), bh)
new_lookupFM1349(wx67, wx680, wx69, wx70, wx71, wx72, wx73, wx740, Succ(wx4540), bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Neg(wx740)), bh)
new_lookupFM157(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx7260), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM294(wx67, Neg(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Zero, bh) → new_lookupFM2196(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM270(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM291(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1355(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx6170), bh) → new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx6170, new_primMulNat0(Succ(wx7400), wx6800), bh)
new_lookupFM269(wx58, Pos(Zero), wx60, wx61, wx62, wx63, wx64, Neg(Zero), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM276(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1177(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, wx760, be) → new_lookupFM1180(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be)
new_lookupFM294(wx67, Pos(Zero), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2189(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2183(wx40000, wx40100, wx41, wx42, wx43, wx44, ba) → new_lookupFM1308(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM1182(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, be) → new_lookupFM(wx27, Float(Neg(wx2800), Neg(wx2810)), be)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2110(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2158(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Zero, bf) → new_lookupFM2168(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1365(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx7180), bh) → new_lookupFM1366(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Zero))), ba) → new_lookupFM155(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1354(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx5320), bh) → new_lookupFM1367(wx67, wx69, wx70, wx71, wx72, wx73, wx5320, new_primMulNat1, bh)
new_lookupFM269(wx58, Pos(Succ(wx5900)), wx60, wx61, wx62, wx63, wx64, Neg(Succ(wx6500)), Succ(wx2560), bf) → new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primPlusNat0(new_primMulNat0(wx6500, wx5900), Succ(wx5900)), wx2560, bf)
new_lookupFM2196(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Zero, bh) → new_lookupFM2197(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba)
new_lookupFM272(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Zero, ba) → new_lookupFM1278(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM292(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM297(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2114(wx40100, wx41, wx42, wx43, wx44, Zero, ba) → new_lookupFM2219(wx40100, wx41, wx42, wx43, wx44, ba)
new_lookupFM1282(Float(Pos(Succ(wx500000)), Neg(Succ(wx500100))), wx501, wx502, wx503, wx504, bg) → new_lookupFM1283(wx500000, wx500100, wx501, wx502, wx503, wx504, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx500100), Succ(wx500100)), bg)
new_lookupFM285(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx3190), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1255(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx77200), Zero, bf) → new_lookupFM1256(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Pos(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM272(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM275(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(wx38400), bh) → new_lookupFM2201(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx34500, wx38400, bh)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Pos(Succ(wx7400)), Succ(wx3450), bh) → new_lookupFM2188(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx3450, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM157(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2165(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, Zero, bf) → new_lookupFM2168(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1325(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM1327(wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Succ(Succ(Succ(wx310000))), wx40100), ba)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Zero), Succ(wx25600), bf) → new_lookupFM2172(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Succ(wx76100), be) → new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx54200, wx76100, be)
new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, Succ(wx54200), Succ(Succ(wx76100)), be) → new_lookupFM1181(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx54200, wx76100, be)
new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1254(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM2162(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Zero, bf) → new_lookupFM1257(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, new_primMulNat0(Succ(wx64), wx58), bf)
new_lookupFM2113(wx40100, wx41, wx42, wx43, wx44, wx310000, Zero, ba) → new_lookupFM2218(wx40100, wx41, wx42, wx43, wx44, wx310000, ba)
new_lookupFM2164(wx58, wx590, wx60, wx61, wx62, wx63, wx64, wx650, bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Pos(wx650)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Succ(wx3000)), Neg(Succ(Zero))), ba) → new_lookupFM143(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM1258(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx59500), Succ(Succ(wx77400)), bf) → new_lookupFM1260(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx77400, wx59500, bf)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM170(wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Succ(Zero), wx40100), ba)
new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx29500), Succ(wx25600), bf) → new_lookupFM2170(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx29500, wx25600, bf)
new_lookupFM2196(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx3780), bh) → new_lookupFM2206(wx67, Succ(wx6800), wx69, wx70, wx71, wx72, wx73, Succ(wx7400), bh)
new_lookupFM1261(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf) → new_lookupFM(wx63, Float(Neg(Succ(wx64)), Neg(Succ(wx6500))), bf)
new_lookupFM287(wx40100, wx41, wx42, wx43, wx44, Succ(wx3250), ba) → new_lookupFM(wx43, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba) → new_lookupFM2109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx310000, wx40100), Succ(wx40100)), Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM1356(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, wx6170, Zero, bh) → new_lookupFM(wx72, Float(Neg(Succ(wx73)), Pos(Succ(wx7400))), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2106(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2112(wx40100, wx41, wx42, wx43, wx44, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx40100)), Succ(wx40100)), ba)
new_lookupFM2100(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx3680), ba) → new_lookupFM1373(wx40100, wx41, wx42, wx43, wx44, wx3000, new_primMulNat0(Succ(Succ(Zero)), wx40100), ba)
new_lookupFM275(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2770), ba) → new_lookupFM2179(wx40100, wx41, wx42, wx43, wx44, wx3000, ba)
new_lookupFM294(wx67, Neg(Zero), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM1353(wx67, wx69, wx70, wx71, wx72, wx73, wx7400, new_primMulNat0(Succ(wx73), wx67), bh)
new_lookupFM294(wx67, Pos(Succ(wx6800)), wx69, wx70, wx71, wx72, wx73, Neg(Succ(wx7400)), Zero, bh) → new_lookupFM2198(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, new_primPlusNat0(new_primMulNat0(wx7400, wx6800), Succ(wx6800)), bh)
new_lookupFM1252(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(wx5940), bf) → new_lookupFM1253(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, wx5940, new_primMulNat0(Succ(wx6500), wx5900), bf)
new_lookupFM277(wx40100, wx41, wx42, wx43, wx44, wx3000, Succ(wx2830), ba) → new_lookupFM(wx43, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1280(wx40100, wx41, wx42, wx43, wx44, wx3000, wx310000, Succ(wx8060), ba) → new_lookupFM(wx44, Float(Neg(Succ(wx3000)), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM269(wx58, Neg(wx590), wx60, wx61, wx62, wx63, wx64, Neg(wx650), Succ(wx2560), bf) → new_lookupFM(wx62, Float(Neg(Succ(wx64)), Neg(wx650)), bf)
new_lookupFM1172(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, Neg(wx2810), Succ(wx5420), be) → new_lookupFM1178(wx22, wx23, wx24, wx25, wx26, wx27, wx2800, wx2810, wx5420, new_primMulNat0(wx2810, wx23), be)
new_lookupFM2192(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, Succ(wx34500), Succ(Zero), bh) → new_lookupFM2209(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx7400, bh)
new_lookupFM2107(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4000), ba) → new_lookupFM1387(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2109(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx4060), ba) → new_lookupFM(wx43, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx310000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx40000)), Neg(Succ(wx40100))), wx41, wx42, wx43, wx44), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM145(wx40000, wx40100, wx41, wx42, wx43, wx44, new_primMulNat0(Zero, wx40000), ba)
new_lookupFM2159(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, Succ(Succ(wx29500)), Zero, bf) → new_lookupFM2171(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx6500, bf)
new_lookupFM2180(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, ba) → new_lookupFM1286(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, new_primMulNat0(Zero, wx40000), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, wx69400, wx52100, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, wx69400, wx52100, bf)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1268(wx58, wx60, wx61, wx62, wx63, wx64, wx69400, wx52100, bf)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Succ(wx72000), bh) → new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx52900, wx72000, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Succ(wx72000), bh) → new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx52900, wx72000, bh)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, Succ(wx52900), Succ(wx72000), bh) → new_lookupFM1360(wx67, wx6800, wx69, wx70, wx71, wx72, wx73, wx52900, wx72000, bh)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, wx53000, wx72200, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, wx53000, wx72200, bh)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1363(wx67, wx69, wx70, wx71, wx72, wx73, wx53000, wx72200, bh)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69200), Succ(wx52000), bf) → new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69200, wx52000, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69200), Succ(wx52000), bf) → new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69200, wx52000, bf)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69200), Succ(wx52000), bf) → new_lookupFM1264(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69200, wx52000, bf)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Succ(wx72400), bh) → new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, wx53200, wx72400, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Succ(wx72400), bh) → new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, wx53200, wx72400, bh)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, Succ(wx53200), Succ(wx72400), bh) → new_lookupFM1368(wx67, wx69, wx70, wx71, wx72, wx73, wx53200, wx72400, bh)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69600), Succ(wx52300), bf) → new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69600, wx52300, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69600), Succ(wx52300), bf) → new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69600, wx52300, bf)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, Succ(wx69600), Succ(wx52300), bf) → new_lookupFM1272(wx58, wx5900, wx60, wx61, wx62, wx63, wx64, wx69600, wx52300, bf)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69800), Succ(wx52400), bf) → new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, wx69800, wx52400, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69800), Succ(wx52400), bf) → new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, wx69800, wx52400, bf)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, Succ(wx69800), Succ(wx52400), bf) → new_lookupFM1276(wx58, wx60, wx61, wx62, wx63, wx64, wx69800, wx52400, bf)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, Succ(wx89000), Succ(wx71300), ba) → new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, wx89000, wx71300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, Succ(wx89000), Succ(wx71300), ba) → new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, wx89000, wx71300, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, Succ(wx89000), Succ(wx71300), ba) → new_lookupFM1342(wx40100, wx41, wx42, wx43, wx44, wx89000, wx71300, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx87800), Succ(wx70700), ba) → new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, wx87800, wx70700, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx87800), Succ(wx70700), ba) → new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, wx87800, wx70700, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx87800), Succ(wx70700), ba) → new_lookupFM1311(wx40000, wx40100, wx41, wx42, wx43, wx44, wx87800, wx70700, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Succ(wx91200), ba) → new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, wx73700, wx91200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Succ(wx91200), ba) → new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, wx73700, wx91200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, Succ(wx73700), Succ(wx91200), ba) → new_lookupFM1429(wx40100, wx41, wx42, wx43, wx44, wx73700, wx91200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Succ(wx61800), ba) → new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, wx49000, wx61800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Succ(wx61800), ba) → new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, wx49000, wx61800, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx49000), Succ(wx61800), ba) → new_lookupFM1379(wx40000, wx40100, wx41, wx42, wx43, wx44, wx49000, wx61800, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, Succ(wx60400), Succ(wx48200), ba) → new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, wx60400, wx48200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, Succ(wx60400), Succ(wx48200), ba) → new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, wx60400, wx48200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, Succ(wx60400), Succ(wx48200), ba) → new_lookupFM1301(wx40000, wx41, wx42, wx43, wx44, wx60400, wx48200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Succ(wx62000), ba) → new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, wx49100, wx62000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Succ(wx62000), ba) → new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, wx49100, wx62000, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, Succ(wx49100), Succ(wx62000), ba) → new_lookupFM1382(wx40000, wx41, wx42, wx43, wx44, wx49100, wx62000, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60200), Succ(wx48100), ba) → new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60200, wx48100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60200), Succ(wx48100), ba) → new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60200, wx48100, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60200), Succ(wx48100), ba) → new_lookupFM1297(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60200, wx48100, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx77800), Succ(wx60100), ba) → new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, wx77800, wx60100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx77800), Succ(wx60100), ba) → new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, wx77800, wx60100, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx77800), Succ(wx60100), ba) → new_lookupFM1293(wx40000, wx40100, wx41, wx42, wx43, wx44, wx77800, wx60100, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, Succ(wx78200), Succ(wx61500), ba) → new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, wx78200, wx61500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, Succ(wx78200), Succ(wx61500), ba) → new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, wx78200, wx61500, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, Succ(wx78200), Succ(wx61500), ba) → new_lookupFM1332(wx40100, wx41, wx42, wx43, wx44, wx78200, wx61500, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88800), Succ(wx71200), ba) → new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88800, wx71200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88800), Succ(wx71200), ba) → new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88800, wx71200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88800), Succ(wx71200), ba) → new_lookupFM1337(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88800, wx71200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87600), Succ(wx70600), ba) → new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87600, wx70600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87600), Succ(wx70600), ba) → new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87600, wx70600, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87600), Succ(wx70600), ba) → new_lookupFM1306(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87600, wx70600, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Succ(wx91000), ba) → new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73600, wx91000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Succ(wx91000), ba) → new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73600, wx91000, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73600), Succ(wx91000), ba) → new_lookupFM1425(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73600, wx91000, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88600), Succ(wx71100), ba) → new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88600, wx71100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88600), Succ(wx71100), ba) → new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88600, wx71100, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx88600), Succ(wx71100), ba) → new_lookupFM1328(wx40100, wx41, wx42, wx43, wx44, wx310000, wx88600, wx71100, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Succ(wx90200), ba) → new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73000, wx90200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Succ(wx90200), ba) → new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73000, wx90200, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx73000), Succ(wx90200), ba) → new_lookupFM1409(wx40100, wx41, wx42, wx43, wx44, wx310000, wx73000, wx90200, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87400), Succ(wx70500), ba) → new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87400, wx70500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87400), Succ(wx70500), ba) → new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87400, wx70500, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx87400), Succ(wx70500), ba) → new_lookupFM1289(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx87400, wx70500, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Succ(wx89600), ba) → new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx72700, wx89600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Succ(wx89600), ba) → new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx72700, wx89600, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, Succ(wx72700), Succ(wx89600), ba) → new_lookupFM1376(wx40000, wx40100, wx41, wx42, wx43, wx44, wx310000, wx72700, wx89600, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60700), Succ(wx48400), ba) → new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60700, wx48400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60700), Succ(wx48400), ba) → new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60700, wx48400, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, Succ(wx60700), Succ(wx48400), ba) → new_lookupFM1319(wx40000, wx40100, wx41, wx42, wx43, wx44, wx60700, wx48400, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, Succ(wx60900), Succ(wx48500), ba) → new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, wx60900, wx48500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, Succ(wx60900), Succ(wx48500), ba) → new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, wx60900, wx48500, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, Succ(wx60900), Succ(wx48500), ba) → new_lookupFM1323(wx40000, wx41, wx42, wx43, wx44, wx60900, wx48500, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: 



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Succ(wx62800), ba) → new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, wx49800, wx62800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx40000) → Succ(wx40000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx40000) → Zero
new_primPlusNat1(Succ(wx800), wx40000) → Succ(Succ(new_primPlusNat0(wx800, wx40000)))
new_primPlusNat0(Succ(wx8000), Zero) → Succ(wx8000)
new_primPlusNat0(Zero, Succ(wx400000)) → Succ(wx400000)
new_primPlusNat0(Succ(wx8000), Succ(wx400000)) → Succ(Succ(new_primPlusNat0(wx8000, wx400000)))
new_primMulNat0(Succ(wx30000), wx40000) → new_primPlusNat1(new_primMulNat0(wx30000, wx40000), wx40000)
new_primMulNat1 → Zero

The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [15] we can delete all non-usable rules [17] from R.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Succ(wx62800), ba) → new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, wx49800, wx62800, ba)

R is empty.
The set Q consists of the following terms:

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.

new_primPlusNat1(Succ(x0), x1)
new_primMulNat1
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primMulNat0(Zero, x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat1(Zero, x0)
new_primMulNat0(Succ(x0), x1)
new_primPlusNat0(Succ(x0), Succ(x1))



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
                                ↳ QDP
                                  ↳ QDPSizeChangeProof

Q DP problem:
The TRS P consists of the following rules:

new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, Succ(wx49800), Succ(wx62800), ba) → new_lookupFM1405(wx40000, wx41, wx42, wx43, wx44, wx49800, wx62800, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By using the subterm criterion [20] together with the size-change analysis [32] we have proven that there are no infinite chains for this DP problem.

From the DPs we obtained the following set of size-change graphs: