YES 163.574 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
  ((lookupWithDefaultFM :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a) :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a)

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 b a) where 

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
lookupFM EmptyFM key Nothing
lookupFM (Branch key elt _ fm_l fm_rkey_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

  lookupWithDefaultFM :: Ord b => FiniteMap b a  ->  a  ->  b  ->  a
lookupWithDefaultFM fm deflt key 
case lookupFM fm key of
  Nothing-> deflt
  Just elt-> elt


module Maybe where
  import qualified FiniteMap
import qualified Prelude



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

is transformed to
lookupWithDefaultFM0 deflt Nothing = deflt
lookupWithDefaultFM0 deflt (Just elt) = elt



↳ HASKELL
  ↳ CR
HASKELL
      ↳ BR

mainModule FiniteMap
  ((lookupWithDefaultFM :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a) :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a)

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 

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key Nothing
lookupFM (Branch key elt _ fm_l fm_rkey_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

  lookupWithDefaultFM :: Ord b => FiniteMap b a  ->  a  ->  b  ->  a
lookupWithDefaultFM fm deflt key lookupWithDefaultFM0 deflt (lookupFM fm key)

  
lookupWithDefaultFM0 deflt Nothing deflt
lookupWithDefaultFM0 deflt (Just eltelt


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
  ((lookupWithDefaultFM :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a) :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a)

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 

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key Nothing
lookupFM (Branch key elt vw fm_l fm_rkey_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

  lookupWithDefaultFM :: Ord a => FiniteMap a b  ->  b  ->  a  ->  b
lookupWithDefaultFM fm deflt key lookupWithDefaultFM0 deflt (lookupFM fm key)

  
lookupWithDefaultFM0 deflt Nothing deflt
lookupWithDefaultFM0 deflt (Just eltelt


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_rkey_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_rkey_to_find = lookupFM3 (Branch key elt vw fm_l fm_rkey_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_rkey_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
  (lookupWithDefaultFM :: FiniteMap (Ratio Int) a  ->  a  ->  Ratio Int  ->  a)

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 b a) where 

  lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a
lookupFM EmptyFM key lookupFM4 EmptyFM key
lookupFM (Branch key elt vw fm_l fm_rkey_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_rkey_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

  lookupWithDefaultFM :: Ord a => FiniteMap a b  ->  b  ->  a  ->  b
lookupWithDefaultFM fm deflt key lookupWithDefaultFM0 deflt (lookupFM fm key)

  
lookupWithDefaultFM0 deflt Nothing deflt
lookupWithDefaultFM0 deflt (Just eltelt


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(wx21100), Succ(wx301000)) → new_primPlusNat(wx21100, wx301000)

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(wx50000), wx30100) → new_primMulNat(wx50000, wx30100)

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_lookupWithDefaultFM0105(wx1298, wx1299, wx1300, wx1301, wx1302, wx1303, wx1304, wx1305, dg) → new_lookupWithDefaultFM020(wx1298, wx1302, :%(Pos(Succ(wx1304)), Neg(Succ(wx1305))), dg)
new_lookupWithDefaultFM0159(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6890), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx231, Zero, h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0175(wx1806, wx1807, wx1808, wx1809, wx1810, wx1811, wx1812, wx1813, ge) → new_lookupWithDefaultFM0417(wx1806, wx1807, wx1808, wx1809, wx1810, wx1811, wx1812, wx1813, ge)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0163(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM062(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3240), ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68000)), Zero, fd) → new_lookupWithDefaultFM0382(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0304(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, cf) → new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, new_primMulNat0(Succ(wx1254), wx1259), cf)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Zero, hh) → new_lookupWithDefaultFM0479(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0447(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9390), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Zero)), hh)
new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx17510), ed) → new_lookupWithDefaultFM0362(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, wx17510, new_primMulNat0(Succ(wx1326), wx1332), ed)
new_lookupWithDefaultFM047(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2770), ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45200)), Succ(wx40400), da) → new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45200, wx40400, da)
new_lookupWithDefaultFM0229(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9520), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0278(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Succ(Zero), bg) → new_lookupWithDefaultFM0280(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, bg)
new_lookupWithDefaultFM049(wx1605, wx1606, wx1607, wx1608, wx1609, wx1610, wx1611, wx1612, bf) → new_lookupWithDefaultFM020(wx1605, wx1610, :%(Pos(Zero), Pos(Succ(wx1612))), bf)
new_lookupWithDefaultFM0115(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11110), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM051(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0479(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0411(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1385), wx1391), fh)
new_lookupWithDefaultFM0384(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Zero, h) → new_lookupWithDefaultFM0550(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM060(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0295(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM044(wx1596, wx1597, wx1598, wx1599, wx1600, wx1601, wx1602, wx1603, be) → new_lookupWithDefaultFM020(wx1596, wx1600, :%(Pos(Succ(wx1602)), Neg(Succ(wx1603))), be)
new_lookupWithDefaultFM0252(wx1911, wx1912, wx1913, wx1914, wx1915, wx1916, wx1917, bbc) → new_lookupWithDefaultFM020(wx1911, wx1915, :%(Neg(Zero), Pos(Succ(wx1917))), bbc)
new_lookupWithDefaultFM0258(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10410), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0199(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0123(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM091(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4270), ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0374(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM030(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0268(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0121(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11120), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0198(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0433(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Succ(wx257000))), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM0140(wx1735, wx1736, wx1737, wx1738, wx1739, wx1740, wx1741, fa) → new_lookupWithDefaultFM0370(wx1735, wx1736, wx1737, wx1738, wx1739, wx1740, wx1741, fa)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0454(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx15820), h) → new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15820, new_primMulNat0(Succ(wx20000), wx20700), h)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Succ(wx257000), h) → new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2310, wx257000, h)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0438(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0131(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5790), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Succ(wx90800)), hh) → new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx90800, hh)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0457(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0256(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0455(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0334(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Zero, ed) → new_lookupWithDefaultFM0363(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, new_primMulNat0(Succ(wx1326), wx1332), ed)
new_lookupWithDefaultFM0523(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0522(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM061(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0295(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0116(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0123(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5490), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM029(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM082(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3880), ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0173(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7480), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM053(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Zero, wx1212), bh)
new_lookupWithDefaultFM0438(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0448(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0505(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, Succ(wx19670), bag) → new_lookupWithDefaultFM0506(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag)
new_lookupWithDefaultFM0356(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx19830), eb) → new_lookupWithDefaultFM020(wx1316, wx1322, :%(Pos(Zero), Neg(Succ(wx1323))), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM066(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Zero, baf) → new_lookupWithDefaultFM0500(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, baf)
new_lookupWithDefaultFM0528(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Succ(Zero), h) → new_lookupWithDefaultFM0530(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM038(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, bd) → new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, new_primMulNat0(Succ(wx1184), wx1190), bd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0215(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0244(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0515(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0178(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0423(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0434(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, hf) → new_lookupWithDefaultFM0435(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, new_primMulNat0(Succ(wx1464), wx1469), hf)
new_lookupWithDefaultFM0185(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7820), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx195000), Zero, da) → new_lookupWithDefaultFM0336(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0267(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(wx8510), wx852, wx853, wx854, wx855, wx856, wx857, Neg(wx8580), Succ(wx8600), hh) → new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM065(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0406(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx72300), Succ(Succ(wx175600)), fd) → new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175600, wx72300, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM041(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM030(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM053(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0268(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, bc) → new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, new_primMulNat0(Succ(wx1175), wx1181), bc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0320(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0174(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx751, ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0355(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx175000), Succ(Succ(wx198200)), eb) → new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, wx198200, wx175000, eb)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(wx40400), da) → new_lookupWithDefaultFM0329(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0183(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7700), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0225(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9340), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0318(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0321(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0147(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM042(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(wx91000), hh) → new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx91000, hh)
new_lookupWithDefaultFM0103(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4730), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0167(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0242(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11380), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0445(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0221(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, bac) → new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, new_primMulNat0(Succ(wx1498), wx1504), bac)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Zero, hh) → new_lookupWithDefaultFM0459(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0150(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0136(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx5890), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM062(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0445(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0457(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0203(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0222(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx11320), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM079(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11040), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0229(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0496(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0202(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0(wx199, Pos(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM06(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0193(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0430(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM072(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0227(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0236(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Zero, wx1526), bag)
new_lookupWithDefaultFM0467(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Succ(Zero), hh) → new_lookupWithDefaultFM0469(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Succ(Zero), hh) → new_lookupWithDefaultFM0466(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0180(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx768, ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0324(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx19490), da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM070(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0216(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0440(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), Zero, hh) → new_lookupWithDefaultFM0471(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM095(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0506(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM020(wx1524, wx1530, :%(Neg(Zero), Neg(Succ(wx1531))), bag)
new_lookupWithDefaultFM0331(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195600), Succ(wx115700), fd) → new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195600, wx115700, fd)
new_lookupWithDefaultFM0205(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8460), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0138(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM03(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx234, h) → new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx234, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0238(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0383(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0248(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10090), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0198(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0534(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM09(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0161(wx1779, wx1780, wx1781, wx1782, wx1783, wx1784, wx1785, wx1786, ga) → new_lookupWithDefaultFM0414(wx1779, wx1780, wx1781, wx1782, wx1783, wx1784, wx1785, wx1786, ga)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0447(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0146(wx622, Pos(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0498(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Succ(Succ(wx202600)), baf) → new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx199600, wx202600, baf)
new_lookupWithDefaultFM010(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0115(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0414(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, gb) → new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, new_primMulNat0(Succ(wx1394), wx1400), gb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0211(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0452(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0453(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0134(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM046(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0129(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0110(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5080), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0454(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9060), hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0417(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf) → new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, new_primMulNat0(Zero, wx1422), gf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0212(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0407(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx17570), fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0(wx199, Pos(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Neg(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM01(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0249(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0191(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx231, Succ(Zero), h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM00(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx231, h) → new_lookupWithDefaultFM016(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0450(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0451(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx18650), gh) → new_lookupWithDefaultFM0426(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx18650, new_primMulNat0(Succ(wx1430), wx1436), gh)
new_lookupWithDefaultFM0184(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7770), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0244(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM033(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0338(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(Succ(wx164000)), da) → new_lookupWithDefaultFM0341(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Zero, da) → new_lookupWithDefaultFM0320(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM076(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0170(wx1411, wx1412, wx1413, wx1414, wx1415, wx1416, wx1417, wx1418, gd) → new_lookupWithDefaultFM020(wx1411, wx1416, :%(Neg(Zero), Pos(Succ(wx1418))), gd)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(wx257000), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM099(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx464, ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0197(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx8170), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164000), Succ(wx49200), da) → new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164000, wx49200, da)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Zero, fd) → new_lookupWithDefaultFM0384(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM075(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0304(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0312(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4920), da) → new_lookupWithDefaultFM0338(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx4920, new_primMulNat0(Zero, wx40200), da)
new_lookupWithDefaultFM021(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0182(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0113(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM092(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0443(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0397(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx115800), Succ(Succ(wx195800)), fd) → new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195800, wx115800, fd)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Zero, fd) → new_lookupWithDefaultFM0394(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0142(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0200(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0224(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM097(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0349(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0263(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM054(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx10980), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM087(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0231(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx960, ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, wx6320, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0345(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM051(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0281(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, Succ(wx19330), cf) → new_lookupWithDefaultFM020(wx1253, wx1258, :%(Pos(Zero), Pos(Succ(wx1259))), cf)
new_lookupWithDefaultFM0293(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM020(wx1219, wx1225, :%(Pos(Zero), Pos(Succ(wx1226))), ca)
new_lookupWithDefaultFM0347(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, dd) → new_lookupWithDefaultFM0348(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, new_primMulNat0(Succ(wx1281), wx1287), dd)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0384(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0378(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0407(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Zero, wx63000), fd)
new_lookupWithDefaultFM037(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0275(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM061(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0139(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0143(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Succ(Succ(wx196400)), hh) → new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116300, wx196400, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0265(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0277(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx19900), bg) → new_lookupWithDefaultFM0278(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx19900, new_primMulNat0(Succ(wx1202), wx1208), bg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0170(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM08(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, Succ(wx2750), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(wx2070)), h)
new_lookupWithDefaultFM0255(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0523(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0213(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0548(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11480, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM070(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0300(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0181(wx1815, wx1816, wx1817, wx1818, wx1819, wx1820, wx1821, wx1822, gg) → new_lookupWithDefaultFM0424(wx1815, wx1816, wx1817, wx1818, wx1819, wx1820, wx1821, wx1822, gg)
new_lookupWithDefaultFM0133(wx4, wx31, wx32, wx33, wx34, wx5100, wx587, ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0296(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx19910), cc) → new_lookupWithDefaultFM0297(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx19910, new_primMulNat0(Succ(wx1229), wx1235), cc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0220(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0225(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0240(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0452(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9040), hh) → new_lookupWithDefaultFM0473(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0223(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9200), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM036(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2260), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0195(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195800), Zero, fd) → new_lookupWithDefaultFM0400(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0498(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx19960, Zero, baf) → new_lookupWithDefaultFM020(wx1515, wx1521, :%(Neg(Zero), Pos(Succ(wx1522))), baf)
new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195600), Zero, fd) → new_lookupWithDefaultFM0390(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0198(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8240), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM021(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0419(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Zero, Succ(Succ(wx198600)), gf) → new_lookupWithDefaultFM0422(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf)
new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Succ(Zero), h) → new_lookupWithDefaultFM025(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0149(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM091(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0346(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0237(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0479(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0338(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx49200), Succ(Succ(wx164000)), da) → new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164000, wx49200, da)
new_lookupWithDefaultFM01(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, wx232, h) → new_lookupWithDefaultFM0531(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h)
new_lookupWithDefaultFM0260(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0527(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0247(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0112(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0352(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0204(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM069(wx1623, wx1624, wx1625, wx1626, wx1627, wx1628, wx1629, cd) → new_lookupWithDefaultFM020(wx1623, wx1627, :%(Pos(Zero), Pos(Succ(wx1629))), cd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0140(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0191(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0430(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0260(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10530), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0221(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM0290(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Zero, wx1221), ca)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0233(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0149(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6450), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0352(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb) → new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, new_primMulNat0(Zero, wx1318), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0117(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0178(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, Zero, ca) → new_lookupWithDefaultFM0292(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Succ(wx1220), wx1226), ca)
new_lookupWithDefaultFM0402(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(Succ(wx175400)), fd) → new_lookupWithDefaultFM0405(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0400(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Succ(Zero), h) → new_lookupWithDefaultFM0547(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0387(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx115700), Succ(Succ(wx195600)), fd) → new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195600, wx115700, fd)
new_lookupWithDefaultFM0494(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, bac) → new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, new_primMulNat0(Succ(wx1498), wx1504), bac)
new_lookupWithDefaultFM0241(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Zero, wx1535), bah)
new_lookupWithDefaultFM043(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx261, ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0165(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0543(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0211(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx876, ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM045(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM08(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), Zero, h) → new_lookupWithDefaultFM0532(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0393(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0299(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, cc) → new_lookupWithDefaultFM020(wx1228, wx1234, :%(Pos(Zero), Neg(Succ(wx1235))), cc)
new_lookupWithDefaultFM0517(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Succ(Succ(wx202800)), bbb) → new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx199700, wx202800, bbb)
new_lookupWithDefaultFM0548(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Succ(Succ(wx194000)), h) → new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114800, wx194000, h)
new_lookupWithDefaultFM092(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0346(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0310(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM0202(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11280), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0292(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, Succ(wx19450), ca) → new_lookupWithDefaultFM0293(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM044(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0220(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9170), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11630, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, Succ(wx19340), bab) → new_lookupWithDefaultFM020(wx1488, wx1493, :%(Neg(Succ(wx1494)), Neg(Succ(wx1495))), bab)
new_lookupWithDefaultFM0232(wx1893, wx1894, wx1895, wx1896, wx1897, wx1898, wx1899, wx1900, bae) → new_lookupWithDefaultFM020(wx1893, wx1898, :%(Neg(Zero), Pos(Succ(wx1900))), bae)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0101(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0234(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM055(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2970), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0236(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM040(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2380), ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0181(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0443(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0455(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0193(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM078(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM076(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0304(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Neg(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM010(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0257(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM025(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM041(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2450), ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0444(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0360(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed) → new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, new_primMulNat0(Zero, wx1327), ed)
new_lookupWithDefaultFM087(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4120), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Neg(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Pos(wx2070), Zero, h) → new_lookupWithDefaultFM09(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Succ(wx201600), cc) → new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx199100, wx201600, cc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0187(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM069(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0186(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0337(wx394, wx3950, wx396, wx397, wx398, wx399, wx400, wx401, wx4020, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(wx4020)), da)
new_lookupWithDefaultFM084(wx1631, wx1632, wx1633, wx1634, wx1635, wx1636, wx1637, cg) → new_lookupWithDefaultFM020(wx1631, wx1635, :%(Pos(Zero), Neg(Succ(wx1637))), cg)
new_lookupWithDefaultFM0156(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx11190), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68200)), Zero, fd) → new_lookupWithDefaultFM0392(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15820, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM043(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM010(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, h) → new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM068(wx4, wx31, wx32, wx33, wx34, wx5100, wx344, ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0452(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM064(wx1614, wx1615, wx1616, wx1617, wx1618, wx1619, wx1620, wx1621, cb) → new_lookupWithDefaultFM020(wx1614, wx1619, :%(Pos(Zero), Neg(Succ(wx1621))), cb)
new_lookupWithDefaultFM0112(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5200), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM09(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, Succ(wx2760), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(wx2070)), h)
new_lookupWithDefaultFM075(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3610), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, Succ(wx15830), bag) → new_lookupWithDefaultFM0504(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, wx15830, new_primMulNat0(Succ(wx1525), wx1531), bag)
new_lookupWithDefaultFM078(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, cf) → new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, new_primMulNat0(Succ(wx1254), wx1259), cf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0230(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0324(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0114(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0538(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM011(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0251(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0171(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0416(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0143(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx6130), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0455(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9420), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Zero)), hh)
new_lookupWithDefaultFM0122(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5420), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0158(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0543(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0336(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM0368(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, Succ(wx19720), eh) → new_lookupWithDefaultFM020(wx1351, wx1356, :%(Pos(Zero), Neg(Succ(wx1357))), eh)
new_lookupWithDefaultFM0294(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0290(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, Succ(wx19750), gb) → new_lookupWithDefaultFM020(wx1393, wx1398, :%(Neg(Succ(wx1399)), Pos(Succ(wx1400))), gb)
new_lookupWithDefaultFM072(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0303(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175400), Succ(wx72000), fd) → new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175400, wx72000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM063(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0461(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM089(wx1269, wx1270, wx1271, wx1272, wx1273, wx1274, wx1275, wx1276, db) → new_lookupWithDefaultFM020(wx1269, wx1273, :%(Pos(Succ(wx1275)), Pos(Succ(wx1276))), db)
new_lookupWithDefaultFM031(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0268(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68000), Zero, fd) → new_lookupWithDefaultFM0382(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Zero)), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0231(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0119(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx540, ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Zero, hh) → new_lookupWithDefaultFM0466(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0328(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0331(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0492(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, bac) → new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, new_primMulNat0(Succ(wx1498), wx1504), bac)
new_lookupWithDefaultFM0157(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6650), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM00(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx231, h) → new_lookupWithDefaultFM015(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0205(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0132(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0366(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0254(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0230(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9570), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0449(wx850, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9410), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Zero)), hh)
new_lookupWithDefaultFM0128(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5690), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0257(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11410), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM071(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0300(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM011(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11470), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Zero)), h)
new_lookupWithDefaultFM0187(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx7850), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0104(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4780), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0227(wx1884, wx1885, wx1886, wx1887, wx1888, wx1889, wx1890, wx1891, bad) → new_lookupWithDefaultFM020(wx1884, wx1888, :%(Neg(Succ(wx1890)), Neg(Succ(wx1891))), bad)
new_lookupWithDefaultFM095(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx11070), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM093(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0259(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10480), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0470(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), wx6320, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM085(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30100), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM034(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0262(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11420), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45200)), Zero, da) → new_lookupWithDefaultFM0318(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM032(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat1(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), wx5100), ba)
new_lookupWithDefaultFM0432(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, Succ(wx19760), hd) → new_lookupWithDefaultFM020(wx1455, wx1460, :%(Neg(Zero), Neg(Succ(wx1461))), hd)
new_lookupWithDefaultFM0484(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Succ(wx40400), da) → new_lookupWithDefaultFM0329(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Succ(wx187200), hh) → new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94300, wx187200, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0107(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0164(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0471(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx18660), hh) → new_lookupWithDefaultFM0472(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0326(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0118(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0453(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0530(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM078(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM083(wx4, wx31, wx32, wx33, wx34, wx5100, wx391, ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0148(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6400), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM034(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10930), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0343(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx16430), da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM0192(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0430(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM062(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0295(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM016(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM06(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0508(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Zero, wx1535), bah)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, Zero, hh) → new_lookupWithDefaultFM0462(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0197(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0433(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM042(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2500), ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM084(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM045(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0276(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0134(wx1727, wx1728, wx1729, wx1730, wx1731, wx1732, wx1733, eg) → new_lookupWithDefaultFM0367(wx1727, wx1728, wx1729, wx1730, wx1731, wx1732, wx1733, eg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0201(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM056(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0111(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0145(wx1367, wx1368, wx1369, wx1370, wx1371, wx1372, wx1373, fc) → new_lookupWithDefaultFM020(wx1367, wx1371, :%(Pos(Zero), Neg(Succ(wx1373))), fc)
new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Zero, gh) → new_lookupWithDefaultFM0427(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, new_primMulNat0(Succ(wx1430), wx1436), gh)
new_lookupWithDefaultFM00(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx231, h) → new_lookupWithDefaultFM017(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM049(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45200), Succ(wx40400), da) → new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45200, wx40400, da)
new_lookupWithDefaultFM0138(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0369(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM074(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0122(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0203(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx8340), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0341(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM0382(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0385(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM067(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3410), ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0532(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx19260), h) → new_lookupWithDefaultFM0533(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0102(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0487(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0453(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM075(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0130(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx5720), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM060(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3120), ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM07(wx199, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11460), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Zero)), h)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Zero)), da)
new_lookupWithDefaultFM0540(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM013(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0228(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0132(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0402(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx72000), Succ(Succ(wx175400)), fd) → new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175400, wx72000, fd)
new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Succ(wx187000), hh) → new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94000, wx187000, hh)
new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, Succ(wx19300), bc) → new_lookupWithDefaultFM020(wx1174, wx1179, :%(Pos(Succ(wx1180)), Neg(Succ(wx1181))), bc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0168(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0186(wx1438, wx1439, wx1440, wx1441, wx1442, wx1443, wx1444, wx1445, ha) → new_lookupWithDefaultFM020(wx1438, wx1443, :%(Neg(Zero), Neg(Succ(wx1445))), ha)
new_lookupWithDefaultFM0139(wx4, wx31, wx32, wx33, wx34, wx5100, wx604, ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0195(wx1841, wx1842, wx1843, wx1844, wx1845, wx1846, wx1847, hc) → new_lookupWithDefaultFM0431(wx1841, wx1842, wx1843, wx1844, wx1845, wx1846, wx1847, hc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM081(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Succ(wx63200), fd) → new_lookupWithDefaultFM0393(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0141(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), wx4040, da)
new_lookupWithDefaultFM0548(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Succ(Zero), h) → new_lookupWithDefaultFM0550(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0480(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0416(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf) → new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, new_primMulNat0(Zero, wx1422), gf)
new_lookupWithDefaultFM0346(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, dd) → new_lookupWithDefaultFM0348(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, new_primMulNat0(Succ(wx1281), wx1287), dd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM049(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0228(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0496(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM073(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0250(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10210), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0146(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30100), Succ(wx30100)), ba)
new_lookupWithDefaultFM0258(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0524(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0316(wx394, wx3950, wx396, wx397, wx398, wx399, wx400, wx401, wx4020, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(wx4020)), da)
new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Zero, hh) → new_lookupWithDefaultFM0484(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0462(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0230(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0496(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0129(wx1343, wx1344, wx1345, wx1346, wx1347, wx1348, wx1349, ef) → new_lookupWithDefaultFM020(wx1343, wx1347, :%(Pos(Zero), Pos(Succ(wx1349))), ef)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM050(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0281(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0117(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0359(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0126(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx11630), hh) → new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11630, new_primMulNat0(Succ(wx85100), wx85800), hh)
new_lookupWithDefaultFM0287(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0283(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0439(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0206(wx1471, wx1472, wx1473, wx1474, wx1475, wx1476, wx1477, hg) → new_lookupWithDefaultFM020(wx1471, wx1475, :%(Neg(Zero), Neg(Succ(wx1477))), hg)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68000), Succ(wx63200), fd) → new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68000, wx63200, fd)
new_lookupWithDefaultFM0(wx199, Neg(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Neg(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM03(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM0371(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, Succ(wx19730), fb) → new_lookupWithDefaultFM020(wx1359, wx1364, :%(Pos(Zero), Pos(Succ(wx1365))), fb)
new_lookupWithDefaultFM085(wx394, Pos(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM082(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68000)), Succ(wx63200), fd) → new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68000, wx63200, fd)
new_lookupWithDefaultFM0204(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8410), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0110(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0528(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Succ(Succ(wx193800)), h) → new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114500, wx193800, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0103(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx194800), Succ(wx115100), da) → new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx194800, wx115100, da)
new_lookupWithDefaultFM0388(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx19570), fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx15850), h) → new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15850, new_primMulNat0(Succ(wx20000), wx20700), h)
new_lookupWithDefaultFM074(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11030), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM079(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0519(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, bbb) → new_lookupWithDefaultFM020(wx1542, wx1548, :%(Neg(Zero), Neg(Succ(wx1549))), bbb)
new_lookupWithDefaultFM085(wx394, Pos(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0312(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM033(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, bc) → new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, new_primMulNat0(Succ(wx1175), wx1181), bc)
new_lookupWithDefaultFM0507(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0503(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0454(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx17500), eb) → new_lookupWithDefaultFM0355(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, wx17500, new_primMulNat0(Succ(wx1317), wx1323), eb)
new_lookupWithDefaultFM0315(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4500), da) → new_lookupWithDefaultFM0337(wx394, Succ(wx39500), wx396, wx397, wx398, wx399, wx400, wx401, Succ(wx40200), da)
new_lookupWithDefaultFM0444(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0456(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0135(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11150), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0110(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0352(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0138(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx6010), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0478(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0485(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Succ(Zero), hh) → new_lookupWithDefaultFM0487(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0162(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM088(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4170), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM092(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4320), ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0136(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0369(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0152(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0189(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx7970), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0155(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0167(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7090), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM03(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx234, h) → new_lookupWithDefaultFM0538(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0185(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM088(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0398(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx19590), fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0214(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8850), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Zero, h) → new_lookupWithDefaultFM021(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM064(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM06(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx11450), h) → new_lookupWithDefaultFM0528(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11450, new_primMulNat0(Zero, wx20700), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM060(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0107(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5000), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Zero), hh) → new_lookupWithDefaultFM0459(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx11580), fd) → new_lookupWithDefaultFM0397(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx11580, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0252(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Zero, gf) → new_lookupWithDefaultFM0420(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, new_primMulNat0(Succ(wx1421), wx1427), gf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0223(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0226(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx937, ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM039(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM084(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx198600), Zero, gf) → new_lookupWithDefaultFM0422(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf)
new_lookupWithDefaultFM0314(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4950), da) → new_lookupWithDefaultFM0342(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx4950, new_primMulNat0(Zero, wx40200), da)
new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Zero, cc) → new_lookupWithDefaultFM0299(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, cc)
new_lookupWithDefaultFM0311(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4460), da) → new_lookupWithDefaultFM0321(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM031(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45200), Zero, da) → new_lookupWithDefaultFM0318(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0375(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6740), fd) → new_lookupWithDefaultFM0385(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0135(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0500(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, baf) → new_lookupWithDefaultFM020(wx1515, wx1521, :%(Neg(Zero), Pos(Succ(wx1522))), baf)
new_lookupWithDefaultFM0550(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0156(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0197(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0(wx199, Pos(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Neg(wx2070), Zero, h) → new_lookupWithDefaultFM08(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0175(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0131(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0366(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0137(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0369(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0152(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0410(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0160(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx692, ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0255(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10380), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0311(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0179(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM038(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, Zero, bh) → new_lookupWithDefaultFM0285(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Succ(wx1211), wx1217), bh)
new_lookupWithDefaultFM098(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0349(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Zero, hh) → new_lookupWithDefaultFM0461(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0300(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, ce) → new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, new_primMulNat0(Succ(wx1246), wx1251), ce)
new_lookupWithDefaultFM0177(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0423(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0104(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM052(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM069(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0378(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx7230), fd) → new_lookupWithDefaultFM0406(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx7230, new_primMulNat0(Zero, wx63000), fd)
new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175600), Zero, fd) → new_lookupWithDefaultFM0409(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0448(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9400), hh) → new_lookupWithDefaultFM0467(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9400, new_primMulNat0(Zero, wx85800), hh)
new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Zero, hh) → new_lookupWithDefaultFM0487(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0106(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0146(wx622, Neg(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0378(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0251(wx4, wx31, wx32, wx33, wx34, wx5100, wx1024, ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM065(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3290), ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0219(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9120), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0112(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM03(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx234, h) → new_lookupWithDefaultFM0540(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM0517(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx19970, Zero, bbb) → new_lookupWithDefaultFM020(wx1542, wx1548, :%(Neg(Zero), Neg(Succ(wx1549))), bbb)
new_lookupWithDefaultFM0297(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx19910, Zero, cc) → new_lookupWithDefaultFM020(wx1228, wx1234, :%(Pos(Zero), Neg(Succ(wx1235))), cc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0246(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0146(wx622, Pos(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0376(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Succ(wx196400), hh) → new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116300, wx196400, hh)
new_lookupWithDefaultFM013(wx199, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11490), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Zero)), h)
new_lookupWithDefaultFM0375(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0429(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh) → new_lookupWithDefaultFM020(wx1429, wx1435, :%(Neg(Zero), Pos(Succ(wx1436))), gh)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0377(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0196(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM056(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0288(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0321(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM055(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0288(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx11620), hh) → new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11620, new_primMulNat0(Succ(wx85100), wx85800), hh)
new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15850, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM0528(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11450, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM0245(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0515(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0124(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5540), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM010(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25500)), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0222(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0271(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0270(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM058(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Zero, wx1221), ca)
new_lookupWithDefaultFM0491(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0490(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0133(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0108(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0285(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, Succ(wx19430), bh) → new_lookupWithDefaultFM0286(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh)
new_lookupWithDefaultFM0182(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11240), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0437(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0188(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0514(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0510(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM029(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Zero, eb) → new_lookupWithDefaultFM0356(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, new_primMulNat0(Succ(wx1317), wx1323), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM055(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0215(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8900), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM027(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10790), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, wx4040, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM0370(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, fb) → new_lookupWithDefaultFM0371(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, new_primMulNat0(Succ(wx1360), wx1365), fb)
new_lookupWithDefaultFM0172(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7430), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0358(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb) → new_lookupWithDefaultFM020(wx1316, wx1322, :%(Pos(Zero), Neg(Succ(wx1323))), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM051(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2890), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0111(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5150), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0431(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, hd) → new_lookupWithDefaultFM0432(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, new_primMulNat0(Succ(wx1456), wx1461), hd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM094(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0117(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5320), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Succ(wx91000)), hh) → new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx91000, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0120(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx198200), Zero, eb) → new_lookupWithDefaultFM0358(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb)
new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Zero, h) → new_lookupWithDefaultFM0547(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM031(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2120), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0235(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0224(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9290), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0314(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM04(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM019(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0192(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0233(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0501(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0446(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0137(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0(wx199, Pos(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Zero), Zero, h) → new_lookupWithDefaultFM07(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx198800), Succ(wx186500), gh) → new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx198800, wx186500, gh)
new_lookupWithDefaultFM0238(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9770), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0127(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5640), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Zero, h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0144(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0238(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0508(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0472(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(wx8580)), hh)
new_lookupWithDefaultFM0146(wx622, Neg(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0217(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM017(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM07(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM047(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0276(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0469(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0109(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0495(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0494(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0430(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, hd) → new_lookupWithDefaultFM0432(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, new_primMulNat0(Succ(wx1456), wx1461), hd)
new_lookupWithDefaultFM028(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10830), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), wx6320, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM057(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0136(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0177(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0456(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9430), hh) → new_lookupWithDefaultFM0485(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9430, new_primMulNat0(Zero, wx85800), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM089(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0281(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Zero, wx1212), bh)
new_lookupWithDefaultFM0261(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, bbe) → new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, new_primMulNat0(Succ(wx1568), wx1573), bbe)
new_lookupWithDefaultFM090(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0346(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(wx3950), wx396, wx397, wx398, wx399, wx400, wx401, Neg(wx4020), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(wx4020)), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM033(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0244(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9990), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0403(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx17550), fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM064(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0218(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0274(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, bd) → new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, new_primMulNat0(Succ(wx1184), wx1190), bd)
new_lookupWithDefaultFM0297(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Succ(Succ(wx201600)), cc) → new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx199100, wx201600, cc)
new_lookupWithDefaultFM0307(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0306(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0142(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx6060), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0173(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), wx4040, da)
new_lookupWithDefaultFM0267(wx1919, wx1920, wx1921, wx1922, wx1923, wx1924, wx1925, bbf) → new_lookupWithDefaultFM020(wx1919, wx1923, :%(Neg(Zero), Neg(Succ(wx1925))), bbf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0259(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, Succ(wx19350), bac) → new_lookupWithDefaultFM020(wx1497, wx1502, :%(Neg(Succ(wx1503)), Pos(Succ(wx1504))), bac)
new_lookupWithDefaultFM0192(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8070), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0111(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0352(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0466(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM0374(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6720), fd) → new_lookupWithDefaultFM0380(wx622, Succ(wx62300), wx624, wx625, wx626, wx627, wx628, wx629, Succ(wx63000), fd)
new_lookupWithDefaultFM0467(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Succ(Succ(wx187000)), hh) → new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94000, wx187000, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM040(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0394(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0286(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM020(wx1210, wx1216, :%(Pos(Zero), Neg(Succ(wx1217))), bh)
new_lookupWithDefaultFM0234(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0501(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0291(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, wx12780, wx1944, ca) → new_lookupWithDefaultFM020(wx1219, wx1225, :%(Pos(Zero), Pos(Succ(wx1226))), ca)
new_lookupWithDefaultFM080(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3760), ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0441(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), Zero, hh) → new_lookupWithDefaultFM0474(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11620, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM0247(wx1902, wx1903, wx1904, wx1905, wx1906, wx1907, wx1908, wx1909, bba) → new_lookupWithDefaultFM020(wx1902, wx1907, :%(Neg(Zero), Neg(Succ(wx1909))), bba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM073(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, ce) → new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, new_primMulNat0(Succ(wx1246), wx1251), ce)
new_lookupWithDefaultFM0363(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx19850), ed) → new_lookupWithDefaultFM020(wx1325, wx1331, :%(Pos(Zero), Pos(Succ(wx1332))), ed)
new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175600), Succ(wx72300), fd) → new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175600, wx72300, fd)
new_lookupWithDefaultFM0265(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10680), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0276(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, bg) → new_lookupWithDefaultFM0277(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, new_primMulNat0(Zero, wx1203), bg)
new_lookupWithDefaultFM0517(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Succ(Zero), bbb) → new_lookupWithDefaultFM0519(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, bbb)
new_lookupWithDefaultFM090(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4200), ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Zero), hh) → new_lookupWithDefaultFM0477(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM050(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0176(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11230), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0333(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(Succ(wx195000)), da) → new_lookupWithDefaultFM0336(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0118(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0359(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Succ(wx193800), h) → new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114500, wx193800, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0124(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0253(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0520(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0213(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8780), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0437(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0447(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0266(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx194800), Zero, da) → new_lookupWithDefaultFM0326(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0498(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Succ(Zero), baf) → new_lookupWithDefaultFM0500(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, baf)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164200), Zero, da) → new_lookupWithDefaultFM0345(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0119(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0409(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0190(wx1447, wx1448, wx1449, wx1450, wx1451, wx1452, wx1453, hb) → new_lookupWithDefaultFM020(wx1447, wx1451, :%(Neg(Zero), Pos(Succ(wx1453))), hb)
new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx198200), Succ(wx175000), eb) → new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, wx198200, wx175000, eb)
new_lookupWithDefaultFM0433(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, hf) → new_lookupWithDefaultFM0435(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, new_primMulNat0(Succ(wx1464), wx1469), hf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, Succ(wx19740), fh) → new_lookupWithDefaultFM020(wx1384, wx1389, :%(Neg(Succ(wx1390)), Neg(Succ(wx1391))), fh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0262(wx4, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0166(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM063(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx327, ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, Succ(wx12770), bh) → new_lookupWithDefaultFM0284(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, wx12770, new_primMulNat0(Succ(wx1211), wx1217), bh)
new_lookupWithDefaultFM0166(wx1402, wx1403, wx1404, wx1405, wx1406, wx1407, wx1408, wx1409, gc) → new_lookupWithDefaultFM020(wx1402, wx1406, :%(Neg(Succ(wx1408)), Neg(Succ(wx1409))), gc)
new_lookupWithDefaultFM0334(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx19510), da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM0155(wx1770, wx1771, wx1772, wx1773, wx1774, wx1775, wx1776, wx1777, fg) → new_lookupWithDefaultFM0411(wx1770, wx1771, wx1772, wx1773, wx1774, wx1775, wx1776, wx1777, fg)
new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Zero, h) → new_lookupWithDefaultFM0530(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0152(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6550), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Zero)), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM071(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0194(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0423(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh) → new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM0446(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9000), hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0159(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0413(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM086(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4050), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0165(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx7060), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0477(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0480(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45400), Zero, da) → new_lookupWithDefaultFM0328(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0379(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM0385(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM052(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0287(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0212(wx1875, wx1876, wx1877, wx1878, wx1879, wx1880, wx1881, wx1882, baa) → new_lookupWithDefaultFM020(wx1875, wx1879, :%(Neg(Succ(wx1881)), Pos(Succ(wx1882))), baa)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Succ(wx91000)), hh) → new_lookupWithDefaultFM0478(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0127(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, Zero, bah) → new_lookupWithDefaultFM0512(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Succ(wx1534), wx1540), bah)
new_lookupWithDefaultFM0188(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx7920), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0184(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0153(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6600), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0100(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0485(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Succ(Succ(wx187200)), hh) → new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94300, wx187200, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM094(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM059(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0146(wx622, Neg(wx6230), wx624, wx625, wx626, wx627, wx628, wx629, Neg(wx6300), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(wx6300)), fd)
new_lookupWithDefaultFM0512(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, Succ(wx19690), bah) → new_lookupWithDefaultFM0513(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah)
new_lookupWithDefaultFM0266(wx4, wx31, wx32, wx33, wx34, wx5100, wx1071, ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0109(wx1307, wx1308, wx1309, wx1310, wx1311, wx1312, wx1313, wx1314, dh) → new_lookupWithDefaultFM020(wx1307, wx1312, :%(Pos(Zero), Pos(Succ(wx1314))), dh)
new_lookupWithDefaultFM0263(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10560), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0388(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM029(wx1587, wx1588, wx1589, wx1590, wx1591, wx1592, wx1593, wx1594, bb) → new_lookupWithDefaultFM020(wx1587, wx1591, :%(Pos(Succ(wx1593)), Pos(Succ(wx1594))), bb)
new_lookupWithDefaultFM0217(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx11310), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0451(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0450(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM096(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0349(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM032(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2170), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0250(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0426(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx186500), Succ(Succ(wx198800)), gh) → new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx198800, wx186500, gh)
new_lookupWithDefaultFM0118(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5370), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Succ(Succ(wx197800)), h) → new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158200, wx197800, h)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx234, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0177(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7530), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0302(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, ce) → new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, new_primMulNat0(Succ(wx1246), wx1251), ce)
new_lookupWithDefaultFM0157(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0413(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0366(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, eh) → new_lookupWithDefaultFM0368(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, new_primMulNat0(Succ(wx1352), wx1357), eh)
new_lookupWithDefaultFM0435(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, Succ(wx19770), hf) → new_lookupWithDefaultFM020(wx1463, wx1468, :%(Neg(Zero), Pos(Succ(wx1469))), hf)
new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Succ(Zero), hh) → new_lookupWithDefaultFM0484(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0394(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primMulNat0(wx5000, wx30100), ba)
new_lookupWithDefaultFM0164(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx7010), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0160(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Zero, hh) → new_lookupWithDefaultFM0477(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0515(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, bbb) → new_lookupWithDefaultFM0516(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, new_primMulNat0(Zero, wx1544), bbb)
new_lookupWithDefaultFM039(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10940), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Zero, bbb) → new_lookupWithDefaultFM0519(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, bbb)
new_lookupWithDefaultFM0209(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8680), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM09(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), Zero, h) → new_lookupWithDefaultFM0535(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM0306(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, cf) → new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, new_primMulNat0(Succ(wx1254), wx1259), cf)
new_lookupWithDefaultFM030(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10870), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0180(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0367(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, eh) → new_lookupWithDefaultFM0368(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, new_primMulNat0(Succ(wx1352), wx1357), eh)
new_lookupWithDefaultFM0171(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7360), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0245(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx10040), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0448(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM050(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2820), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0253(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10260), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Succ(wx197800), h) → new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158200, wx197800, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0450(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9020), hh) → new_lookupWithDefaultFM0470(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM032(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0271(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM048(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx280, ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM098(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4610), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0303(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0302(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0178(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7600), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0513(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM020(wx1533, wx1539, :%(Neg(Zero), Pos(Succ(wx1540))), bah)
new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Zero, bg) → new_lookupWithDefaultFM0280(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, bg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0392(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0395(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx11570), fd) → new_lookupWithDefaultFM0387(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx11570, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM010(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM0543(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0(wx199, Pos(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Zero), Zero, h) → new_lookupWithDefaultFM05(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, Zero, bag) → new_lookupWithDefaultFM0505(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Succ(wx1525), wx1531), bag)
new_lookupWithDefaultFM0312(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0339(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Zero, wx40200), da)
new_lookupWithDefaultFM0459(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0462(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0288(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Zero, wx1221), ca)
new_lookupWithDefaultFM0313(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM083(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0333(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx115200), Succ(Succ(wx195000)), da) → new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx195000, wx115200, da)
new_lookupWithDefaultFM0295(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, cc) → new_lookupWithDefaultFM0296(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, new_primMulNat0(Zero, wx1230), cc)
new_lookupWithDefaultFM0547(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0183(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0234(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9690), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0342(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx49500), Succ(Succ(wx164200)), da) → new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164200, wx49500, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM026(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0161(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0490(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, bab) → new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, new_primMulNat0(Succ(wx1489), wx1495), bab)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0245(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0210(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0214(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0488(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(wx8510), wx852, wx853, wx854, wx855, wx856, wx857, Pos(wx8580), Succ(wx8600), hh) → new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM071(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3530), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0350(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, df) → new_lookupWithDefaultFM0351(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, new_primMulNat0(Succ(wx1290), wx1296), df)
new_lookupWithDefaultFM0235(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0507(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Zero)), fd)
new_lookupWithDefaultFM0539(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM012(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM091(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0330(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM026(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10730), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0171(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0461(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Succ(wx90800)), hh) → new_lookupWithDefaultFM0460(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0162(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx11200), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0237(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11360), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0270(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, bc) → new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, new_primMulNat0(Succ(wx1175), wx1181), bc)
new_lookupWithDefaultFM0516(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx19970), bbb) → new_lookupWithDefaultFM0517(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx19970, new_primMulNat0(Succ(wx1543), wx1549), bbb)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Succ(Succ(Succ(wx259000))), h) → new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2340, wx259000, h)
new_lookupWithDefaultFM0496(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, baf) → new_lookupWithDefaultFM0497(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, new_primMulNat0(Zero, wx1517), baf)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Succ(Succ(Succ(wx257000))), h) → new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2310, wx257000, h)
new_lookupWithDefaultFM085(wx394, Pos(wx3950), wx396, wx397, wx398, wx399, wx400, wx401, Pos(wx4020), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(wx4020)), da)
new_lookupWithDefaultFM0278(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Succ(Succ(wx201400)), bg) → new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx199000, wx201400, bg)
new_lookupWithDefaultFM0446(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0390(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM073(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0501(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Zero, wx1526), bag)
new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx198800), Zero, gh) → new_lookupWithDefaultFM0429(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM035(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0488(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, bab) → new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, new_primMulNat0(Succ(wx1489), wx1495), bab)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45400)), Zero, da) → new_lookupWithDefaultFM0328(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0(wx199, Pos(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM04(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM080(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0272(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, bd) → new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, new_primMulNat0(Succ(wx1184), wx1190), bd)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Zero, h) → new_lookupWithDefaultFM0543(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0355(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Zero, Succ(Succ(wx198200)), eb) → new_lookupWithDefaultFM0358(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb)
new_lookupWithDefaultFM0323(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(Succ(wx194800)), da) → new_lookupWithDefaultFM0326(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM099(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0376(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0403(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Zero, wx63000), fd)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Succ(wx40400), da) → new_lookupWithDefaultFM0319(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0422(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf) → new_lookupWithDefaultFM020(wx1420, wx1426, :%(Neg(Zero), Neg(Succ(wx1427))), gf)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45400), Succ(wx40400), da) → new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45400, wx40400, da)
new_lookupWithDefaultFM0283(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Zero, wx1212), bh)
new_lookupWithDefaultFM0313(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4480), da) → new_lookupWithDefaultFM0331(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0144(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx6180), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0456(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0449(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM044(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0531(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM08(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0362(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx175100), Succ(Succ(wx198400)), ed) → new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, wx198400, wx175100, ed)
new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175400), Zero, fd) → new_lookupWithDefaultFM0405(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, Succ(wx19310), bd) → new_lookupWithDefaultFM020(wx1183, wx1188, :%(Pos(Succ(wx1189)), Pos(Succ(wx1190))), bd)
new_lookupWithDefaultFM0130(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0366(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Zero, da) → new_lookupWithDefaultFM0330(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0278(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx19900, Zero, bg) → new_lookupWithDefaultFM020(wx1201, wx1207, :%(Pos(Zero), Pos(Succ(wx1208))), bg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM053(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM045(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2630), ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0233(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9620), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0157(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0159(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0194(wx4, wx31, wx32, wx33, wx34, wx5100, wx815, ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(wx63200), fd) → new_lookupWithDefaultFM0393(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM096(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4370), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM037(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2350), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0172(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0416(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0475(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(wx8580)), hh)
new_lookupWithDefaultFM0439(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0449(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0208(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Succ(wx202600), baf) → new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx199600, wx202600, baf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM036(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM04(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25300)), h) → new_lookupWithDefaultFM018(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, wx2010, wx25300, h)
new_lookupWithDefaultFM0146(wx622, Pos(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Zero)), fd)
new_lookupWithDefaultFM0137(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5960), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0261(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, Succ(wx9280), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(wx8580)), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM037(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM067(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0210(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8730), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68200), Succ(wx63200), fd) → new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68200, wx63200, fd)
new_lookupWithDefaultFM0254(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0520(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0151(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0451(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0169(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7330), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68200), Zero, fd) → new_lookupWithDefaultFM0392(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx11520), da) → new_lookupWithDefaultFM0333(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx11520, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM096(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, Zero, hh) → new_lookupWithDefaultFM0480(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM077(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3730), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0401(wx622, wx6230, wx624, wx625, wx626, wx627, wx628, wx629, wx6300, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(wx6300)), fd)
new_lookupWithDefaultFM0397(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(Succ(wx195800)), fd) → new_lookupWithDefaultFM0400(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68200)), Succ(wx63200), fd) → new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68200, wx63200, fd)
new_lookupWithDefaultFM0353(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb) → new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, new_primMulNat0(Zero, wx1318), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0260(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0395(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0125(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0106(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx4810), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM048(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM04(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, h) → new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0(wx199, Neg(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Pos(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM02(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Succ(wx196200), hh) → new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116200, wx196200, hh)
new_lookupWithDefaultFM04(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25300)), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM0406(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(Succ(wx175600)), fd) → new_lookupWithDefaultFM0409(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0226(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0426(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Zero, Succ(Succ(wx198800)), gh) → new_lookupWithDefaultFM0429(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh)
new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Succ(wx202800), bbb) → new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx199700, wx202800, bbb)
new_lookupWithDefaultFM0218(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0492(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0151(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0410(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0163(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6940), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0158(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0413(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0410(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1385), wx1391), fh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0264(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10630), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0510(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Zero, wx1535), bah)
new_lookupWithDefaultFM0256(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, bbd) → new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, new_primMulNat0(Succ(wx1560), wx1565), bbd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0176(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM072(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3580), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Neg(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Zero), Zero, h) → new_lookupWithDefaultFM011(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0174(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx198400), Zero, ed) → new_lookupWithDefaultFM0365(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed)
new_lookupWithDefaultFM0329(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(wx40400), da) → new_lookupWithDefaultFM0319(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0125(wx1334, wx1335, wx1336, wx1337, wx1338, wx1339, wx1340, wx1341, ee) → new_lookupWithDefaultFM020(wx1334, wx1339, :%(Pos(Zero), Neg(Succ(wx1341))), ee)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Succ(wx194000), h) → new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114800, wx194000, h)
new_lookupWithDefaultFM057(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3090), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0520(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, bbd) → new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, new_primMulNat0(Succ(wx1560), wx1565), bbd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0242(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx198400), Succ(wx175100), ed) → new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, wx198400, wx175100, ed)
new_lookupWithDefaultFM0314(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0343(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Zero, wx40200), da)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx234, Zero, h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM00(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx231, h) → new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx231, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM0310(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4440), da) → new_lookupWithDefaultFM0316(wx394, Succ(wx39500), wx396, wx397, wx398, wx399, wx400, wx401, Succ(wx40200), da)
new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx195000), Succ(wx115200), da) → new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx195000, wx115200, da)
new_lookupWithDefaultFM0239(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0508(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0387(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(Succ(wx195600)), fd) → new_lookupWithDefaultFM0390(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM054(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM027(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0208(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8610), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0209(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM059(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx11000), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM056(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3040), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Succ(wx259000), h) → new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2340, wx259000, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0121(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primMulNat0(Zero, wx5100), ba)
new_lookupWithDefaultFM0191(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx8000), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0141(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11160), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Zero), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(wx90800), hh) → new_lookupWithDefaultFM0460(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0457(wx850, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9440), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Zero)), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0190(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM035(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2190), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0243(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9920), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0216(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, bab) → new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, new_primMulNat0(Succ(wx1489), wx1495), bab)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(wx91000), hh) → new_lookupWithDefaultFM0478(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM04(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM021(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0351(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, Succ(wx19710), df) → new_lookupWithDefaultFM020(wx1289, wx1294, :%(Pos(Succ(wx1295)), Pos(Succ(wx1296))), df)
new_lookupWithDefaultFM0151(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6480), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0153(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0410(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM038(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM035(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0272(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM05(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11440), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Zero)), h)
new_lookupWithDefaultFM0467(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9400, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Zero)), da)
new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195800), Succ(wx115800), fd) → new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195800, wx115800, fd)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0330(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0193(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8120), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0232(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0101(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx11080), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Succ(wx63200), fd) → new_lookupWithDefaultFM0383(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0375(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM0213(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0488(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, Succ(wx15840), bah) → new_lookupWithDefaultFM0511(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, wx15840, new_primMulNat0(Succ(wx1534), wx1540), bah)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0243(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0259(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0524(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM047(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0264(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Zero, h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Succ(Succ(wx198000)), h) → new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158500, wx198000, h)
new_lookupWithDefaultFM0179(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7650), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0235(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9740), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Succ(wx201400), bg) → new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx199000, wx201400, bg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0172(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0253(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0533(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(wx2070)), h)
new_lookupWithDefaultFM0420(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx19870), gf) → new_lookupWithDefaultFM020(wx1420, wx1426, :%(Neg(Zero), Neg(Succ(wx1427))), gf)
new_lookupWithDefaultFM0215(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0491(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0503(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Zero, wx1526), bag)
new_lookupWithDefaultFM0113(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx523, ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0485(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9430, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0380(wx622, wx6230, wx624, wx625, wx626, wx627, wx628, wx629, wx6300, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(wx6300)), fd)
new_lookupWithDefaultFM0254(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10330), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Succ(wx198000), h) → new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158500, wx198000, h)
new_lookupWithDefaultFM0376(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx7200), fd) → new_lookupWithDefaultFM0402(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx7200, new_primMulNat0(Zero, wx63000), fd)
new_lookupWithDefaultFM0377(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6760), fd) → new_lookupWithDefaultFM0395(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0158(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6840), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0218(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8930), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0120(wx1701, wx1702, wx1703, wx1704, wx1705, wx1706, wx1707, wx1708, ec) → new_lookupWithDefaultFM0360(wx1701, wx1702, wx1703, wx1704, wx1705, wx1706, wx1707, wx1708, ec)
new_lookupWithDefaultFM0132(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5840), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0339(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx16410), da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM0342(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(Succ(wx164200)), da) → new_lookupWithDefaultFM0345(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM081(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3830), ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0246(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx1007, ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0201(wx1849, wx1850, wx1851, wx1852, wx1853, wx1854, wx1855, he) → new_lookupWithDefaultFM0434(wx1849, wx1850, wx1851, wx1852, wx1853, wx1854, wx1855, he)
new_lookupWithDefaultFM036(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0272(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM086(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0189(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0196(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx11270), ba) → new_lookupWithDefaultFM020(wx4, wx34, :%(Neg(Zero), Neg(Succ(wx5100))), ba)
new_lookupWithDefaultFM0460(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0229(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(wx63200), fd) → new_lookupWithDefaultFM0383(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM052(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2940), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Neg(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM012(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM066(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3360), ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Zero, h) → new_lookupWithDefaultFM025(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0511(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, wx15840, wx1968, bah) → new_lookupWithDefaultFM020(wx1533, wx1539, :%(Neg(Zero), Pos(Succ(wx1540))), bah)
new_lookupWithDefaultFM0102(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4660), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0535(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx19280), h) → new_lookupWithDefaultFM0536(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0320(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0173(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0416(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0153(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM02(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, wx233, h) → new_lookupWithDefaultFM0534(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h)
new_lookupWithDefaultFM0200(wx4, wx31, wx32, wx33, wx34, wx5100, wx832, ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0524(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, bbe) → new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, new_primMulNat0(Succ(wx1568), wx1573), bbe)
new_lookupWithDefaultFM046(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2700), ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0150(wx1375, wx1376, wx1377, wx1378, wx1379, wx1380, wx1381, wx1382, ff) → new_lookupWithDefaultFM020(wx1375, wx1379, :%(Neg(Succ(wx1381)), Pos(Succ(wx1382))), ff)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0313(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM0379(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6780), fd) → new_lookupWithDefaultFM0401(wx622, Succ(wx62300), wx624, wx625, wx626, wx627, wx628, wx629, Succ(wx63000), fd)
new_lookupWithDefaultFM0527(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0526(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM076(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3680), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0243(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0515(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0315(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM0116(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5250), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0255(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM077(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0297(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Succ(Zero), cc) → new_lookupWithDefaultFM0299(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, cc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM089(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0179(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0423(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0504(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, wx15830, wx1966, bag) → new_lookupWithDefaultFM020(wx1524, wx1530, :%(Neg(Zero), Neg(Succ(wx1531))), bag)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0258(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0526(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, bbe) → new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, new_primMulNat0(Succ(wx1568), wx1573), bbe)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0206(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0241(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0474(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx18680), hh) → new_lookupWithDefaultFM0475(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0147(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6330), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx18640), gf) → new_lookupWithDefaultFM0419(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx18640, new_primMulNat0(Succ(wx1421), wx1427), gf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM098(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0536(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(wx2070)), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0146(wx622, Pos(wx6230), wx624, wx625, wx626, wx627, wx628, wx629, Pos(wx6300), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(wx6300)), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0131(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164200), Succ(wx49500), da) → new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164200, wx49500, da)
new_lookupWithDefaultFM0280(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, bg) → new_lookupWithDefaultFM020(wx1201, wx1207, :%(Pos(Zero), Pos(Succ(wx1208))), bg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM028(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0154(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx663, ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0108(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5050), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM061(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3190), ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, Succ(wx19370), bbe) → new_lookupWithDefaultFM020(wx1567, wx1572, :%(Neg(Zero), Pos(Succ(wx1573))), bbe)
new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx11510), da) → new_lookupWithDefaultFM0323(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx11510, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM010(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25500)), h) → new_lookupWithDefaultFM0541(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, wx2010, wx25500, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0169(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0(wx199, Neg(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Zero), Zero, h) → new_lookupWithDefaultFM013(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0275(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0274(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM057(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0294(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0323(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx115100), Succ(Succ(wx194800)), da) → new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx194800, wx115100, da)
new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, Succ(wx12780), ca) → new_lookupWithDefaultFM0291(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, wx12780, new_primMulNat0(Succ(wx1220), wx1226), ca)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0145(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0248(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0473(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0522(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, bbd) → new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, new_primMulNat0(Succ(wx1560), wx1565), bbd)
new_lookupWithDefaultFM0146(wx622, Neg(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Zero)), fd)
new_lookupWithDefaultFM0362(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Zero, Succ(Succ(wx198400)), ed) → new_lookupWithDefaultFM0365(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0239(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0105(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0207(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30100), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0369(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, fb) → new_lookupWithDefaultFM0371(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, new_primMulNat0(Succ(wx1360), wx1365), fb)
new_lookupWithDefaultFM0365(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed) → new_lookupWithDefaultFM020(wx1325, wx1331, :%(Pos(Zero), Pos(Succ(wx1332))), ed)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Succ(wx259000))), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0214(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(wx90800), hh) → new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx90800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM097(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0349(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, df) → new_lookupWithDefaultFM0351(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, new_primMulNat0(Succ(wx1290), wx1296), df)
new_lookupWithDefaultFM0424(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh) → new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, wx4040, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM046(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0276(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM094(wx1656, wx1657, wx1658, wx1659, wx1660, wx1661, wx1662, wx1663, dc) → new_lookupWithDefaultFM0347(wx1656, wx1657, wx1658, wx1659, wx1660, wx1661, wx1662, wx1663, dc)
new_lookupWithDefaultFM093(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx435, ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0220(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0495(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0100(wx1665, wx1666, wx1667, wx1668, wx1669, wx1670, wx1671, wx1672, de) → new_lookupWithDefaultFM0350(wx1665, wx1666, wx1667, wx1668, wx1669, wx1670, wx1671, wx1672, de)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM090(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Pos(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Pos(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM00(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM0348(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, Succ(wx19700), dd) → new_lookupWithDefaultFM020(wx1280, wx1285, :%(Pos(Succ(wx1286)), Neg(Succ(wx1287))), dd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0219(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0240(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9890), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0319(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0148(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0126(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx5570), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM058(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0413(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, gb) → new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, new_primMulNat0(Succ(wx1394), wx1400), gb)
new_lookupWithDefaultFM0199(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0433(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0228(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9450), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(wx259000), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164000), Zero, da) → new_lookupWithDefaultFM0341(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM070(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3460), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, Succ(wx19320), ce) → new_lookupWithDefaultFM020(wx1245, wx1250, :%(Pos(Zero), Neg(Succ(wx1251))), ce)
new_lookupWithDefaultFM0377(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0240(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0514(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx198600), Succ(wx186400), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx198600, wx186400, gf)
new_lookupWithDefaultFM0219(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0492(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0116(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0359(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0419(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx186400), Succ(Succ(wx198600)), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx198600, wx186400, gf)
new_lookupWithDefaultFM0114(wx1692, wx1693, wx1694, wx1695, wx1696, wx1697, wx1698, wx1699, ea) → new_lookupWithDefaultFM0353(wx1692, wx1693, wx1694, wx1695, wx1696, wx1697, wx1698, wx1699, ea)
new_lookupWithDefaultFM077(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0307(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Zero, hh) → new_lookupWithDefaultFM0469(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM085(wx394, Pos(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Zero)), da)
new_lookupWithDefaultFM0199(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8290), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0398(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM012(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx11480), h) → new_lookupWithDefaultFM0548(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11480, new_primMulNat0(Zero, wx20700), h)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0311(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0128(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, wx6320, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Succ(Succ(wx196200)), hh) → new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116200, wx196200, hh)
new_lookupWithDefaultFM0427(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx19890), gh) → new_lookupWithDefaultFM020(wx1429, wx1435, :%(Neg(Zero), Pos(Succ(wx1436))), gh)
new_lookupWithDefaultFM0405(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM058(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM0249(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10160), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM03(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx234, h) → new_lookupWithDefaultFM0539(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM015(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM05(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0497(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx19960), baf) → new_lookupWithDefaultFM0498(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx19960, new_primMulNat0(Succ(wx1516), wx1522), baf)
new_lookupWithDefaultFM0359(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed) → new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, new_primMulNat0(Zero, wx1327), ed)
new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, Succ(wx9270), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(wx8580)), hh)
new_lookupWithDefaultFM0284(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, wx12770, wx1942, bh) → new_lookupWithDefaultFM020(wx1210, wx1216, :%(Pos(Zero), Neg(Succ(wx1217))), bh)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45400)), Succ(wx40400), da) → new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45400, wx40400, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0154(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0168(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7280), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0239(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9840), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM097(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4560), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, Succ(wx19360), bbd) → new_lookupWithDefaultFM020(wx1559, wx1564, :%(Neg(Zero), Neg(Succ(wx1565))), bbd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM068(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0130(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 22 SCCs with 164 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

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

new_lookupWithDefaultFM068(wx4, wx31, wx32, wx33, wx34, wx5100, wx344, ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0120(wx1701, wx1702, wx1703, wx1704, wx1705, wx1706, wx1707, wx1708, ec) → new_lookupWithDefaultFM0360(wx1701, wx1702, wx1703, wx1704, wx1705, wx1706, wx1707, wx1708, ec)
new_lookupWithDefaultFM058(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Zero, wx1221), ca)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0108(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0304(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, cf) → new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, new_primMulNat0(Succ(wx1254), wx1259), cf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM049(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0127(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM047(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2770), ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM075(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3610), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM049(wx1605, wx1606, wx1607, wx1608, wx1609, wx1610, wx1611, wx1612, bf) → new_lookupWithDefaultFM020(wx1605, wx1610, :%(Pos(Zero), Pos(Succ(wx1612))), bf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM076(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM055(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0370(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, fb) → new_lookupWithDefaultFM0371(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, new_primMulNat0(Succ(wx1360), wx1365), fb)
new_lookupWithDefaultFM078(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, cf) → new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, new_primMulNat0(Succ(wx1254), wx1259), cf)
new_lookupWithDefaultFM0109(wx1307, wx1308, wx1309, wx1310, wx1311, wx1312, wx1313, wx1314, dh) → new_lookupWithDefaultFM020(wx1307, wx1312, :%(Pos(Zero), Pos(Succ(wx1314))), dh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM066(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3360), ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM075(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0304(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0129(wx1343, wx1344, wx1345, wx1346, wx1347, wx1348, wx1349, ef) → new_lookupWithDefaultFM020(wx1343, wx1347, :%(Pos(Zero), Pos(Succ(wx1349))), ef)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0117(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0359(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM045(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2630), ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0126(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM046(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2700), ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0140(wx1735, wx1736, wx1737, wx1738, wx1739, wx1740, wx1741, fa) → new_lookupWithDefaultFM0370(wx1735, wx1736, wx1737, wx1738, wx1739, wx1740, wx1741, fa)
new_lookupWithDefaultFM0117(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5320), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0118(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5370), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0371(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, Succ(wx19730), fb) → new_lookupWithDefaultFM020(wx1359, wx1364, :%(Pos(Zero), Pos(Succ(wx1365))), fb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0120(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0294(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0290(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM076(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3680), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0116(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5250), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0137(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5960), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0137(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM067(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM077(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, Succ(wx19330), cf) → new_lookupWithDefaultFM020(wx1253, wx1258, :%(Pos(Zero), Pos(Succ(wx1259))), cf)
new_lookupWithDefaultFM0293(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM020(wx1219, wx1225, :%(Pos(Zero), Pos(Succ(wx1226))), ca)
new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Zero, ed) → new_lookupWithDefaultFM0363(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, new_primMulNat0(Succ(wx1326), wx1332), ed)
new_lookupWithDefaultFM0127(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5640), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM077(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3730), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0116(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0306(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, cf) → new_lookupWithDefaultFM0305(wx1253, wx1254, wx1255, wx1256, wx1257, wx1258, wx1259, new_primMulNat0(Succ(wx1254), wx1259), cf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0139(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0109(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0106(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx4810), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM048(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM057(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM066(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM048(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx280, ba) → new_lookupWithDefaultFM049(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0136(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0108(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5050), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0119(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx540, ba) → new_lookupWithDefaultFM0120(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0138(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx6010), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM057(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0294(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0136(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0369(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM078(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0128(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5690), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM065(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0107(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5000), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM057(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3090), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0288(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Zero, wx1221), ca)
new_lookupWithDefaultFM0307(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0306(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0369(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, fb) → new_lookupWithDefaultFM0371(wx1359, wx1360, wx1361, wx1362, wx1363, wx1364, wx1365, new_primMulNat0(Succ(wx1360), wx1365), fb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0120(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0140(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM069(wx1623, wx1624, wx1625, wx1626, wx1627, wx1628, wx1629, cd) → new_lookupWithDefaultFM020(wx1623, wx1627, :%(Pos(Zero), Pos(Succ(wx1629))), cd)
new_lookupWithDefaultFM0290(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca) → new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Zero, wx1221), ca)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0117(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0107(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0289(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, Zero, ca) → new_lookupWithDefaultFM0292(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, new_primMulNat0(Succ(wx1220), wx1226), ca)
new_lookupWithDefaultFM056(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3040), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0118(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM078(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0136(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx5890), ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0363(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx19850), ed) → new_lookupWithDefaultFM020(wx1325, wx1331, :%(Pos(Zero), Pos(Succ(wx1332))), ed)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM045(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM058(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0126(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx5570), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0118(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0359(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0137(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0369(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM056(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0129(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0292(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, Succ(wx19450), ca) → new_lookupWithDefaultFM0293(wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx1226, ca)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM049(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0138(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0369(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0116(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0359(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM047(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM077(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0307(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM055(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2970), ba) → new_lookupWithDefaultFM058(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0119(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0138(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM069(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM067(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3410), ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0106(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM078(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0128(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0109(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM075(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM065(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3290), ba) → new_lookupWithDefaultFM069(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM076(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0304(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM058(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0360(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed) → new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, new_primMulNat0(Zero, wx1327), ed)
new_lookupWithDefaultFM0359(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, ed) → new_lookupWithDefaultFM0361(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, new_primMulNat0(Zero, wx1327), ed)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM069(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0139(wx4, wx31, wx32, wx33, wx34, wx5100, wx604, ba) → new_lookupWithDefaultFM0140(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM046(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM056(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0288(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM055(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0288(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0129(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM068(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx198400), Succ(wx175100), ed) → new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, wx198400, wx175100, ed)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx198400), Succ(wx175100), ed) → new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, wx198400, wx175100, ed)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, Succ(wx198400), Succ(wx175100), ed) → new_lookupWithDefaultFM0364(wx1325, wx1326, wx1327, wx1328, wx1329, wx1330, wx1331, wx1332, wx198400, wx175100, ed)

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
                          ↳ 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_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Succ(wx201400), bg) → new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx199000, wx201400, bg)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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
                          ↳ 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_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Succ(wx201400), bg) → new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx199000, wx201400, bg)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ 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_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, Succ(wx199000), Succ(wx201400), bg) → new_lookupWithDefaultFM0279(wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx1208, wx199000, wx201400, bg)

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
                          ↳ 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_lookupWithDefaultFM064(wx1614, wx1615, wx1616, wx1617, wx1618, wx1619, wx1620, wx1621, cb) → new_lookupWithDefaultFM020(wx1614, wx1619, :%(Pos(Zero), Neg(Succ(wx1621))), cb)
new_lookupWithDefaultFM0132(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5840), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0112(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5200), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM062(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3240), ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0133(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM081(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3830), ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0285(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, Succ(wx19430), bh) → new_lookupWithDefaultFM0286(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh)
new_lookupWithDefaultFM052(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0287(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM073(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0283(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Zero, wx1212), bh)
new_lookupWithDefaultFM0144(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx6180), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Zero, eb) → new_lookupWithDefaultFM0356(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, new_primMulNat0(Succ(wx1317), wx1323), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM051(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM052(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2940), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0130(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0366(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM053(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0114(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0113(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0123(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM050(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0281(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0142(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM051(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2890), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0111(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5150), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0143(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx6130), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0122(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5420), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0287(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0283(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0131(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx5790), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0368(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, Succ(wx19720), eh) → new_lookupWithDefaultFM020(wx1351, wx1356, :%(Pos(Zero), Neg(Succ(wx1357))), eh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM072(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0303(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM082(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0302(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, ce) → new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, new_primMulNat0(Succ(wx1246), wx1251), ce)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM063(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0366(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, eh) → new_lookupWithDefaultFM0368(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, new_primMulNat0(Succ(wx1352), wx1357), eh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0110(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM051(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0281(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0144(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM061(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0353(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb) → new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, new_primMulNat0(Zero, wx1318), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0143(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0123(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5490), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0125(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0367(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, eh) → new_lookupWithDefaultFM0368(wx1351, wx1352, wx1353, wx1354, wx1355, wx1356, wx1357, new_primMulNat0(Succ(wx1352), wx1357), eh)
new_lookupWithDefaultFM082(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3880), ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM053(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Zero, wx1212), bh)
new_lookupWithDefaultFM050(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx2820), ba) → new_lookupWithDefaultFM053(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0356(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx19830), eb) → new_lookupWithDefaultFM020(wx1316, wx1322, :%(Pos(Zero), Neg(Succ(wx1323))), eb)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0131(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0281(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Zero, wx1212), bh)
new_lookupWithDefaultFM0110(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0352(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM061(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3190), ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM070(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0300(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0132(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0366(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0133(wx4, wx31, wx32, wx33, wx34, wx5100, wx587, ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0303(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0302(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM064(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0145(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM071(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0300(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM072(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3580), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM053(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0125(wx1334, wx1335, wx1336, wx1337, wx1338, wx1339, wx1340, wx1341, ee) → new_lookupWithDefaultFM020(wx1334, wx1339, :%(Pos(Zero), Neg(Succ(wx1341))), ee)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM064(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM060(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM083(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0142(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx6060), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0145(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0112(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0352(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM084(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0111(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0352(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0352(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, eb) → new_lookupWithDefaultFM0354(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, new_primMulNat0(Zero, wx1318), eb)
new_lookupWithDefaultFM0286(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, bh) → new_lookupWithDefaultFM020(wx1210, wx1216, :%(Pos(Zero), Neg(Succ(wx1217))), bh)
new_lookupWithDefaultFM083(wx4, wx31, wx32, wx33, wx34, wx5100, wx391, ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM080(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3760), ba) → new_lookupWithDefaultFM084(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM062(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM073(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, ce) → new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, new_primMulNat0(Succ(wx1246), wx1251), ce)
new_lookupWithDefaultFM071(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx3530), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM050(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0131(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0366(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM084(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM072(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0134(wx1727, wx1728, wx1729, wx1730, wx1731, wx1732, wx1733, eg) → new_lookupWithDefaultFM0367(wx1727, wx1728, wx1729, wx1730, wx1731, wx1732, wx1733, eg)
new_lookupWithDefaultFM070(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx3460), ba) → new_lookupWithDefaultFM073(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0124(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, Succ(wx19320), ce) → new_lookupWithDefaultFM020(wx1245, wx1250, :%(Pos(Zero), Neg(Succ(wx1251))), ce)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0111(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0145(wx1367, wx1368, wx1369, wx1370, wx1371, wx1372, wx1373, fc) → new_lookupWithDefaultFM020(wx1367, wx1371, :%(Pos(Zero), Neg(Succ(wx1373))), fc)
new_lookupWithDefaultFM0282(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, Zero, bh) → new_lookupWithDefaultFM0285(wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx1217, new_primMulNat0(Succ(wx1211), wx1217), bh)
new_lookupWithDefaultFM0300(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, ce) → new_lookupWithDefaultFM0301(wx1245, wx1246, wx1247, wx1248, wx1249, wx1250, wx1251, new_primMulNat0(Succ(wx1246), wx1251), ce)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM070(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0122(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0114(wx1692, wx1693, wx1694, wx1695, wx1696, wx1697, wx1698, wx1699, ea) → new_lookupWithDefaultFM0353(wx1692, wx1693, wx1694, wx1695, wx1696, wx1697, wx1698, wx1699, ea)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM052(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0130(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx5720), ba) → new_lookupWithDefaultFM0134(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM060(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx3120), ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM063(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx327, ba) → new_lookupWithDefaultFM064(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0112(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM073(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0113(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx523, ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0132(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0134(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM084(wx1631, wx1632, wx1633, wx1634, wx1635, wx1636, wx1637, cg) → new_lookupWithDefaultFM020(wx1631, wx1635, :%(Pos(Zero), Neg(Succ(wx1637))), cg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM081(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM080(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM071(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0110(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5080), ba) → new_lookupWithDefaultFM0114(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0130(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0124(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx5540), ba) → new_lookupWithDefaultFM0125(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx198200), Succ(wx175000), eb) → new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, wx198200, wx175000, eb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx198200), Succ(wx175000), eb) → new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, wx198200, wx175000, eb)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, Succ(wx198200), Succ(wx175000), eb) → new_lookupWithDefaultFM0357(wx1316, wx1317, wx1318, wx1319, wx1320, wx1321, wx1322, wx1323, wx198200, wx175000, eb)

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

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

new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Succ(wx201600), cc) → new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx199100, wx201600, cc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Succ(wx201600), cc) → new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx199100, wx201600, cc)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, Succ(wx199100), Succ(wx201600), cc) → new_lookupWithDefaultFM0298(wx1228, wx1229, wx1230, wx1231, wx1232, wx1233, wx1234, wx1235, wx199100, wx201600, cc)

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

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

new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0416(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf) → new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, new_primMulNat0(Zero, wx1422), gf)
new_lookupWithDefaultFM0175(wx1806, wx1807, wx1808, wx1809, wx1810, wx1811, wx1812, wx1813, ge) → new_lookupWithDefaultFM0417(wx1806, wx1807, wx1808, wx1809, wx1810, wx1811, wx1812, wx1813, ge)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0191(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0246(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx1007, ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0244(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0184(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0184(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7770), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0266(wx4, wx31, wx32, wx33, wx34, wx5100, wx1071, ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0263(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10560), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0172(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7430), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0173(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0416(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0233(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9620), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0171(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0416(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0194(wx4, wx31, wx32, wx33, wx34, wx5100, wx815, ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0431(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, hd) → new_lookupWithDefaultFM0432(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, new_primMulNat0(Succ(wx1456), wx1461), hd)
new_lookupWithDefaultFM0172(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0416(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0206(wx1471, wx1472, wx1473, wx1474, wx1475, wx1476, wx1477, hg) → new_lookupWithDefaultFM020(wx1471, wx1475, :%(Neg(Zero), Neg(Succ(wx1477))), hg)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0235(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0263(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0256(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0192(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0233(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0501(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0204(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8410), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0255(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0254(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0520(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0523(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0522(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0206(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0245(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx10040), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0171(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7360), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0173(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7480), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0430(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, hd) → new_lookupWithDefaultFM0432(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, new_primMulNat0(Succ(wx1456), wx1461), hd)
new_lookupWithDefaultFM0505(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, Succ(wx19670), bag) → new_lookupWithDefaultFM0506(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag)
new_lookupWithDefaultFM0507(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0503(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0253(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10260), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0265(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0255(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0523(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0244(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9990), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0205(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0254(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0264(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10630), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0256(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, bbd) → new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, new_primMulNat0(Succ(wx1560), wx1565), bbd)
new_lookupWithDefaultFM0185(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7820), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0195(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0267(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0185(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0175(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0174(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, Zero, bag) → new_lookupWithDefaultFM0505(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Succ(wx1525), wx1531), bag)
new_lookupWithDefaultFM0522(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, bbd) → new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, new_primMulNat0(Succ(wx1560), wx1565), bbd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0520(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, bbd) → new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, new_primMulNat0(Succ(wx1560), wx1565), bbd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0173(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0234(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9690), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0183(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0247(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Zero, gf) → new_lookupWithDefaultFM0420(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, new_primMulNat0(Succ(wx1421), wx1427), gf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0204(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0267(wx1919, wx1920, wx1921, wx1922, wx1923, wx1924, wx1925, bbf) → new_lookupWithDefaultFM020(wx1919, wx1923, :%(Neg(Zero), Neg(Succ(wx1925))), bbf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0174(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx751, ba) → new_lookupWithDefaultFM0175(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0191(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0430(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0432(wx1455, wx1456, wx1457, wx1458, wx1459, wx1460, wx1461, Succ(wx19760), hd) → new_lookupWithDefaultFM020(wx1455, wx1460, :%(Neg(Zero), Neg(Succ(wx1461))), hd)
new_lookupWithDefaultFM0192(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8070), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0183(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7700), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0245(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0233(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0191(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx8000), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0234(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0501(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0243(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9920), ba) → new_lookupWithDefaultFM0247(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0247(wx1902, wx1903, wx1904, wx1905, wx1906, wx1907, wx1908, wx1909, bba) → new_lookupWithDefaultFM020(wx1902, wx1907, :%(Neg(Zero), Neg(Succ(wx1909))), bba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0203(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0265(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10680), ba) → new_lookupWithDefaultFM0267(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0192(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0430(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0175(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0235(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0507(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0193(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0430(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0193(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8120), ba) → new_lookupWithDefaultFM0195(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0255(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10380), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0236(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Zero, wx1526), bag)
new_lookupWithDefaultFM0253(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0520(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0266(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0171(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0243(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0234(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0506(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM020(wx1524, wx1530, :%(Neg(Zero), Neg(Succ(wx1531))), bag)
new_lookupWithDefaultFM0203(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx8340), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0264(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0236(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0205(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8460), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0186(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0193(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0235(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9740), ba) → new_lookupWithDefaultFM0236(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0172(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0253(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0420(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx19870), gf) → new_lookupWithDefaultFM020(wx1420, wx1426, :%(Neg(Zero), Neg(Succ(wx1427))), gf)
new_lookupWithDefaultFM0503(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Zero, wx1526), bag)
new_lookupWithDefaultFM0501(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, bag) → new_lookupWithDefaultFM0502(wx1524, wx1525, wx1526, wx1527, wx1528, wx1529, wx1530, wx1531, new_primMulNat0(Zero, wx1526), bag)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0246(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0186(wx1438, wx1439, wx1440, wx1441, wx1442, wx1443, wx1444, wx1445, ha) → new_lookupWithDefaultFM020(wx1438, wx1443, :%(Neg(Zero), Neg(Succ(wx1445))), ha)
new_lookupWithDefaultFM0195(wx1841, wx1842, wx1843, wx1844, wx1845, wx1846, wx1847, hc) → new_lookupWithDefaultFM0431(wx1841, wx1842, wx1843, wx1844, wx1845, wx1846, wx1847, hc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0186(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0254(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10330), ba) → new_lookupWithDefaultFM0256(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0521(wx1559, wx1560, wx1561, wx1562, wx1563, wx1564, wx1565, Succ(wx19360), bbd) → new_lookupWithDefaultFM020(wx1559, wx1564, :%(Neg(Zero), Neg(Succ(wx1565))), bbd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0194(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0417(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf) → new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, new_primMulNat0(Zero, wx1422), gf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0206(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx198600), Succ(wx186400), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx198600, wx186400, gf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx198600), Succ(wx186400), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx198600, wx186400, gf)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx198600), Succ(wx186400), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx198600, wx186400, gf)

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

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

new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Succ(wx202800), bbb) → new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx199700, wx202800, bbb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Succ(wx202800), bbb) → new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx199700, wx202800, bbb)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, Succ(wx199700), Succ(wx202800), bbb) → new_lookupWithDefaultFM0518(wx1542, wx1543, wx1544, wx1545, wx1546, wx1547, wx1548, wx1549, wx199700, wx202800, bbb)

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
                          ↳ 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_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0249(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0201(wx1849, wx1850, wx1851, wx1852, wx1853, wx1854, wx1855, he) → new_lookupWithDefaultFM0434(wx1849, wx1850, wx1851, wx1852, wx1853, wx1854, wx1855, he)
new_lookupWithDefaultFM0250(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10210), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0189(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0229(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9520), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, Zero, bah) → new_lookupWithDefaultFM0512(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Succ(wx1534), wx1540), bah)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0188(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0188(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx7920), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0514(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0510(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0229(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0170(wx1411, wx1412, wx1413, wx1414, wx1415, wx1416, wx1417, wx1418, gd) → new_lookupWithDefaultFM020(wx1411, wx1416, :%(Neg(Zero), Pos(Succ(wx1418))), gd)
new_lookupWithDefaultFM0512(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, Succ(wx19690), bah) → new_lookupWithDefaultFM0513(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah)
new_lookupWithDefaultFM0258(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0524(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0197(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx8170), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0230(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0252(wx1911, wx1912, wx1913, wx1914, wx1915, wx1916, wx1917, bbc) → new_lookupWithDefaultFM020(wx1911, wx1915, :%(Neg(Zero), Pos(Succ(wx1917))), bbc)
new_lookupWithDefaultFM0258(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10410), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0199(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0251(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0200(wx4, wx31, wx32, wx33, wx34, wx5100, wx832, ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0200(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0524(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, bbe) → new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, new_primMulNat0(Succ(wx1568), wx1573), bbe)
new_lookupWithDefaultFM0198(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0433(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0250(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0527(wx4, wx31, wx32, wx33, wx34, wx5100, ba) → new_lookupWithDefaultFM0526(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0177(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7530), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0231(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx960, ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0261(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0435(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, Succ(wx19770), hf) → new_lookupWithDefaultFM020(wx1463, wx1468, :%(Neg(Zero), Pos(Succ(wx1469))), hf)
new_lookupWithDefaultFM0169(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7330), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0238(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9770), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0179(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0423(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0238(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0508(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0258(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0526(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, bbe) → new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, new_primMulNat0(Succ(wx1568), wx1573), bbe)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0241(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0180(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0260(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0231(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0170(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0177(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0261(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, bbe) → new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, new_primMulNat0(Succ(wx1568), wx1573), bbe)
new_lookupWithDefaultFM0525(wx1567, wx1568, wx1569, wx1570, wx1571, wx1572, wx1573, Succ(wx19370), bbe) → new_lookupWithDefaultFM020(wx1567, wx1572, :%(Neg(Zero), Pos(Succ(wx1573))), bbe)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0181(wx1815, wx1816, wx1817, wx1818, wx1819, wx1820, wx1821, wx1822, gg) → new_lookupWithDefaultFM0424(wx1815, wx1816, wx1817, wx1818, wx1819, wx1820, wx1821, wx1822, gg)
new_lookupWithDefaultFM0178(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0423(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0434(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, hf) → new_lookupWithDefaultFM0435(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, new_primMulNat0(Succ(wx1464), wx1469), hf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0169(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0178(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7600), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0510(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Zero, wx1535), bah)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0240(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0513(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM020(wx1533, wx1539, :%(Neg(Zero), Pos(Succ(wx1540))), bah)
new_lookupWithDefaultFM0230(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9570), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0189(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx7970), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0167(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7090), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0198(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8240), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0248(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0187(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx7850), ba) → new_lookupWithDefaultFM0190(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0239(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0252(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0259(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10480), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0260(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0527(wx4, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0259(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0260(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10530), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0239(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0508(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0424(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh) → new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0178(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0167(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0241(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Zero, wx1535), bah)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0190(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Zero), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0240(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9890), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0261(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0197(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0199(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0433(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0508(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, bah) → new_lookupWithDefaultFM0509(wx1533, wx1534, wx1535, wx1536, wx1537, wx1538, wx1539, wx1540, new_primMulNat0(Zero, wx1535), bah)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0228(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9450), ba) → new_lookupWithDefaultFM0232(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0197(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0433(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0240(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0514(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0232(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0201(wx4, Zero, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Zero, gh) → new_lookupWithDefaultFM0427(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, new_primMulNat0(Succ(wx1430), wx1436), gh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0179(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0180(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, wx768, ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Zero)), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0232(wx1893, wx1894, wx1895, wx1896, wx1897, wx1898, wx1899, wx1900, bae) → new_lookupWithDefaultFM020(wx1893, wx1898, :%(Neg(Zero), Pos(Succ(wx1900))), bae)
new_lookupWithDefaultFM0177(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0423(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0259(wx4, wx31, wx32, wx33, wx34, wx5100, Zero, ba) → new_lookupWithDefaultFM0524(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0181(wx4, Zero, wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0190(wx1447, wx1448, wx1449, wx1450, wx1451, wx1452, wx1453, hb) → new_lookupWithDefaultFM020(wx1447, wx1451, :%(Neg(Zero), Pos(Succ(wx1453))), hb)
new_lookupWithDefaultFM0199(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx8290), ba) → new_lookupWithDefaultFM0201(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0179(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7650), ba) → new_lookupWithDefaultFM0181(wx4, Succ(Succ(Succ(Zero))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0433(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, hf) → new_lookupWithDefaultFM0435(wx1463, wx1464, wx1465, wx1466, wx1467, wx1468, wx1469, new_primMulNat0(Succ(wx1464), wx1469), hf)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0238(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0248(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, Succ(wx10090), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0251(wx4, wx31, wx32, wx33, wx34, wx5100, wx1024, ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0427(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx19890), gh) → new_lookupWithDefaultFM020(wx1429, wx1435, :%(Neg(Zero), Pos(Succ(wx1436))), gh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0198(wx4, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0249(wx4, wx31, wx32, wx33, wx34, wx5100, Succ(wx10160), ba) → new_lookupWithDefaultFM0252(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0228(wx4, wx3000000000, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0187(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Zero), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0168(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0168(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx7280), ba) → new_lookupWithDefaultFM0170(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0239(wx4, wx30100, wx31, wx32, wx33, wx34, wx5100, Succ(wx9840), ba) → new_lookupWithDefaultFM0241(wx4, Succ(Succ(Succ(Succ(Zero)))), wx30100, wx31, wx32, wx33, wx34, wx5100, ba)
new_lookupWithDefaultFM0423(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, gh) → new_lookupWithDefaultFM0425(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, new_primMulNat0(Zero, wx1431), gh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx198800), Succ(wx186500), gh) → new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx198800, wx186500, gh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx198800), Succ(wx186500), gh) → new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx198800, wx186500, gh)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, Succ(wx198800), Succ(wx186500), gh) → new_lookupWithDefaultFM0428(wx1429, wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx198800, wx186500, gh)

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

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

new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Succ(wx202600), baf) → new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx199600, wx202600, baf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Succ(wx202600), baf) → new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx199600, wx202600, baf)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, Succ(wx199600), Succ(wx202600), baf) → new_lookupWithDefaultFM0499(wx1515, wx1516, wx1517, wx1518, wx1519, wx1520, wx1521, wx1522, wx199600, wx202600, baf)

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
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0452(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0159(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6890), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0163(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0491(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0490(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68000)), Zero, fd) → new_lookupWithDefaultFM0382(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Zero, hh) → new_lookupWithDefaultFM0479(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0447(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9390), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Zero)), hh)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0437(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0456(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0449(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0479(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0215(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8900), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0384(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0411(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1385), wx1391), fh)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0374(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0157(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0159(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0455(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9420), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Zero)), hh)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(wx63200), fd) → new_lookupWithDefaultFM0393(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0454(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0158(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0475(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(wx8580)), hh)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Succ(wx91000)), hh) → new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx91000, hh)
new_lookupWithDefaultFM0439(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0449(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0208(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0438(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, Succ(wx19750), gb) → new_lookupWithDefaultFM020(wx1393, wx1398, :%(Neg(Succ(wx1399)), Pos(Succ(wx1400))), gb)
new_lookupWithDefaultFM0224(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9290), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Succ(wx90800)), hh) → new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx90800, hh)
new_lookupWithDefaultFM0146(wx622, Pos(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Zero)), fd)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0457(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0461(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0446(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, Succ(wx9280), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(wx8580)), hh)
new_lookupWithDefaultFM0210(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8730), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68200), Succ(wx63200), fd) → new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68200, wx63200, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0151(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0451(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0455(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68200), Zero, fd) → new_lookupWithDefaultFM0392(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, Zero, hh) → new_lookupWithDefaultFM0480(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0401(wx622, wx6230, wx624, wx625, wx626, wx627, wx628, wx629, wx6300, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(wx6300)), fd)
new_lookupWithDefaultFM0146(wx622, Neg(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0397(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(Succ(wx195800)), fd) → new_lookupWithDefaultFM0400(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0472(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(wx8580)), hh)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68200)), Succ(wx63200), fd) → new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68200, wx63200, fd)
new_lookupWithDefaultFM0395(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0495(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0494(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0438(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0448(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), wx6320, fd)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68000), Zero, fd) → new_lookupWithDefaultFM0382(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Zero)), fd)
new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Succ(wx196200), hh) → new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116200, wx196200, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0226(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0218(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0492(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0456(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9430), hh) → new_lookupWithDefaultFM0485(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9430, new_primMulNat0(Zero, wx85800), hh)
new_lookupWithDefaultFM0151(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0410(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0163(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6940), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Zero, hh) → new_lookupWithDefaultFM0466(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0492(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, bac) → new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, new_primMulNat0(Succ(wx1498), wx1504), bac)
new_lookupWithDefaultFM0157(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6650), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0215(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0158(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0413(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0410(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1385), wx1391), fh)
new_lookupWithDefaultFM0207(wx850, Pos(wx8510), wx852, wx853, wx854, wx855, wx856, wx857, Neg(wx8580), Succ(wx8600), hh) → new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0218(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0449(wx850, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9410), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Zero)), hh)
new_lookupWithDefaultFM0227(wx1884, wx1885, wx1886, wx1887, wx1888, wx1889, wx1890, wx1891, bad) → new_lookupWithDefaultFM020(wx1884, wx1888, :%(Neg(Succ(wx1890)), Neg(Succ(wx1891))), bad)
new_lookupWithDefaultFM0470(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), wx6320, fd)
new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, Succ(wx19350), bac) → new_lookupWithDefaultFM020(wx1497, wx1502, :%(Neg(Succ(wx1503)), Pos(Succ(wx1504))), bac)
new_lookupWithDefaultFM0484(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0466(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM0387(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(Succ(wx195600)), fd) → new_lookupWithDefaultFM0390(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0225(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9340), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0374(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6720), fd) → new_lookupWithDefaultFM0380(wx622, Succ(wx62300), wx624, wx625, wx626, wx627, wx628, wx629, Succ(wx63000), fd)
new_lookupWithDefaultFM0208(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8610), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0147(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0209(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(wx91000), hh) → new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx91000, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0164(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0394(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(wx90800), hh) → new_lookupWithDefaultFM0460(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0471(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx18660), hh) → new_lookupWithDefaultFM0472(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0445(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0453(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0150(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0221(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, bac) → new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, new_primMulNat0(Succ(wx1498), wx1504), bac)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Zero, hh) → new_lookupWithDefaultFM0459(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0457(wx850, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx9440), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Zero)), hh)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0148(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6400), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0441(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), Zero, hh) → new_lookupWithDefaultFM0474(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11620, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM0216(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, bab) → new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, new_primMulNat0(Succ(wx1489), wx1495), bab)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(wx91000), hh) → new_lookupWithDefaultFM0478(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0445(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0457(wx850, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0151(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6480), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0153(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0410(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Zero), hh) → new_lookupWithDefaultFM0477(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx8600, Zero, hh) → new_lookupWithDefaultFM0462(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0467(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9400, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195800), Succ(wx115800), fd) → new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195800, wx115800, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0227(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0213(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8780), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0146(wx622, Pos(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0375(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Succ(wx63200), fd) → new_lookupWithDefaultFM0383(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0213(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0488(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0437(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0447(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Succ(Zero), hh) → new_lookupWithDefaultFM0466(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0216(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0440(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), Zero, hh) → new_lookupWithDefaultFM0471(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195600), Succ(wx115700), fd) → new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195600, wx115700, fd)
new_lookupWithDefaultFM0382(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0385(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, Succ(wx19740), fh) → new_lookupWithDefaultFM020(wx1384, wx1389, :%(Neg(Succ(wx1390)), Neg(Succ(wx1391))), fh)
new_lookupWithDefaultFM0383(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0453(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0166(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0161(wx1779, wx1780, wx1781, wx1782, wx1783, wx1784, wx1785, wx1786, ga) → new_lookupWithDefaultFM0414(wx1779, wx1780, wx1781, wx1782, wx1783, wx1784, wx1785, wx1786, ga)
new_lookupWithDefaultFM0215(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0491(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0166(wx1402, wx1403, wx1404, wx1405, wx1406, wx1407, wx1408, wx1409, gc) → new_lookupWithDefaultFM020(wx1402, wx1406, :%(Neg(Succ(wx1408)), Neg(Succ(wx1409))), gc)
new_lookupWithDefaultFM0146(wx622, Pos(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0447(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0155(wx1770, wx1771, wx1772, wx1773, wx1774, wx1775, wx1776, wx1777, fg) → new_lookupWithDefaultFM0411(wx1770, wx1771, wx1772, wx1773, wx1774, wx1775, wx1776, wx1777, fg)
new_lookupWithDefaultFM0485(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9430, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0414(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, gb) → new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, new_primMulNat0(Succ(wx1394), wx1400), gb)
new_lookupWithDefaultFM0152(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6550), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0211(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0380(wx622, wx6230, wx624, wx625, wx626, wx627, wx628, wx629, wx6300, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(wx6300)), fd)
new_lookupWithDefaultFM0452(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0453(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Succ(wx63200), fd) → new_lookupWithDefaultFM0393(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0377(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6760), fd) → new_lookupWithDefaultFM0395(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0454(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9060), hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0480(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0212(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0446(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9000), hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM0158(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6840), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0218(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8930), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0159(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0413(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0165(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx7060), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0477(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0480(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Neg(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0379(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM0385(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0450(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0451(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0212(wx1875, wx1876, wx1877, wx1878, wx1879, wx1880, wx1881, wx1882, baa) → new_lookupWithDefaultFM020(wx1875, wx1879, :%(Neg(Succ(wx1881)), Pos(Succ(wx1882))), baa)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Succ(wx91000)), hh) → new_lookupWithDefaultFM0478(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0460(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Pos(Succ(wx85800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0153(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6600), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0146(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30100), Succ(wx30100)), ba)
new_lookupWithDefaultFM0146(wx622, Neg(wx6230), wx624, wx625, wx626, wx627, wx628, wx629, Neg(wx6300), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(wx6300)), fd)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Succ(wx63200), fd) → new_lookupWithDefaultFM0383(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Zero, hh) → new_lookupWithDefaultFM0484(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0462(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Zero, fd) → new_lookupWithDefaultFM0384(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0388(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0161(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0451(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0153(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0397(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx115800), Succ(Succ(wx195800)), fd) → new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195800, wx115800, fd)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0443(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0391(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, Zero, fd) → new_lookupWithDefaultFM0394(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0450(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primPlusNat0(new_primMulNat0(wx85100, wx85800), Succ(wx85800)), hh)
new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx11630), hh) → new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11630, new_primMulNat0(Succ(wx85100), wx85800), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0224(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0150(wx1375, wx1376, wx1377, wx1378, wx1379, wx1380, wx1381, wx1382, ff) → new_lookupWithDefaultFM020(wx1375, wx1379, :%(Neg(Succ(wx1381)), Pos(Succ(wx1382))), ff)
new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx68000), Succ(wx63200), fd) → new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68000, wx63200, fd)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Succ(wx8600), hh) → new_lookupWithDefaultFM0439(wx850, wx852, wx853, wx854, wx855, wx856, wx857, hh)
new_lookupWithDefaultFM0379(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6780), fd) → new_lookupWithDefaultFM0401(wx622, Succ(wx62300), wx624, wx625, wx626, wx627, wx628, wx629, Succ(wx63000), fd)
new_lookupWithDefaultFM0207(wx850, Pos(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68000)), Succ(wx63200), fd) → new_lookupWithDefaultFM0381(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx68000, wx63200, fd)
new_lookupWithDefaultFM0157(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0413(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, wx6320, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Succ(Zero), hh) → new_lookupWithDefaultFM0484(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0394(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0164(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx7010), ba) → new_lookupWithDefaultFM0166(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0372(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0384(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0388(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx19570), fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0160(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0476(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Zero, hh) → new_lookupWithDefaultFM0477(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0209(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8680), ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Succ(Succ(wx196400)), hh) → new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116300, wx196400, hh)
new_lookupWithDefaultFM0474(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx18680), hh) → new_lookupWithDefaultFM0475(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0147(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6330), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx850, Zero, wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM0207(wx850, Pos(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Succ(wx85800)), Zero, hh) → new_lookupWithDefaultFM0448(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0454(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0481(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0146(wx622, Pos(wx6230), wx624, wx625, wx626, wx627, wx628, wx629, Pos(wx6300), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(wx6300)), fd)
new_lookupWithDefaultFM0450(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9020), hh) → new_lookupWithDefaultFM0470(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0444(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0456(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0154(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx663, ba) → new_lookupWithDefaultFM0155(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0213(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0478(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM020(wx850, wx855, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0220(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0225(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0223(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9200), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0452(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9040), hh) → new_lookupWithDefaultFM0473(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Succ(wx85800), hh)
new_lookupWithDefaultFM0399(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195800), Zero, fd) → new_lookupWithDefaultFM0400(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0152(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0155(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0392(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM0395(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx195600), Zero, fd) → new_lookupWithDefaultFM0390(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx11570), fd) → new_lookupWithDefaultFM0387(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx11570, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM0398(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx19590), fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0149(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0473(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, hh) → new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0214(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx8850), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0459(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0462(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0442(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0479(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0146(wx622, Neg(Zero), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Zero)), fd)
new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx11580), fd) → new_lookupWithDefaultFM0397(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx11580, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(Zero), hh) → new_lookupWithDefaultFM0459(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0207(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30100), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx86000), Succ(wx90800), hh) → new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx86000, wx90800, hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0214(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0223(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0226(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx937, ba) → new_lookupWithDefaultFM0227(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0221(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0161(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0490(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, bab) → new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, new_primMulNat0(Succ(wx1489), wx1495), bab)
new_lookupWithDefaultFM0149(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx6450), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0216(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0150(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0375(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx6740), fd) → new_lookupWithDefaultFM0385(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0220(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0495(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0400(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0387(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx115700), Succ(Succ(wx195600)), fd) → new_lookupWithDefaultFM0389(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx195600, wx115700, fd)
new_lookupWithDefaultFM0494(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, bac) → new_lookupWithDefaultFM0493(wx1497, wx1498, wx1499, wx1500, wx1501, wx1502, wx1503, wx1504, new_primMulNat0(Succ(wx1498), wx1504), bac)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0165(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0210(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0211(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx876, ba) → new_lookupWithDefaultFM0212(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0219(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0214(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0488(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(wx8510), wx852, wx853, wx854, wx855, wx856, wx857, Pos(wx8580), Succ(wx8600), hh) → new_lookupWithDefaultFM0441(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0155(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0148(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0227(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0393(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0413(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, gb) → new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, new_primMulNat0(Succ(wx1394), wx1400), gb)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Zero), Succ(wx6320), fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Zero)), fd)
new_lookupWithDefaultFM0152(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0410(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0160(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx692, ba) → new_lookupWithDefaultFM0161(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0377(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0220(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9170), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0461(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh) → new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0436(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Succ(Succ(wx90800)), hh) → new_lookupWithDefaultFM0460(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0482(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11630, Zero, hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(Succ(wx85800))), hh)
new_lookupWithDefaultFM0458(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, Zero, hh) → new_lookupWithDefaultFM0461(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0219(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0492(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, Succ(wx19340), bab) → new_lookupWithDefaultFM020(wx1488, wx1493, :%(Neg(Succ(wx1494)), Neg(Succ(wx1495))), bab)
new_lookupWithDefaultFM0443(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, hh) → new_lookupWithDefaultFM0455(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0396(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0398(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx62300), wx63000), fd)
new_lookupWithDefaultFM0448(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx9400), hh) → new_lookupWithDefaultFM0467(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx9400, new_primMulNat0(Zero, wx85800), hh)
new_lookupWithDefaultFM0446(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Zero, hh) → new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, new_primMulNat0(Succ(wx857), wx852), hh)
new_lookupWithDefaultFM0390(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd) → new_lookupWithDefaultFM020(wx622, wx628, :%(Neg(Succ(wx629)), Neg(Succ(wx63000))), fd)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, wx6320, fd) → new_lookupWithDefaultFM020(wx622, wx627, :%(Neg(Succ(wx629)), Pos(Succ(wx63000))), fd)
new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116200), Succ(Succ(wx196200)), hh) → new_lookupWithDefaultFM0465(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116200, wx196200, hh)
new_lookupWithDefaultFM0219(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx9120), ba) → new_lookupWithDefaultFM0221(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0207(wx850, Neg(Succ(wx85100)), wx852, wx853, wx854, wx855, wx856, wx857, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx850, Succ(wx85100), wx852, wx853, wx854, wx855, wx856, wx857, Zero, hh)
new_lookupWithDefaultFM0207(wx850, Neg(Zero), wx852, wx853, wx854, wx855, wx856, wx857, Neg(Succ(wx85800)), Succ(wx8600), hh) → new_lookupWithDefaultFM0444(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, hh)
new_lookupWithDefaultFM0488(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, bab) → new_lookupWithDefaultFM0489(wx1488, wx1489, wx1490, wx1491, wx1492, wx1493, wx1494, wx1495, new_primMulNat0(Succ(wx1489), wx1495), bab)
new_lookupWithDefaultFM0440(wx850, wx8510, wx852, wx853, wx854, wx855, wx856, wx857, wx8580, Succ(wx9270), hh) → new_lookupWithDefaultFM020(wx850, wx856, :%(Neg(Succ(wx857)), Neg(wx8580)), hh)
new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx116300), Succ(wx196400), hh) → new_lookupWithDefaultFM0483(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx116300, wx196400, hh)
new_lookupWithDefaultFM0375(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Zero, fd) → new_lookupWithDefaultFM0386(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primMulNat0(Succ(wx629), wx624), fd)
new_lookupWithDefaultFM0146(wx622, Neg(Succ(wx62300)), wx624, wx625, wx626, wx627, wx628, wx629, Pos(Succ(wx63000)), Zero, fd) → new_lookupWithDefaultFM0377(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, new_primPlusNat0(new_primMulNat0(wx62300, wx63000), Succ(wx63000)), fd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Neg(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0154(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0373(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(Succ(wx68200)), Zero, fd) → new_lookupWithDefaultFM0392(wx622, wx62300, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, fd)
new_lookupWithDefaultFM0463(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx11620), hh) → new_lookupWithDefaultFM0464(wx850, wx85100, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx11620, new_primMulNat0(Succ(wx85100), wx85800), hh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175600), Succ(wx72300), fd) → new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175600, wx72300, fd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175600), Succ(wx72300), fd) → new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175600, wx72300, fd)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175600), Succ(wx72300), fd) → new_lookupWithDefaultFM0408(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175600, wx72300, fd)

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

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

new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Succ(wx187000), hh) → new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94000, wx187000, hh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Succ(wx187000), hh) → new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94000, wx187000, hh)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94000), Succ(wx187000), hh) → new_lookupWithDefaultFM0468(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94000, wx187000, hh)

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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175400), Succ(wx72000), fd) → new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175400, wx72000, fd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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
                          ↳ UsableRulesProof
QDP
                              ↳ QReductionProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175400), Succ(wx72000), fd) → new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175400, wx72000, fd)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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
                          ↳ UsableRulesProof
                            ↳ QDP
                              ↳ QReductionProof
QDP
                                  ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, Succ(wx175400), Succ(wx72000), fd) → new_lookupWithDefaultFM0404(wx622, wx624, wx625, wx626, wx627, wx628, wx629, wx63000, wx175400, wx72000, fd)

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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Succ(wx187200), hh) → new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94300, wx187200, hh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Succ(wx187200), hh) → new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94300, wx187200, hh)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, Succ(wx94300), Succ(wx187200), hh) → new_lookupWithDefaultFM0486(wx850, wx852, wx853, wx854, wx855, wx856, wx857, wx85800, wx94300, wx187200, hh)

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
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0105(wx1298, wx1299, wx1300, wx1301, wx1302, wx1303, wx1304, wx1305, dg) → new_lookupWithDefaultFM020(wx1298, wx1302, :%(Pos(Succ(wx1304)), Neg(Succ(wx1305))), dg)
new_lookupWithDefaultFM010(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25500)), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15820, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM043(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM010(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, h) → new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0323(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(Succ(wx194800)), da) → new_lookupWithDefaultFM0326(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx231, Zero, h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0271(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0270(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM099(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Succ(wx40400), da) → new_lookupWithDefaultFM0319(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM09(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, Succ(wx2760), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(wx2070)), h)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45400), Succ(wx40400), da) → new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45400, wx40400, da)
new_lookupWithDefaultFM0313(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4480), da) → new_lookupWithDefaultFM0331(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45200)), Succ(wx40400), da) → new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45200, wx40400, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM029(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM044(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0531(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM08(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, wx4040, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM027(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10790), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, Succ(wx19310), bd) → new_lookupWithDefaultFM020(wx1183, wx1188, :%(Pos(Succ(wx1189)), Pos(Succ(wx1190))), bd)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Zero, da) → new_lookupWithDefaultFM0330(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM044(wx1596, wx1597, wx1598, wx1599, wx1600, wx1601, wx1602, wx1603, be) → new_lookupWithDefaultFM020(wx1596, wx1600, :%(Pos(Succ(wx1602)), Neg(Succ(wx1603))), be)
new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0324(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM0538(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM011(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM091(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4270), ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM030(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0268(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Succ(wx257000))), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx15820), h) → new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15820, new_primMulNat0(Succ(wx20000), wx20700), h)
new_lookupWithDefaultFM096(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4370), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM037(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2350), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM094(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0543(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0336(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Succ(wx257000), h) → new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2310, wx257000, h)
new_lookupWithDefaultFM031(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2120), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Zero, h) → new_lookupWithDefaultFM0547(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM036(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM04(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25300)), h) → new_lookupWithDefaultFM018(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, wx2010, wx25300, h)
new_lookupWithDefaultFM04(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM019(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM037(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0(wx199, Pos(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Zero), Zero, h) → new_lookupWithDefaultFM07(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0334(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx11520), da) → new_lookupWithDefaultFM0333(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx11520, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM096(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Zero, h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM089(wx1269, wx1270, wx1271, wx1272, wx1273, wx1274, wx1275, wx1276, db) → new_lookupWithDefaultFM020(wx1269, wx1273, :%(Pos(Succ(wx1275)), Pos(Succ(wx1276))), db)
new_lookupWithDefaultFM017(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM07(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM029(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM031(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0268(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM028(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10830), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM04(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, h) → new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0(wx199, Neg(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Pos(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM02(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM04(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25300)), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM089(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM090(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0346(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0328(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0331(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM085(wx394, Neg(wx3950), wx396, wx397, wx398, wx399, wx400, wx401, Neg(wx4020), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(wx4020)), da)
new_lookupWithDefaultFM038(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, bd) → new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, new_primMulNat0(Succ(wx1184), wx1190), bd)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM033(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM00(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx231, h) → new_lookupWithDefaultFM015(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx195000), Zero, da) → new_lookupWithDefaultFM0336(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0274(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, bd) → new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, new_primMulNat0(Succ(wx1184), wx1190), bd)
new_lookupWithDefaultFM0(wx199, Neg(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Zero), Zero, h) → new_lookupWithDefaultFM011(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM041(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM030(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0329(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(wx40400), da) → new_lookupWithDefaultFM0319(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM011(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11470), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Zero)), h)
new_lookupWithDefaultFM0268(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, bc) → new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, new_primMulNat0(Succ(wx1175), wx1181), bc)
new_lookupWithDefaultFM0104(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4780), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM093(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(Succ(new_primPlusNat0(wx5100, wx5100)), wx5100), ba)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx234, Zero, h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM00(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx231, h) → new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx231, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM0310(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4440), da) → new_lookupWithDefaultFM0316(wx394, Succ(wx39500), wx396, wx397, wx398, wx399, wx400, wx401, Succ(wx40200), da)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), wx4040, da)
new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0320(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM085(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30100), Succ(wx30100)), ba)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45200)), Zero, da) → new_lookupWithDefaultFM0318(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM032(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat1(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), wx5100), ba)
new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx195000), Succ(wx115200), da) → new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx195000, wx115200, da)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(wx40400), da) → new_lookupWithDefaultFM0329(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM027(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0318(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0321(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Succ(wx40400), da) → new_lookupWithDefaultFM0329(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM042(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM040(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0103(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4730), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Succ(wx259000), h) → new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2340, wx259000, h)
new_lookupWithDefaultFM0326(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM035(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2190), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM04(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM021(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0351(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, Succ(wx19710), df) → new_lookupWithDefaultFM020(wx1289, wx1294, :%(Pos(Succ(wx1295)), Pos(Succ(wx1296))), df)
new_lookupWithDefaultFM090(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4200), ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM038(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM035(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0272(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM016(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM06(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM05(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11440), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Zero)), h)
new_lookupWithDefaultFM0333(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Succ(Succ(wx195000)), da) → new_lookupWithDefaultFM0336(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0(wx199, Pos(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM06(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM042(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2500), ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Zero)), da)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0330(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM00(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx231, h) → new_lookupWithDefaultFM017(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx194800), Zero, da) → new_lookupWithDefaultFM0326(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45200), Succ(wx40400), da) → new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45200, wx40400, da)
new_lookupWithDefaultFM0324(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx19490), da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM0331(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Zero, h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Succ(Succ(wx198000)), h) → new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158500, wx198000, h)
new_lookupWithDefaultFM03(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx234, h) → new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx234, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM0532(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx19260), h) → new_lookupWithDefaultFM0533(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0102(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0533(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(wx2070)), h)
new_lookupWithDefaultFM0534(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM09(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Zero)), da)
new_lookupWithDefaultFM07(wx199, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11460), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Zero)), h)
new_lookupWithDefaultFM0540(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM013(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0334(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx19510), da) → new_lookupWithDefaultFM020(wx394, wx400, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM010(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, Succ(wx19300), bc) → new_lookupWithDefaultFM020(wx1174, wx1179, :%(Pos(Succ(wx1180)), Neg(Succ(wx1181))), bc)
new_lookupWithDefaultFM085(wx394, Neg(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Zero)), da)
new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Succ(wx198000), h) → new_lookupWithDefaultFM0546(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158500, wx198000, h)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), wx4040, da)
new_lookupWithDefaultFM086(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4050), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0346(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, dd) → new_lookupWithDefaultFM0348(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, new_primMulNat0(Succ(wx1281), wx1287), dd)
new_lookupWithDefaultFM0(wx199, Pos(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Neg(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM01(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx231, Succ(Zero), h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45400), Zero, da) → new_lookupWithDefaultFM0328(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM00(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx231, h) → new_lookupWithDefaultFM016(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM036(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0272(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM086(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM033(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM0100(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, Zero, da) → new_lookupWithDefaultFM0320(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM094(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM099(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx464, ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(wx257000), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM0316(wx394, wx3950, wx396, wx397, wx398, wx399, wx400, wx401, wx4020, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(wx4020)), da)
new_lookupWithDefaultFM0(wx199, Neg(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM012(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM029(wx1587, wx1588, wx1589, wx1590, wx1591, wx1592, wx1593, wx1594, bb) → new_lookupWithDefaultFM020(wx1587, wx1591, :%(Pos(Succ(wx1593)), Pos(Succ(wx1594))), bb)
new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Zero, h) → new_lookupWithDefaultFM025(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0102(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4660), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0535(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx19280), h) → new_lookupWithDefaultFM0536(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), h)
new_lookupWithDefaultFM021(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0308(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0320(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM092(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM02(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, wx233, h) → new_lookupWithDefaultFM0534(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h)
new_lookupWithDefaultFM096(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0349(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM032(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2170), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM097(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0349(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0313(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM0(wx199, Neg(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Neg(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM03(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Succ(Succ(wx197800)), h) → new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158200, wx197800, h)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx234, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM085(wx394, Pos(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM087(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM085(wx394, Neg(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0315(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0103(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0347(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, dd) → new_lookupWithDefaultFM0348(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, new_primMulNat0(Succ(wx1281), wx1287), dd)
new_lookupWithDefaultFM020(wx4, Branch(:%(wx300, Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0(wx4, wx300, wx30100, wx31, wx32, wx33, wx34, wx5000, wx51, new_primMulNat0(wx5000, wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM089(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx194800), Succ(wx115100), da) → new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx194800, wx115100, da)
new_lookupWithDefaultFM0544(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx15850), h) → new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15850, new_primMulNat0(Succ(wx20000), wx20700), h)
new_lookupWithDefaultFM037(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0275(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM09(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), Zero, h) → new_lookupWithDefaultFM0535(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM030(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10870), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM098(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM033(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, bc) → new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, new_primMulNat0(Succ(wx1175), wx1181), bc)
new_lookupWithDefaultFM0536(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(wx2070)), h)
new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Succ(wx197800), h) → new_lookupWithDefaultFM024(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx158200, wx197800, h)
new_lookupWithDefaultFM0315(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4500), da) → new_lookupWithDefaultFM0337(wx394, Succ(wx39500), wx396, wx397, wx398, wx399, wx400, wx401, Succ(wx40200), da)
new_lookupWithDefaultFM032(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0271(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM08(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, Succ(wx2750), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(wx2070)), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM028(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM098(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4610), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx11510), da) → new_lookupWithDefaultFM0323(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx11510, new_primMulNat0(Succ(wx39500), wx40200), da)
new_lookupWithDefaultFM0548(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11480, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM010(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Succ(wx25500)), h) → new_lookupWithDefaultFM0541(wx199, wx20000, Succ(wx2010), wx202, wx203, wx204, wx205, wx206, wx20700, wx2010, wx25500, h)
new_lookupWithDefaultFM088(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4170), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0275(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, ba) → new_lookupWithDefaultFM0274(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM036(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2260), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Neg(Zero), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Zero), Zero, h) → new_lookupWithDefaultFM013(wx199, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM092(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4320), ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0323(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx115100), Succ(Succ(wx194800)), da) → new_lookupWithDefaultFM0325(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx194800, wx115100, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM088(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM03(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx234, h) → new_lookupWithDefaultFM0538(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM010(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(Zero), h) → new_lookupWithDefaultFM0543(wx199, wx20000, Zero, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM021(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM023(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158200), Succ(Zero), h) → new_lookupWithDefaultFM025(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0(wx199, Pos(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Zero), Zero, h) → new_lookupWithDefaultFM05(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM091(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0346(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Zero, h) → new_lookupWithDefaultFM021(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM06(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx11450), h) → new_lookupWithDefaultFM0528(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11450, new_primMulNat0(Zero, wx20700), h)
new_lookupWithDefaultFM0313(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Zero)), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0105(wx4, Zero, wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0333(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx115200), Succ(Succ(wx195000)), da) → new_lookupWithDefaultFM0335(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx195000, wx115200, da)
new_lookupWithDefaultFM01(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, wx232, h) → new_lookupWithDefaultFM0531(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, h)
new_lookupWithDefaultFM0547(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Succ(wx259000))), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM019(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM022(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM026(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM097(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM033(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0349(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, df) → new_lookupWithDefaultFM0351(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, new_primMulNat0(Succ(wx1290), wx1296), df)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, wx4040, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM085(wx394, Neg(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(Succ(wx40200))), da)
new_lookupWithDefaultFM094(wx1656, wx1657, wx1658, wx1659, wx1660, wx1661, wx1662, wx1663, dc) → new_lookupWithDefaultFM0347(wx1656, wx1657, wx1658, wx1659, wx1660, wx1661, wx1662, wx1663, dc)
new_lookupWithDefaultFM0311(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx4460), da) → new_lookupWithDefaultFM0321(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM093(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx435, ba) → new_lookupWithDefaultFM094(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0317(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx45200), Zero, da) → new_lookupWithDefaultFM0318(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM031(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0100(wx1665, wx1666, wx1667, wx1668, wx1669, wx1670, wx1671, wx1672, de) → new_lookupWithDefaultFM0350(wx1665, wx1666, wx1667, wx1668, wx1669, wx1670, wx1671, wx1672, de)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM090(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx158500), Succ(Zero), h) → new_lookupWithDefaultFM0547(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Zero)))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Pos(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Pos(wx2070), Succ(wx2080), h) → new_lookupWithDefaultFM00(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primPlusNat0(wx2080, wx201), h)
new_lookupWithDefaultFM043(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, wx261, ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Zero)))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM038(wx4, Succ(Succ(Zero)), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0348(wx1280, wx1281, wx1282, wx1283, wx1284, wx1285, wx1286, wx1287, Succ(wx19700), dd) → new_lookupWithDefaultFM020(wx1280, wx1285, :%(Pos(Succ(wx1286)), Neg(Succ(wx1287))), dd)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0543(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0105(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Pos(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Neg(wx2070), Zero, h) → new_lookupWithDefaultFM08(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM0319(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Succ(wx40200))), da)
new_lookupWithDefaultFM08(wx199, Succ(wx20000), wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), Zero, h) → new_lookupWithDefaultFM0532(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM0350(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, df) → new_lookupWithDefaultFM0351(wx1289, wx1290, wx1291, wx1292, wx1293, wx1294, wx1295, wx1296, new_primMulNat0(Succ(wx1290), wx1296), df)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Succ(wx259000), h) → new_lookupWithDefaultFM020(wx199, wx204, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)
new_lookupWithDefaultFM0539(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM012(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM091(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0330(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0332(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM026(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx10730), ba) → new_lookupWithDefaultFM029(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0311(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Zero, da) → new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Pos(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0310(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM092(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0346(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM038(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM098(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Zero, ba) → new_lookupWithDefaultFM0349(wx4, Succ(Succ(Succ(Zero))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Zero))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM044(wx4, Succ(Zero), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0270(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, bc) → new_lookupWithDefaultFM0269(wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, wx1181, new_primMulNat0(Succ(wx1175), wx1181), bc)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Zero))))), Neg(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Neg(Succ(wx5100))), ba) → new_lookupWithDefaultFM0104(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0537(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2340), Succ(Succ(Succ(wx259000))), h) → new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2340, wx259000, h)
new_lookupWithDefaultFM040(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2380), ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Succ(Succ(Succ(wx3000000000))))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM014(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx2310), Succ(Succ(Succ(wx257000))), h) → new_lookupWithDefaultFM018(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx2310, wx257000, h)
new_lookupWithDefaultFM085(wx394, Pos(wx3950), wx396, wx397, wx398, wx399, wx400, wx401, Pos(wx4020), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Pos(wx4020)), da)
new_lookupWithDefaultFM085(wx394, Pos(Zero), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Zero), Succ(wx4040), da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(Zero)), da)
new_lookupWithDefaultFM012(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx11480), h) → new_lookupWithDefaultFM0548(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11480, new_primMulNat0(Zero, wx20700), h)
new_lookupWithDefaultFM085(wx394, Pos(Succ(wx39500)), wx396, wx397, wx398, wx399, wx400, wx401, Neg(Succ(wx40200)), Zero, da) → new_lookupWithDefaultFM0311(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primPlusNat0(new_primMulNat0(wx39500, wx40200), Succ(wx40200)), da)
new_lookupWithDefaultFM0(wx199, Neg(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Neg(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM010(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM03(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx20700), wx234, h) → new_lookupWithDefaultFM0539(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM025(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM03(wx199, Zero, wx201, wx202, wx203, wx204, wx205, wx206, Zero, wx234, h) → new_lookupWithDefaultFM0540(wx199, wx201, wx202, wx203, wx204, wx205, wx206, h)
new_lookupWithDefaultFM041(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx2450), ba) → new_lookupWithDefaultFM044(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM015(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, h) → new_lookupWithDefaultFM05(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM087(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4120), ba) → new_lookupWithDefaultFM089(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0(wx199, Neg(wx2000), wx201, wx202, wx203, wx204, wx205, wx206, Pos(wx2070), Zero, h) → new_lookupWithDefaultFM09(wx199, wx2000, wx201, wx202, wx203, wx204, wx205, wx206, wx2070, new_primMulNat0(Succ(wx206), wx201), h)
new_lookupWithDefaultFM020(wx4, Branch(:%(Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx3000000000))))))), Pos(Zero)), wx31, wx32, wx33, wx34), :%(Pos(Succ(wx5000)), Pos(Succ(wx5100))), ba) → new_lookupWithDefaultFM035(wx4, wx3000000000, wx31, wx32, wx33, wx34, wx5000, wx5100, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx3000000000, wx5100), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), Succ(wx5100)), ba)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45400)), Zero, da) → new_lookupWithDefaultFM0328(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da)
new_lookupWithDefaultFM0309(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(Succ(wx45400)), Succ(wx40400), da) → new_lookupWithDefaultFM0327(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx45400, wx40400, da)
new_lookupWithDefaultFM013(wx199, wx201, wx202, wx203, wx204, wx205, wx206, Succ(wx11490), h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Zero)), h)
new_lookupWithDefaultFM0337(wx394, wx3950, wx396, wx397, wx398, wx399, wx400, wx401, wx4020, da) → new_lookupWithDefaultFM020(wx394, wx399, :%(Pos(Succ(wx401)), Neg(wx4020)), da)
new_lookupWithDefaultFM0(wx199, Pos(Succ(wx20000)), wx201, wx202, wx203, wx204, wx205, wx206, Pos(Succ(wx20700)), Zero, h) → new_lookupWithDefaultFM04(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, new_primPlusNat0(new_primMulNat0(wx20000, wx20700), Succ(wx20700)), h)
new_lookupWithDefaultFM097(wx4, wx31, wx32, wx33, wx34, wx5000, wx5100, Succ(wx4560), ba) → new_lookupWithDefaultFM0100(wx4, Succ(Succ(Succ(Succ(Zero)))), wx31, wx32, wx33, wx34, wx5000, wx5100, ba)
new_lookupWithDefaultFM0321(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, da) → new_lookupWithDefaultFM0322(wx394, wx39500, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, new_primMulNat0(Succ(wx401), wx396), da)
new_lookupWithDefaultFM0272(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, bd) → new_lookupWithDefaultFM0273(wx1183, wx1184, wx1185, wx1186, wx1187, wx1188, wx1189, wx1190, new_primMulNat0(Succ(wx1184), wx1190), bd)
new_lookupWithDefaultFM0541(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Zero, Zero, h) → new_lookupWithDefaultFM0543(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, h)
new_lookupWithDefaultFM0528(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx11450, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Pos(Succ(wx20700))), h)
new_lookupWithDefaultFM0545(wx199, wx20000, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx15850, Zero, h) → new_lookupWithDefaultFM020(wx199, wx205, :%(Pos(Succ(wx206)), Neg(Succ(wx20700))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Succ(wx194000), h) → new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114800, wx194000, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Succ(wx194000), h) → new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114800, wx194000, h)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114800), Succ(wx194000), h) → new_lookupWithDefaultFM0549(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114800, wx194000, 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
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
QDP
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164000), Succ(wx49200), da) → new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164000, wx49200, da)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164000), Succ(wx49200), da) → new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164000, wx49200, da)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164000), Succ(wx49200), da) → new_lookupWithDefaultFM0340(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164000, wx49200, da)

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

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

new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Succ(wx193800), h) → new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114500, wx193800, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Succ(wx193800), h) → new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114500, wx193800, h)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, Succ(wx114500), Succ(wx193800), h) → new_lookupWithDefaultFM0529(wx199, wx201, wx202, wx203, wx204, wx205, wx206, wx20700, wx114500, wx193800, 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
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
QDP
                          ↳ UsableRulesProof

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

new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164200), Succ(wx49500), da) → new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164200, wx49500, da)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30100) → Succ(wx30100)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30100) → Zero
new_primPlusNat1(Succ(wx2110), wx30100) → Succ(Succ(new_primPlusNat0(wx2110, wx30100)))
new_primPlusNat0(Succ(wx21100), Zero) → Succ(wx21100)
new_primPlusNat0(Zero, Succ(wx301000)) → Succ(wx301000)
new_primPlusNat0(Succ(wx21100), Succ(wx301000)) → Succ(Succ(new_primPlusNat0(wx21100, wx301000)))
new_primMulNat0(Succ(wx50000), wx30100) → new_primPlusNat1(new_primMulNat0(wx50000, wx30100), wx30100)

The set Q consists of the following terms:

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

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

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

new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164200), Succ(wx49500), da) → new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164200, wx49500, da)

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

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

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_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Succ(x0), Succ(x1))
new_primPlusNat0(Zero, Zero)
new_primPlusNat1(Succ(x0), x1)
new_primMulNat0(Succ(x0), x1)
new_primMulNat0(Zero, x0)
new_primPlusNat1(Zero, x0)



↳ 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

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

new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, Succ(wx164200), Succ(wx49500), da) → new_lookupWithDefaultFM0344(wx394, wx396, wx397, wx398, wx399, wx400, wx401, wx40200, wx164200, wx49500, da)

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: