YES 165.052 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 Float a  ->  a  ->  Float  ->  a) :: FiniteMap Float a  ->  a  ->  Float  ->  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 a b) 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 
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 Float a  ->  a  ->  Float  ->  a) :: FiniteMap Float a  ->  a  ->  Float  ->  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 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 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



Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
HASKELL
          ↳ COR

mainModule FiniteMap
  ((lookupWithDefaultFM :: FiniteMap Float a  ->  a  ->  Float  ->  a) :: FiniteMap Float a  ->  a  ->  Float  ->  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 a b) 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 Float a  ->  a  ->  Float  ->  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 a b) where 

  lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b
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 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



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(wx21500), Succ(wx300000)) → new_primPlusNat(wx21500, wx300000)

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), wx30000) → new_primMulNat(wx50000, wx30000)

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_lookupWithDefaultFM0508(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Zero, wx1538), bah)
new_lookupWithDefaultFM011(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx11510), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM0159(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6810), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx235, Zero, h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0175(wx1790, wx1791, wx1792, wx1793, wx1794, wx1795, wx1796, wx1797, ge) → new_lookupWithDefaultFM0417(wx1790, wx1791, wx1792, wx1793, wx1794, wx1795, wx1796, wx1797, ge)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0239(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0300(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, ce) → new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, new_primMulNat0(Succ(wx1241), wx1236), ce)
new_lookupWithDefaultFM062(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3280), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0(wx203, wx204, Pos(wx2050), wx206, wx207, wx208, wx209, wx210, Neg(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM02(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67200)), Zero, fd) → new_lookupWithDefaultFM0382(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Zero, hh) → new_lookupWithDefaultFM0479(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0438(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0448(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM047(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2790), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45600)), Succ(wx40800), da) → new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45600, wx40800, da)
new_lookupWithDefaultFM0229(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9260), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0278(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Succ(Zero), bg) → new_lookupWithDefaultFM0280(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, bg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0104(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0118(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0533(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(wx2110)), h)
new_lookupWithDefaultFM0432(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, Succ(wx19800), hd) → new_lookupWithDefaultFM020(wx1457, wx1462, Float(Neg(Zero), Pos(Succ(wx1463))), hd)
new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Zero, h) → new_lookupWithDefaultFM0550(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0543(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0522(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, bbd) → new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, new_primMulNat0(Succ(wx1569), wx1564), bbd)
new_lookupWithDefaultFM0125(wx1330, wx1331, wx1332, wx1333, wx1334, wx1335, wx1336, wx1337, ee) → new_lookupWithDefaultFM020(wx1330, wx1335, Float(Pos(Zero), Neg(Succ(wx1337))), ee)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0154(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Zero, eb) → new_lookupWithDefaultFM0356(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, new_primMulNat0(Succ(wx1317), wx1312), eb)
new_lookupWithDefaultFM060(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3160), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM091(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4310), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM034(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx10970), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Succ(wx5000)), Pos(Zero)), ba)
new_lookupWithDefaultFM0198(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0433(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0140(wx1729, wx1730, wx1731, wx1732, wx1733, wx1734, wx1735, fa) → new_lookupWithDefaultFM0370(wx1729, wx1730, wx1731, wx1732, wx1733, wx1734, wx1735, fa)
new_lookupWithDefaultFM06(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx11490), h) → new_lookupWithDefaultFM0528(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11490, new_primMulNat0(Zero, wx20500), h)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Succ(wx261000), h) → new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2350, wx261000, h)
new_lookupWithDefaultFM0131(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5710), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Succ(wx88800)), hh) → new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx88800, hh)
new_lookupWithDefaultFM0367(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, eh) → new_lookupWithDefaultFM0368(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, new_primMulNat0(Succ(wx1353), wx1348), eh)
new_lookupWithDefaultFM0401(wx614, wx615, wx6160, wx617, wx618, wx619, wx620, wx621, wx6220, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(wx6220)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM0135(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0457(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0187(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0116(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM04(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, h) → new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0523(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0522(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0226(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM061(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0295(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0173(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM053(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Zero, wx1201), bh)
new_lookupWithDefaultFM0129(wx1339, wx1340, wx1341, wx1342, wx1343, wx1344, wx1345, ef) → new_lookupWithDefaultFM020(wx1339, wx1343, Float(Pos(Zero), Pos(Succ(wx1345))), ef)
new_lookupWithDefaultFM0123(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5410), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM0262(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM079(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11080), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM082(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3920), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM025(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM0173(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7280), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0221(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, bac) → new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, new_primMulNat0(Succ(wx1508), wx1502), bac)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0130(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0505(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, Succ(wx19710), bag) → new_lookupWithDefaultFM0506(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Zero)), ba) → new_lookupWithDefaultFM0162(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0259(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0141(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11200), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM070(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0300(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM03(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx238, h) → new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx238, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Zero, baf) → new_lookupWithDefaultFM0500(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, baf)
new_lookupWithDefaultFM0528(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Succ(Zero), h) → new_lookupWithDefaultFM0530(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM050(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0281(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0450(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0435(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, Succ(wx19810), hf) → new_lookupWithDefaultFM020(wx1465, wx1470, Float(Neg(Zero), Neg(Succ(wx1471))), hf)
new_lookupWithDefaultFM0475(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(wx8380)), hh)
new_lookupWithDefaultFM0375(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0244(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0515(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, Succ(wx9120), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(wx8380)), hh)
new_lookupWithDefaultFM0178(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0423(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0182(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11280), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM083(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0185(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7620), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195400), Zero, da) → new_lookupWithDefaultFM0336(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM096(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, wx4080, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM081(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0193(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM0196(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0466(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0406(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx108500), Succ(Succ(wx191600)), fd) → new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191600, wx108500, fd)
new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19000, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0177(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0225(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, Succ(wx19360), ce) → new_lookupWithDefaultFM020(wx1235, wx1240, Float(Pos(Zero), Pos(Succ(wx1241))), ce)
new_lookupWithDefaultFM0474(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx19240), hh) → new_lookupWithDefaultFM0475(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0295(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, cc) → new_lookupWithDefaultFM0296(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, new_primMulNat0(Zero, wx1219), cc)
new_lookupWithDefaultFM0213(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0488(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0431(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, hd) → new_lookupWithDefaultFM0432(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, new_primMulNat0(Succ(wx1463), wx1458), hd)
new_lookupWithDefaultFM0228(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9190), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0169(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0443(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0455(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0174(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx731, ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0355(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx191000), Succ(Succ(wx198600)), eb) → new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, wx198600, wx191000, eb)
new_lookupWithDefaultFM0225(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx9140), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(wx40800), da) → new_lookupWithDefaultFM0329(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0318(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0321(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, Succ(wx19380), bab) → new_lookupWithDefaultFM020(wx1492, wx1497, Float(Neg(Succ(wx1498)), Pos(Succ(wx1499))), bab)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(wx89000), hh) → new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx89000, hh)
new_lookupWithDefaultFM0103(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4770), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0445(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Zero, hh) → new_lookupWithDefaultFM0459(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0445(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0457(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM067(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0229(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0496(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0547(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM098(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx12620), da) → new_lookupWithDefaultFM0333(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx12620, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM0193(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0430(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0222(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx11360), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Succ(wx5000)), Neg(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0214(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0467(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Succ(Zero), hh) → new_lookupWithDefaultFM0469(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Succ(Zero), hh) → new_lookupWithDefaultFM0466(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0352(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb) → new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, new_primMulNat0(Zero, wx1311), eb)
new_lookupWithDefaultFM0180(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx748, ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM060(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0295(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196000), Succ(wx137100), fd) → new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196000, wx137100, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0111(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0296(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx19950), cc) → new_lookupWithDefaultFM0297(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx19950, new_primMulNat0(Succ(wx1225), wx1220), cc)
new_lookupWithDefaultFM0205(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8260), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0240(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM092(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0531(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM08(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0321(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM0161(wx1763, wx1764, wx1765, wx1766, wx1767, wx1768, wx1769, wx1770, ga) → new_lookupWithDefaultFM0414(wx1763, wx1764, wx1765, wx1766, wx1767, wx1768, wx1769, wx1770, ga)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0160(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0130(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0366(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0498(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Succ(Succ(wx203000)), baf) → new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx200000, wx203000, baf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0350(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, df) → new_lookupWithDefaultFM0351(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, new_primMulNat0(Succ(wx1290), wx1284), df)
new_lookupWithDefaultFM0(wx203, wx204, Pos(wx2050), wx206, wx207, wx208, wx209, wx210, Pos(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM00(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM045(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx2670), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0135(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11190), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0143(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM03(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Zero, wx238, h) → new_lookupWithDefaultFM0539(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx235, Succ(Zero), h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM021(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0254(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0184(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7570), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0338(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Zero, Succ(Succ(wx190400)), da) → new_lookupWithDefaultFM0341(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, da)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Zero, da) → new_lookupWithDefaultFM0320(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0427(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx19930), gh) → new_lookupWithDefaultFM020(wx1430, wx1436, Float(Neg(Zero), Neg(Succ(wx1437))), gh)
new_lookupWithDefaultFM0208(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx8410), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM099(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx468, ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190400), Succ(wx107000), da) → new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190400, wx107000, da)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Zero, fd) → new_lookupWithDefaultFM0384(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0126(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5490), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0260(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM09(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, Succ(wx2830), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(wx2110)), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM0121(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0397(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx137200), Succ(Succ(wx196200)), fd) → new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196200, wx137200, fd)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Zero, fd) → new_lookupWithDefaultFM0394(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0516(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx20010), bbb) → new_lookupWithDefaultFM0517(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx20010, new_primMulNat0(Succ(wx1553), wx1548), bbb)
new_lookupWithDefaultFM0329(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM047(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM097(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0349(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Zero)), fd)
new_lookupWithDefaultFM0231(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx934, ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0147(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(wx2050), wx206, wx207, wx208, wx209, wx210, Neg(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM03(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0315(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4540), da) → new_lookupWithDefaultFM0337(wx398, wx399, Succ(wx40000), wx401, wx402, wx403, wx404, wx405, Succ(wx40600), da)
new_lookupWithDefaultFM051(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0281(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0380(wx614, wx615, wx6160, wx617, wx618, wx619, wx620, wx621, wx6220, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(wx6220)), fd)
new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, Succ(wx19780), fh) → new_lookupWithDefaultFM020(wx1384, wx1389, Float(Neg(Succ(wx1390)), Pos(Succ(wx1391))), fh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0384(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0452(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM037(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0275(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Succ(Succ(wx196800)), hh) → new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148100, wx196800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM068(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0255(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0523(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0299(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, cc) → new_lookupWithDefaultFM020(wx1218, wx1224, Float(Pos(Zero), Neg(Succ(wx1225))), cc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0181(wx1799, wx1800, wx1801, wx1802, wx1803, wx1804, wx1805, wx1806, gg) → new_lookupWithDefaultFM0424(wx1799, wx1800, wx1801, wx1802, wx1803, wx1804, wx1805, wx1806, gg)
new_lookupWithDefaultFM0133(wx4, wx30100, wx31, wx32, wx33, wx34, wx579, ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0331(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM036(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2300), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, Succ(wx12600), bh) → new_lookupWithDefaultFM0284(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx12600, new_primMulNat0(Succ(wx1207), wx1202), bh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0447(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196200), Zero, fd) → new_lookupWithDefaultFM0400(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196000), Zero, fd) → new_lookupWithDefaultFM0390(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM065(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM052(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0198(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8040), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM021(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0419(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Zero, Succ(Succ(wx199000)), gf) → new_lookupWithDefaultFM0422(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf)
new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Succ(Zero), h) → new_lookupWithDefaultFM025(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0133(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0341(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Pos(Zero)), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0144(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM091(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0346(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0479(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM044(wx1596, wx1597, wx1598, wx1599, wx1600, wx1601, wx1602, wx1603, be) → new_lookupWithDefaultFM020(wx1596, wx1600, Float(Pos(Succ(wx1602)), Neg(Succ(wx1603))), be)
new_lookupWithDefaultFM0338(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx107000), Succ(Succ(wx190400)), da) → new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190400, wx107000, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM00(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Zero, wx235, h) → new_lookupWithDefaultFM016(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM01(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, wx236, h) → new_lookupWithDefaultFM0531(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h)
new_lookupWithDefaultFM050(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx2860), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0260(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0527(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(wx6160), wx617, wx618, wx619, wx620, wx621, Pos(wx6220), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(wx6220)), fd)
new_lookupWithDefaultFM0112(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0352(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM096(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0349(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0121(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11160), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM0530(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Zero)), h)
new_lookupWithDefaultFM0370(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, fb) → new_lookupWithDefaultFM0371(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, new_primMulNat0(Succ(wx1361), wx1356), fb)
new_lookupWithDefaultFM0260(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10270), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0149(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6370), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Zero)), da)
new_lookupWithDefaultFM0(wx203, wx204, Neg(wx2050), wx206, wx207, wx208, wx209, wx210, Pos(wx2110), Zero, h) → new_lookupWithDefaultFM08(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0188(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0232(wx1867, wx1868, wx1869, wx1870, wx1871, wx1872, wx1873, wx1874, bae) → new_lookupWithDefaultFM020(wx1867, wx1872, Float(Neg(Zero), Pos(Succ(wx1874))), bae)
new_lookupWithDefaultFM0402(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Zero, Succ(Succ(wx191400)), fd) → new_lookupWithDefaultFM0405(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, fd)
new_lookupWithDefaultFM0395(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Succ(Zero), h) → new_lookupWithDefaultFM0547(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0387(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx137100), Succ(Succ(wx196000)), fd) → new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196000, wx137100, fd)
new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0455(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx10930), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM043(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx265, ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0543(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0211(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx856, ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, Zero, bah) → new_lookupWithDefaultFM0512(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Succ(wx1544), wx1539), bah)
new_lookupWithDefaultFM04(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25700)), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Zero), wx206, wx207, wx208, wx209, wx210, Pos(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM05(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0(wx203, wx204, Pos(wx2050), wx206, wx207, wx208, wx209, wx210, Neg(wx2110), Zero, h) → new_lookupWithDefaultFM09(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0358(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb) → new_lookupWithDefaultFM020(wx1310, wx1316, Float(Pos(Zero), Pos(Succ(wx1317))), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0185(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0443(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0451(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0517(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Succ(Succ(wx203200)), bbb) → new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx200100, wx203200, bbb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Zero)), ba) → new_lookupWithDefaultFM034(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0548(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Succ(Succ(wx194400)), h) → new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx115200, wx194400, h)
new_lookupWithDefaultFM092(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0346(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, Zero, bag) → new_lookupWithDefaultFM0505(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Succ(wx1535), wx1530), bag)
new_lookupWithDefaultFM0292(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, Succ(wx19490), ca) → new_lookupWithDefaultFM0293(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca)
new_lookupWithDefaultFM0220(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8970), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM077(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0200(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Zero)), ba) → new_lookupWithDefaultFM0156(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0444(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0456(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0497(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx20000), baf) → new_lookupWithDefaultFM0498(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx20000, new_primMulNat0(Succ(wx1526), wx1521), baf)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0374(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0324(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM0339(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx19050), da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Pos(Zero)), da)
new_lookupWithDefaultFM073(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, ce) → new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, new_primMulNat0(Succ(wx1241), wx1236), ce)
new_lookupWithDefaultFM0539(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM012(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM0257(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0449(wx830, wx831, wx833, wx834, wx835, wx836, wx837, Succ(wx10920), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Zero)), hh)
new_lookupWithDefaultFM076(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0304(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0276(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, bg) → new_lookupWithDefaultFM0277(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, new_primMulNat0(Zero, wx1192), bg)
new_lookupWithDefaultFM040(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx2420), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0138(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM041(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2490), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM087(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4160), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0314(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Zero, da) → new_lookupWithDefaultFM0343(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, new_primMulNat0(Zero, wx40000), da)
new_lookupWithDefaultFM0343(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx19070), da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Neg(Zero)), da)
new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Succ(wx202000), cc) → new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx199500, wx202000, cc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0479(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0310(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4480), da) → new_lookupWithDefaultFM0316(wx398, wx399, Succ(wx40000), wx401, wx402, wx403, wx404, wx405, Succ(wx40600), da)
new_lookupWithDefaultFM0456(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx10940), hh) → new_lookupWithDefaultFM0485(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10940, new_primMulNat0(Zero, wx83200), hh)
new_lookupWithDefaultFM055(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3010), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0179(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67400)), Zero, fd) → new_lookupWithDefaultFM0392(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0484(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM068(wx4, wx30100, wx31, wx32, wx33, wx34, wx348, ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Zero)), ba) → new_lookupWithDefaultFM0217(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0112(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5120), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0184(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0438(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0326(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0189(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM026(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx10470), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Zero)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0131(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, wx6240, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM030(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx10600), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0202(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11320), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Succ(wx263000))), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM076(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0167(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0143(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx6050), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(wx8320), wx833, wx834, wx835, wx836, wx837, Pos(wx8380), Succ(wx8400), hh) → new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx12590), da) → new_lookupWithDefaultFM0323(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx12590, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM0294(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0290(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM0182(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0177(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0423(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0377(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM072(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0303(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0235(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191400), Succ(wx108200), fd) → new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191400, wx108200, fd)
new_lookupWithDefaultFM029(wx1587, wx1588, wx1589, wx1590, wx1591, wx1592, wx1593, wx1594, bb) → new_lookupWithDefaultFM020(wx1587, wx1591, Float(Pos(Succ(wx1593)), Pos(Succ(wx1594))), bb)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0461(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, Succ(wx12610), ca) → new_lookupWithDefaultFM0291(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx12610, new_primMulNat0(Succ(wx1216), wx1211), ca)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0219(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0418(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx19200), gf) → new_lookupWithDefaultFM0419(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx19200, new_primMulNat0(Succ(wx1427), wx1422), gf)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0455(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM0202(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0284(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, wx12600, wx1946, bh) → new_lookupWithDefaultFM020(wx1200, wx1206, Float(Pos(Zero), Pos(Succ(wx1207))), bh)
new_lookupWithDefaultFM096(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4410), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0312(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx10700), da) → new_lookupWithDefaultFM0338(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx10700, new_primMulNat0(Zero, wx40000), da)
new_lookupWithDefaultFM0257(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11450), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM031(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0268(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0110(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5000), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67200), Zero, fd) → new_lookupWithDefaultFM0382(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0119(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx532, ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Zero, hh) → new_lookupWithDefaultFM0466(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0328(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0331(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0132(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0366(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, Zero, bh) → new_lookupWithDefaultFM0285(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Succ(wx1207), wx1202), bh)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Zero), wx617, wx618, wx619, wx620, wx621, Pos(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Zero)), fd)
new_lookupWithDefaultFM0230(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9310), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0447(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx10900), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0128(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5610), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, wx6240, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM0448(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx10910), hh) → new_lookupWithDefaultFM0467(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10910, new_primMulNat0(Zero, wx83200), hh)
new_lookupWithDefaultFM071(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0300(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0462(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0469(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Zero)), hh)
new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx19100), eb) → new_lookupWithDefaultFM0355(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, wx19100, new_primMulNat0(Succ(wx1317), wx1312), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM088(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM095(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx11110), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Succ(wx5000)), Pos(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM041(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0104(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4820), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0506(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM020(wx1528, wx1534, Float(Neg(Zero), Pos(Succ(wx1535))), bag)
new_lookupWithDefaultFM0259(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10220), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, Succ(wx19370), cf) → new_lookupWithDefaultFM020(wx1243, wx1248, Float(Pos(Zero), Neg(Succ(wx1249))), cf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0224(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0263(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx10300), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45600)), Zero, da) → new_lookupWithDefaultFM0318(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0116(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0359(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0233(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9360), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Succ(wx40800), da) → new_lookupWithDefaultFM0329(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM080(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Succ(wx192800), hh) → new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109400, wx192800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0218(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0320(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM083(wx4, wx30100, wx31, wx32, wx33, wx34, wx395, ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0148(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6320), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(wx2050), wx206, wx207, wx208, wx209, wx210, Pos(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM01(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19010), h) → new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19010, new_primMulNat0(Succ(wx21100), wx20500), h)
new_lookupWithDefaultFM0192(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0430(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM062(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0295(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0528(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11490, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Zero)), h)
new_lookupWithDefaultFM0136(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5810), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, Succ(wx16050), bah) → new_lookupWithDefaultFM0511(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, wx16050, new_primMulNat0(Succ(wx1544), wx1539), bah)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, Zero, hh) → new_lookupWithDefaultFM0462(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM042(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2540), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0134(wx1721, wx1722, wx1723, wx1724, wx1725, wx1726, wx1727, eg) → new_lookupWithDefaultFM0367(wx1721, wx1722, wx1723, wx1724, wx1725, wx1726, wx1727, eg)
new_lookupWithDefaultFM0410(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1391), wx1385), fh)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Zero), wx401, wx402, wx403, wx404, wx405, Neg(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Zero)), da)
new_lookupWithDefaultFM0102(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4700), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, Succ(wx19340), bc) → new_lookupWithDefaultFM020(wx1164, wx1169, Float(Pos(Succ(wx1170)), Pos(Succ(wx1171))), bc)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Zero), Zero, fd) → new_lookupWithDefaultFM0376(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM00(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Zero, wx235, h) → new_lookupWithDefaultFM017(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0347(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, dd) → new_lookupWithDefaultFM0348(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, new_primMulNat0(Succ(wx1281), wx1275), dd)
new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx14800), hh) → new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14800, new_primMulNat0(Succ(wx83800), wx83200), hh)
new_lookupWithDefaultFM0280(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, bg) → new_lookupWithDefaultFM020(wx1191, wx1197, Float(Pos(Zero), Pos(Succ(wx1198))), bg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0128(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45600), Succ(wx40800), da) → new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45600, wx40800, da)
new_lookupWithDefaultFM0138(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0369(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0388(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM0115(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0302(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, ce) → new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, new_primMulNat0(Succ(wx1241), wx1236), ce)
new_lookupWithDefaultFM0382(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0385(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, Succ(wx16040), bag) → new_lookupWithDefaultFM0504(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, wx16040, new_primMulNat0(Succ(wx1535), wx1530), bag)
new_lookupWithDefaultFM067(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3450), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0205(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0460(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0183(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7500), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0540(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM013(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0238(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9510), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), 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, wx1421), gf)
new_lookupWithDefaultFM0402(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx108200), Succ(Succ(wx191400)), fd) → new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191400, wx108200, fd)
new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Succ(wx192600), hh) → new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109100, wx192600, hh)
new_lookupWithDefaultFM035(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx2230), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0204(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0139(wx4, wx30100, wx31, wx32, wx33, wx34, wx596, ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0195(wx1825, wx1826, wx1827, wx1828, wx1829, wx1830, wx1831, hc) → new_lookupWithDefaultFM0431(wx1825, wx1826, wx1827, wx1828, wx1829, wx1830, wx1831, hc)
new_lookupWithDefaultFM015(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM05(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Succ(wx62400), fd) → new_lookupWithDefaultFM0393(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0213(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0178(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0548(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Succ(Zero), h) → new_lookupWithDefaultFM0550(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0444(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM072(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0351(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, Succ(wx19750), df) → new_lookupWithDefaultFM020(wx1283, wx1288, Float(Pos(Succ(wx1289)), Neg(Succ(wx1290))), df)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Pos(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM04(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), wx6240, fd)
new_lookupWithDefaultFM0319(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0157(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0413(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0441(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), Zero, hh) → new_lookupWithDefaultFM0474(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0117(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM010(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, h) → new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0272(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, bd) → new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, new_primMulNat0(Succ(wx1180), wx1174), bd)
new_lookupWithDefaultFM0250(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx9950), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0450(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0375(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Zero, hh) → new_lookupWithDefaultFM0484(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0230(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0496(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0157(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6570), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0407(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx19170), fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Neg(Zero)), fd)
new_lookupWithDefaultFM0117(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0359(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0230(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0250(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0287(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0283(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0439(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67200), Succ(wx62400), fd) → new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67200, wx62400, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0156(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx11230), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Succ(wx5000)), Pos(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0163(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Zero), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67200)), Succ(wx62400), fd) → new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67200, wx62400, fd)
new_lookupWithDefaultFM0515(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, bbb) → new_lookupWithDefaultFM0516(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, new_primMulNat0(Zero, wx1547), bbb)
new_lookupWithDefaultFM0204(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8210), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0528(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Succ(Succ(wx194200)), h) → new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx114900, wx194200, h)
new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195200), Succ(wx125900), da) → new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195200, wx125900, da)
new_lookupWithDefaultFM0472(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(wx8380)), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM071(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0314(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx10730), da) → new_lookupWithDefaultFM0342(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx10730, new_primMulNat0(Zero, wx40000), da)
new_lookupWithDefaultFM039(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx10980), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Succ(wx5000)), Neg(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0211(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0112(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0142(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0507(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0503(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0498(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx20000, Zero, baf) → new_lookupWithDefaultFM020(wx1519, wx1525, Float(Neg(Zero), Pos(Succ(wx1526))), baf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0243(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Zero, gh) → new_lookupWithDefaultFM0427(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, new_primMulNat0(Succ(wx1437), wx1432), gh)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0313(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM0138(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5930), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0304(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, cf) → new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, new_primMulNat0(Succ(wx1249), wx1244), cf)
new_lookupWithDefaultFM0501(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Zero, wx1529), bag)
new_lookupWithDefaultFM0485(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Succ(Zero), hh) → new_lookupWithDefaultFM0487(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM088(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4210), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0150(wx1375, wx1376, wx1377, wx1378, wx1379, wx1380, wx1381, wx1382, ff) → new_lookupWithDefaultFM020(wx1375, wx1379, Float(Neg(Succ(wx1381)), Pos(Succ(wx1382))), ff)
new_lookupWithDefaultFM092(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4360), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0189(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7770), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19000), h) → new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19000, new_primMulNat0(Succ(wx21100), wx20500), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0126(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), 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, wx1421), gf)
new_lookupWithDefaultFM0288(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Zero, wx1210), ca)
new_lookupWithDefaultFM0197(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0433(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0214(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8650), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0110(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Zero, h) → new_lookupWithDefaultFM021(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0107(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4920), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Zero), hh) → new_lookupWithDefaultFM0459(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM048(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0253(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx10000), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM055(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0288(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0226(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx917, ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM099(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx199000), Zero, gf) → new_lookupWithDefaultFM0422(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf)
new_lookupWithDefaultFM089(wx1265, wx1266, wx1267, wx1268, wx1269, wx1270, wx1271, wx1272, db) → new_lookupWithDefaultFM020(wx1265, wx1269, Float(Pos(Succ(wx1271)), Pos(Succ(wx1272))), db)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Zero, cc) → new_lookupWithDefaultFM0299(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, cc)
new_lookupWithDefaultFM0311(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4500), da) → new_lookupWithDefaultFM0321(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45600), Zero, da) → new_lookupWithDefaultFM0318(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0375(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6660), fd) → new_lookupWithDefaultFM0385(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0487(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Zero)), hh)
new_lookupWithDefaultFM03(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx238, h) → new_lookupWithDefaultFM0538(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM085(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30000), Succ(wx30000)), ba)
new_lookupWithDefaultFM0388(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx19610), fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0165(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM04(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25700)), h) → new_lookupWithDefaultFM018(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2040, wx25700, h)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0446(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM086(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM060(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM0242(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0131(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0366(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0137(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0369(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0152(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0410(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0160(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx684, ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0255(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10120), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), wx4080, da)
new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19010, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM0488(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, bab) → new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, new_primMulNat0(Succ(wx1499), wx1493), bab)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM028(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM098(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0349(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Zero, hh) → new_lookupWithDefaultFM0461(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(wx8320), wx833, wx834, wx835, wx836, wx837, Neg(wx8380), Succ(wx8400), hh) → new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx13720), fd) → new_lookupWithDefaultFM0397(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx13720, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM0191(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7800), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0194(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0448(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM090(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4240), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0420(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx19910), gf) → new_lookupWithDefaultFM020(wx1420, wx1426, Float(Neg(Zero), Pos(Succ(wx1427))), gf)
new_lookupWithDefaultFM058(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Zero, wx1210), ca)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191600), Zero, fd) → new_lookupWithDefaultFM0409(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, fd)
new_lookupWithDefaultFM0452(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Zero, hh) → new_lookupWithDefaultFM0487(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0251(wx4, wx30100, wx31, wx32, wx33, wx34, wx998, ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0246(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0219(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8920), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0315(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM04(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM019(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM03(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Zero, wx238, h) → new_lookupWithDefaultFM0540(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), wx6240, fd)
new_lookupWithDefaultFM069(wx1625, wx1626, wx1627, wx1628, wx1629, wx1630, wx1631, cd) → new_lookupWithDefaultFM020(wx1625, wx1629, Float(Pos(Zero), Pos(Succ(wx1631))), cd)
new_lookupWithDefaultFM010(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25900)), h) → new_lookupWithDefaultFM0541(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2040, wx25900, h)
new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Succ(wx196800), hh) → new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148100, wx196800, hh)
new_lookupWithDefaultFM0105(wx1292, wx1293, wx1294, wx1295, wx1296, wx1297, wx1298, wx1299, dg) → new_lookupWithDefaultFM020(wx1292, wx1296, Float(Pos(Succ(wx1298)), Neg(Succ(wx1299))), dg)
new_lookupWithDefaultFM056(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0288(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0109(wx1301, wx1302, wx1303, wx1304, wx1305, wx1306, wx1307, wx1308, dh) → new_lookupWithDefaultFM020(wx1301, wx1306, Float(Pos(Zero), Pos(Succ(wx1308))), dh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM066(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM050(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0245(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0515(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0124(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5460), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, Succ(wx19400), bbd) → new_lookupWithDefaultFM020(wx1563, wx1568, Float(Neg(Zero), Pos(Succ(wx1569))), bbd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0271(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0270(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0198(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0532(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19300), h) → new_lookupWithDefaultFM0533(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), h)
new_lookupWithDefaultFM0446(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0491(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0490(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0494(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, bac) → new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, new_primMulNat0(Succ(wx1508), wx1502), bac)
new_lookupWithDefaultFM0285(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, Succ(wx19470), bh) → new_lookupWithDefaultFM0286(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh)
new_lookupWithDefaultFM0453(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0440(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), Zero, hh) → new_lookupWithDefaultFM0471(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0132(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0514(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0510(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0215(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8700), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM027(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx10530), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0471(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx19220), hh) → new_lookupWithDefaultFM0472(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0424(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh) → new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM0172(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7230), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM056(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0203(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM016(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM06(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0190(wx1449, wx1450, wx1451, wx1452, wx1453, wx1454, wx1455, hb) → new_lookupWithDefaultFM020(wx1449, wx1453, Float(Neg(Zero), Pos(Succ(wx1455))), hb)
new_lookupWithDefaultFM00(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx235, h) → new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx235, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0480(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0172(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0454(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8860), hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM051(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2930), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0111(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5070), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0473(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0117(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5240), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0374(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6640), fd) → new_lookupWithDefaultFM0380(wx614, wx615, Succ(wx61600), wx617, wx618, wx619, wx620, wx621, Succ(wx62200), fd)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Succ(wx89000)), hh) → new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx89000, hh)
new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx198600), Zero, eb) → new_lookupWithDefaultFM0358(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb)
new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Zero, h) → new_lookupWithDefaultFM0547(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM031(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2160), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0224(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx9070), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0106(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0110(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0352(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0385(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Zero), wx401, wx402, wx403, wx404, wx405, Pos(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Zero)), da)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Zero), Zero, da) → new_lookupWithDefaultFM0314(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Zero), wx206, wx207, wx208, wx209, wx210, Pos(Zero), Zero, h) → new_lookupWithDefaultFM07(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx199200), Succ(wx192100), gh) → new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, wx199200, wx192100, gh)
new_lookupWithDefaultFM0127(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5560), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM059(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Zero, h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Zero, ed) → new_lookupWithDefaultFM0363(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, new_primMulNat0(Succ(wx1327), wx1322), ed)
new_lookupWithDefaultFM0376(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Zero, fd) → new_lookupWithDefaultFM0403(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, new_primMulNat0(Zero, wx61600), fd)
new_lookupWithDefaultFM0378(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Zero, fd) → new_lookupWithDefaultFM0407(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, new_primMulNat0(Zero, wx61600), fd)
new_lookupWithDefaultFM017(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM07(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0183(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM047(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0276(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0495(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0494(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM090(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0346(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM028(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx10570), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primMulNat0(wx5000, wx30000), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM055(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0394(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx13710), fd) → new_lookupWithDefaultFM0387(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx13710, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM078(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, cf) → new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, new_primMulNat0(Succ(wx1249), wx1244), cf)
new_lookupWithDefaultFM0151(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6400), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM09(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), Zero, h) → new_lookupWithDefaultFM0535(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0513(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM020(wx1537, wx1543, Float(Neg(Zero), Neg(Succ(wx1544))), bah)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM062(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0215(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM0141(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0244(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9730), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Zero)), ba) → new_lookupWithDefaultFM095(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, Succ(wx19350), bd) → new_lookupWithDefaultFM020(wx1173, wx1178, Float(Pos(Succ(wx1179)), Neg(Succ(wx1180))), bd)
new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14810, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM00(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx235, h) → new_lookupWithDefaultFM015(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0228(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0174(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM045(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0297(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Succ(Succ(wx202000)), cc) → new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx199500, wx202000, cc)
new_lookupWithDefaultFM0307(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0306(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM070(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3500), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0192(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7870), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0111(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0352(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0519(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, bbb) → new_lookupWithDefaultFM020(wx1546, wx1552, Float(Neg(Zero), Neg(Succ(wx1553))), bbb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0457(wx830, wx831, wx833, wx834, wx835, wx836, wx837, Succ(wx10950), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Zero)), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Zero)), ba) → new_lookupWithDefaultFM039(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0467(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Succ(Succ(wx192600)), hh) → new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109100, wx192600, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0176(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11270), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0394(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0196(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11310), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM0234(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0501(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM075(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3650), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0145(wx1363, wx1364, wx1365, wx1366, wx1367, wx1368, wx1369, fc) → new_lookupWithDefaultFM020(wx1363, wx1367, Float(Pos(Zero), Neg(Succ(wx1369))), fc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM030(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0237(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11400), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191600), Succ(wx108500), fd) → new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191600, wx108500, fd)
new_lookupWithDefaultFM0265(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10420), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0517(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Succ(Zero), bbb) → new_lookupWithDefaultFM0519(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, bbb)
new_lookupWithDefaultFM059(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11040), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Neg(Zero)), 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(wx1400), wx1394), gb)
new_lookupWithDefaultFM05(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx11480), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Zero), hh) → new_lookupWithDefaultFM0477(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0223(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0333(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(Succ(wx195400)), da) → new_lookupWithDefaultFM0336(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0118(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0359(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Succ(wx194200), h) → new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx114900, wx194200, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0159(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0258(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx10150), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195200), Zero, da) → new_lookupWithDefaultFM0326(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0498(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Succ(Zero), baf) → new_lookupWithDefaultFM0500(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, baf)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM0166(wx1402, wx1403, wx1404, wx1405, wx1406, wx1407, wx1408, wx1409, gc) → new_lookupWithDefaultFM020(wx1402, wx1406, Float(Neg(Succ(wx1408)), Neg(Succ(wx1409))), gc)
new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190600), Zero, da) → new_lookupWithDefaultFM0345(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, da)
new_lookupWithDefaultFM0216(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, bab) → new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, new_primMulNat0(Succ(wx1499), wx1493), bab)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0102(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0149(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0122(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0393(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx198600), Succ(wx191000), eb) → new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, wx198600, wx191000, eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0180(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0400(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0218(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0492(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM063(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx331, ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0261(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, bbe) → new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, new_primMulNat0(Succ(wx1577), wx1572), bbe)
new_lookupWithDefaultFM0155(wx1754, wx1755, wx1756, wx1757, wx1758, wx1759, wx1760, wx1761, fg) → new_lookupWithDefaultFM0411(wx1754, wx1755, wx1756, wx1757, wx1758, wx1759, wx1760, wx1761, fg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM097(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM087(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0199(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Zero, h) → new_lookupWithDefaultFM0530(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0277(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx19940), bg) → new_lookupWithDefaultFM0278(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx19940, new_primMulNat0(Succ(wx1198), wx1193), bg)
new_lookupWithDefaultFM0152(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6470), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0253(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0520(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0243(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0515(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0243(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9660), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0170(wx1411, wx1412, wx1413, wx1414, wx1415, wx1416, wx1417, wx1418, gd) → new_lookupWithDefaultFM020(wx1411, wx1416, Float(Neg(Zero), Pos(Succ(wx1418))), gd)
new_lookupWithDefaultFM0452(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8840), hh) → new_lookupWithDefaultFM0473(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0192(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0212(wx1849, wx1850, wx1851, wx1852, wx1853, wx1854, wx1855, wx1856, baa) → new_lookupWithDefaultFM020(wx1849, wx1853, Float(Neg(Succ(wx1855)), Pos(Succ(wx1856))), baa)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM036(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0124(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0437(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0233(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0159(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0413(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0165(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6980), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0349(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, df) → new_lookupWithDefaultFM0351(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, new_primMulNat0(Succ(wx1290), wx1284), df)
new_lookupWithDefaultFM0477(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0480(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0353(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb) → new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, new_primMulNat0(Zero, wx1311), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM082(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM091(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM061(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45800), Zero, da) → new_lookupWithDefaultFM0328(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0363(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx19890), ed) → new_lookupWithDefaultFM020(wx1320, wx1326, Float(Pos(Zero), Neg(Succ(wx1327))), ed)
new_lookupWithDefaultFM0511(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, wx16050, wx1972, bah) → new_lookupWithDefaultFM020(wx1537, wx1543, Float(Neg(Zero), Neg(Succ(wx1544))), bah)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM051(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM052(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0287(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0398(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Succ(wx89000)), hh) → new_lookupWithDefaultFM0478(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0446(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8800), hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0265(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0283(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Zero, wx1201), bh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0188(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7720), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0153(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6520), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0450(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8820), hh) → new_lookupWithDefaultFM0470(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM046(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0252(wx1885, wx1886, wx1887, wx1888, wx1889, wx1890, wx1891, bbc) → new_lookupWithDefaultFM020(wx1885, wx1889, Float(Neg(Zero), Pos(Succ(wx1891))), bbc)
new_lookupWithDefaultFM0503(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Zero, wx1529), bag)
new_lookupWithDefaultFM0485(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Succ(Succ(wx192800)), hh) → new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109400, wx192800, hh)
new_lookupWithDefaultFM0512(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, Succ(wx19730), bah) → new_lookupWithDefaultFM0513(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah)
new_lookupWithDefaultFM0266(wx4, wx30100, wx31, wx32, wx33, wx34, wx1045, ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0371(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, Succ(wx19770), fb) → new_lookupWithDefaultFM020(wx1355, wx1360, Float(Pos(Zero), Neg(Succ(wx1361))), fb)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0365(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed) → new_lookupWithDefaultFM020(wx1320, wx1326, Float(Pos(Zero), Neg(Succ(wx1327))), ed)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Neg(Zero), Zero, h) → new_lookupWithDefaultFM012(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM032(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2210), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0423(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh) → new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM0426(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx192100), Succ(Succ(wx199200)), gh) → new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, wx199200, wx192100, gh)
new_lookupWithDefaultFM0118(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5290), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0256(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, bbd) → new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, new_primMulNat0(Succ(wx1569), wx1564), bbd)
new_lookupWithDefaultFM0241(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Zero, wx1538), bah)
new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Succ(Succ(wx198200)), h) → new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190000, wx198200, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0312(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Zero, da) → new_lookupWithDefaultFM0339(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, new_primMulNat0(Zero, wx40000), da)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx238, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0535(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19320), h) → new_lookupWithDefaultFM0536(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), h)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Zero), wx617, wx618, wx619, wx620, wx621, Neg(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Zero)), fd)
new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Succ(Zero), hh) → new_lookupWithDefaultFM0484(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0164(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6930), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0384(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Zero, hh) → new_lookupWithDefaultFM0477(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0236(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Zero, wx1529), bag)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0157(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM049(wx1607, wx1608, wx1609, wx1610, wx1611, wx1612, wx1613, wx1614, bf) → new_lookupWithDefaultFM020(wx1607, wx1612, Float(Pos(Zero), Pos(Succ(wx1614))), bf)
new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Zero, bbb) → new_lookupWithDefaultFM0519(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, bbb)
new_lookupWithDefaultFM07(wx203, wx204, wx206, wx207, wx208, wx209, wx210, Succ(wx11500), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Zero)), h)
new_lookupWithDefaultFM0209(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8480), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0130(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5640), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0262(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11460), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM0517(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx20010, Zero, bbb) → new_lookupWithDefaultFM020(wx1546, wx1552, Float(Neg(Zero), Neg(Succ(wx1553))), bbb)
new_lookupWithDefaultFM0245(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9780), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0115(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11150), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM045(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0276(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Succ(wx198200), h) → new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190000, wx198200, h)
new_lookupWithDefaultFM032(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0271(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM048(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx284, ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM098(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4650), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0411(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1391), wx1385), fh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0437(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0447(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0158(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0303(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0302(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0178(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7400), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM031(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0526(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, bbe) → new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, new_primMulNat0(Succ(wx1577), wx1572), bbe)
new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Zero, bg) → new_lookupWithDefaultFM0280(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, bg)
new_lookupWithDefaultFM0392(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0395(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0359(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed) → new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, new_primMulNat0(Zero, wx1321), ed)
new_lookupWithDefaultFM010(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM0543(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0108(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0459(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0462(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(wx6160), wx617, wx618, wx619, wx620, wx621, Neg(wx6220), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(wx6220)), fd)
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(wx1427), wx1422), gf)
new_lookupWithDefaultFM0433(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, hf) → new_lookupWithDefaultFM0435(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, new_primMulNat0(Succ(wx1471), wx1466), hf)
new_lookupWithDefaultFM0333(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx126200), Succ(Succ(wx195400)), da) → new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195400, wx126200, da)
new_lookupWithDefaultFM0234(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9430), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0342(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx107300), Succ(Succ(wx190600)), da) → new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190600, wx107300, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), 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(wx1400), wx1394), gb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM093(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0106(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx4850), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM074(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0242(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11420), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0266(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Zero), Zero, fd) → new_lookupWithDefaultFM0378(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM054(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx11020), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Zero), wx206, wx207, wx208, wx209, wx210, Neg(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM011(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0485(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10940, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Zero)), hh)
new_lookupWithDefaultFM0214(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0488(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0534(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM09(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM071(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3570), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0500(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, baf) → new_lookupWithDefaultFM020(wx1519, wx1525, Float(Neg(Zero), Pos(Succ(wx1526))), baf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0206(wx1473, wx1474, wx1475, wx1476, wx1477, wx1478, wx1479, hg) → new_lookupWithDefaultFM020(wx1473, wx1477, Float(Neg(Zero), Neg(Succ(wx1479))), hg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0235(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0507(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0536(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(wx2110)), h)
new_lookupWithDefaultFM0379(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6700), fd) → new_lookupWithDefaultFM0401(wx614, wx615, Succ(wx61600), wx617, wx618, wx619, wx620, wx621, Succ(wx62200), fd)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Succ(wx88800)), hh) → new_lookupWithDefaultFM0460(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0356(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx19870), eb) → new_lookupWithDefaultFM020(wx1310, wx1316, Float(Pos(Zero), Pos(Succ(wx1317))), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0164(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx14810), hh) → new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14810, new_primMulNat0(Succ(wx83800), wx83200), hh)
new_lookupWithDefaultFM0504(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, wx16040, wx1970, bag) → new_lookupWithDefaultFM020(wx1528, wx1534, Float(Neg(Zero), Pos(Succ(wx1535))), bag)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Succ(Succ(Succ(wx263000))), h) → new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2380, wx263000, h)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Succ(Succ(Succ(wx261000))), h) → new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2350, wx261000, h)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0454(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0258(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0524(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0377(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0368(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, Succ(wx19760), eh) → new_lookupWithDefaultFM020(wx1347, wx1352, Float(Pos(Zero), Pos(Succ(wx1353))), eh)
new_lookupWithDefaultFM013(wx203, wx204, wx206, wx207, wx208, wx209, wx210, Succ(wx11530), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Zero)), h)
new_lookupWithDefaultFM0278(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Succ(Succ(wx201800)), bg) → new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx199400, wx201800, bg)
new_lookupWithDefaultFM0360(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed) → new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, new_primMulNat0(Zero, wx1321), ed)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM042(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0247(wx1876, wx1877, wx1878, wx1879, wx1880, wx1881, wx1882, wx1883, bba) → new_lookupWithDefaultFM020(wx1876, wx1881, Float(Neg(Zero), Neg(Succ(wx1883))), bba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), wx4080, da)
new_lookupWithDefaultFM0524(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, bbe) → new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, new_primMulNat0(Succ(wx1577), wx1572), bbe)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx199200), Zero, gh) → new_lookupWithDefaultFM0429(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh)
new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx19110), ed) → new_lookupWithDefaultFM0362(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, wx19110, new_primMulNat0(Succ(wx1327), wx1322), ed)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45800)), Zero, da) → new_lookupWithDefaultFM0328(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Zero), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0248(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0336(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0208(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM037(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Zero, h) → new_lookupWithDefaultFM0543(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0378(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx10850), fd) → new_lookupWithDefaultFM0406(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx10850, new_primMulNat0(Zero, wx61600), fd)
new_lookupWithDefaultFM0297(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx19950, Zero, cc) → new_lookupWithDefaultFM020(wx1218, wx1224, Float(Pos(Zero), Neg(Succ(wx1225))), cc)
new_lookupWithDefaultFM0355(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Zero, Succ(Succ(wx198600)), eb) → new_lookupWithDefaultFM0358(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb)
new_lookupWithDefaultFM0323(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(Succ(wx195200)), da) → new_lookupWithDefaultFM0326(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0313(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0263(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Succ(wx40800), da) → new_lookupWithDefaultFM0319(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM030(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0268(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0492(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, bac) → new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, new_primMulNat0(Succ(wx1508), wx1502), bac)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Neg(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM010(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0248(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9830), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45800), Succ(wx40800), da) → new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45800, wx40800, da)
new_lookupWithDefaultFM0313(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4520), da) → new_lookupWithDefaultFM0331(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0144(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx6100), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0449(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0362(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx191100), Succ(Succ(wx198800)), ed) → new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, wx198800, wx191100, ed)
new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191400), Zero, fd) → new_lookupWithDefaultFM0405(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM075(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Zero)), ba) → new_lookupWithDefaultFM0101(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0171(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7160), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Zero, da) → new_lookupWithDefaultFM0330(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM043(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0268(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, bc) → new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, new_primMulNat0(Succ(wx1171), wx1165), bc)
new_lookupWithDefaultFM0194(wx4, wx30100, wx31, wx32, wx33, wx34, wx795, ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(wx62400), fd) → new_lookupWithDefaultFM0393(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM037(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2390), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0172(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0416(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0490(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, bab) → new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, new_primMulNat0(Succ(wx1499), wx1493), bab)
new_lookupWithDefaultFM0439(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0449(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Succ(wx203000), baf) → new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx200000, wx203000, baf)
new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, Succ(wx19390), bac) → new_lookupWithDefaultFM020(wx1501, wx1506, Float(Neg(Succ(wx1507)), Neg(Succ(wx1508))), bac)
new_lookupWithDefaultFM0334(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx19550), da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0251(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0210(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0137(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5880), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0210(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8530), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67400), Succ(wx62400), fd) → new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67400, wx62400, fd)
new_lookupWithDefaultFM0254(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0520(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM090(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0253(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0467(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10910, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Zero)), hh)
new_lookupWithDefaultFM0213(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx8580), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0169(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7130), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0470(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67400), Zero, fd) → new_lookupWithDefaultFM0392(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0229(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, Zero, hh) → new_lookupWithDefaultFM0480(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM077(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3770), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0122(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5340), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0397(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(Succ(wx196200)), fd) → new_lookupWithDefaultFM0400(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0390(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67400)), Succ(wx62400), fd) → new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67400, wx62400, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Succ(wx196600), hh) → new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148000, wx196600, hh)
new_lookupWithDefaultFM08(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), Zero, h) → new_lookupWithDefaultFM0532(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0147(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6250), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Zero)), ba) → new_lookupWithDefaultFM0222(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0406(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Zero, Succ(Succ(wx191600)), fd) → new_lookupWithDefaultFM0409(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0426(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Zero, Succ(Succ(wx199200)), gh) → new_lookupWithDefaultFM0429(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh)
new_lookupWithDefaultFM0337(wx398, wx399, wx4000, wx401, wx402, wx403, wx404, wx405, wx4060, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(wx4060)), da)
new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Succ(wx203200), bbb) → new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx200100, wx203200, bbb)
new_lookupWithDefaultFM0293(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM020(wx1209, wx1215, Float(Pos(Zero), Neg(Succ(wx1216))), ca)
new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx19210), gh) → new_lookupWithDefaultFM0426(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, wx19210, new_primMulNat0(Succ(wx1437), wx1432), gh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0158(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0413(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0264(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10370), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Pos(Zero), Zero, h) → new_lookupWithDefaultFM06(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM010(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Zero), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM072(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3620), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0107(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM032(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat1(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0209(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx198800), Zero, ed) → new_lookupWithDefaultFM0365(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(wx40800), da) → new_lookupWithDefaultFM0319(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM026(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0456(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Succ(wx194400), h) → new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx115200, wx194400, h)
new_lookupWithDefaultFM057(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3130), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0231(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx198800), Succ(wx191100), ed) → new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, wx198800, wx191100, ed)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0264(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx238, Zero, h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0311(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0461(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195400), Succ(wx126200), da) → new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195400, wx126200, da)
new_lookupWithDefaultFM0239(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0508(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0387(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(Succ(wx196000)), fd) → new_lookupWithDefaultFM0390(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0207(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30000), Succ(wx30000)), ba)
new_lookupWithDefaultFM0538(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM011(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM056(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3080), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Succ(wx263000), h) → new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2380, wx263000, h)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(wx88800), hh) → new_lookupWithDefaultFM0460(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0548(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11520, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Zero)), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0146(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30000), Succ(wx30000)), ba)
new_lookupWithDefaultFM0162(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx11240), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Succ(wx5000)), Neg(Zero)), ba)
new_lookupWithDefaultFM0238(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0508(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0136(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0369(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(wx89000), hh) → new_lookupWithDefaultFM0478(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM04(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM021(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0223(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx9000), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0153(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0410(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, Succ(wx9130), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(wx8380)), hh)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Zero), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM063(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM075(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0304(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0167(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7010), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196200), Succ(wx137200), fd) → new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196200, wx137200, fd)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0330(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0193(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7920), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0249(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Succ(wx62400), fd) → new_lookupWithDefaultFM0383(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupWithDefaultFM079(wx4, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Succ(wx261000))), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM084(wx1633, wx1634, wx1635, wx1636, wx1637, wx1638, wx1639, cg) → new_lookupWithDefaultFM020(wx1633, wx1637, Float(Pos(Zero), Neg(Succ(wx1639))), cg)
new_lookupWithDefaultFM0434(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, hf) → new_lookupWithDefaultFM0435(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, new_primMulNat0(Succ(wx1471), wx1466), hf)
new_lookupWithDefaultFM0259(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0524(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Zero, h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0403(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx19150), fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Pos(Zero)), fd)
new_lookupWithDefaultFM0281(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Zero, wx1201), bh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Succ(Succ(wx198400)), h) → new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190100, wx198400, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0113(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0179(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7450), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM074(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx11070), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupWithDefaultFM0235(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9480), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM033(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, bc) → new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, new_primMulNat0(Succ(wx1171), wx1165), bc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0330(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Succ(wx201800), bg) → new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx199400, wx201800, bg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0215(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0491(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM0176(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0244(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0113(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx515, ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0383(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0234(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0286(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM020(wx1200, wx1206, Float(Pos(Zero), Pos(Succ(wx1207))), bh)
new_lookupWithDefaultFM0254(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10070), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Succ(wx198400), h) → new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190100, wx198400, h)
new_lookupWithDefaultFM0228(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0496(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0520(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, bbd) → new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, new_primMulNat0(Succ(wx1569), wx1564), bbd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Zero)), da)
new_lookupWithDefaultFM0191(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0430(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0377(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6680), fd) → new_lookupWithDefaultFM0395(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0158(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6760), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0422(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, gf) → new_lookupWithDefaultFM020(wx1420, wx1426, Float(Neg(Zero), Pos(Succ(wx1427))), gf)
new_lookupWithDefaultFM0120(wx1695, wx1696, wx1697, wx1698, wx1699, wx1700, wx1701, wx1702, ec) → new_lookupWithDefaultFM0360(wx1695, wx1696, wx1697, wx1698, wx1699, wx1700, wx1701, wx1702, ec)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0127(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0132(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5760), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0342(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Zero, Succ(Succ(wx190600)), da) → new_lookupWithDefaultFM0345(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0151(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM081(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3870), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0246(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx981, ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0201(wx1833, wx1834, wx1835, wx1836, wx1837, wx1838, wx1839, he) → new_lookupWithDefaultFM0434(wx1833, wx1834, wx1835, wx1836, wx1837, wx1838, wx1839, he)
new_lookupWithDefaultFM036(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0272(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0218(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx8730), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0510(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Zero, wx1538), bah)
new_lookupWithDefaultFM0290(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Zero, wx1210), ca)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0255(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Zero), Zero, da) → new_lookupWithDefaultFM0312(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(wx62400), fd) → new_lookupWithDefaultFM0383(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM052(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2980), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM066(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3400), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Zero, h) → new_lookupWithDefaultFM025(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0320(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0173(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0416(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM02(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, wx237, h) → new_lookupWithDefaultFM0534(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h)
new_lookupWithDefaultFM0200(wx4, wx30100, wx31, wx32, wx33, wx34, wx812, ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM046(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2740), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(wx261000), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14800, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0123(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0334(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM0237(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0527(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0526(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(wx4000), wx401, wx402, wx403, wx404, wx405, Neg(wx4060), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(wx4060)), da)
new_lookupWithDefaultFM076(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3720), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0187(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7650), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0348(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, Succ(wx19740), dd) → new_lookupWithDefaultFM020(wx1274, wx1279, Float(Pos(Succ(wx1280)), Pos(Succ(wx1281))), dd)
new_lookupWithDefaultFM0346(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, dd) → new_lookupWithDefaultFM0348(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, new_primMulNat0(Succ(wx1281), wx1275), dd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0311(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0148(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0297(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Succ(Zero), cc) → new_lookupWithDefaultFM0299(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, cc)
new_lookupWithDefaultFM0398(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx19630), fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0171(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0179(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0423(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM035(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0272(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0278(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx19940, Zero, bg) → new_lookupWithDefaultFM020(wx1191, wx1197, Float(Pos(Zero), Pos(Succ(wx1198))), bg)
new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, Zero, ca) → new_lookupWithDefaultFM0292(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Succ(wx1216), wx1211), ca)
new_lookupWithDefaultFM0267(wx1893, wx1894, wx1895, wx1896, wx1897, wx1898, wx1899, bbf) → new_lookupWithDefaultFM020(wx1893, wx1897, Float(Neg(Zero), Neg(Succ(wx1899))), bbf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM035(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0197(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM038(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, bd) → new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, new_primMulNat0(Succ(wx1180), wx1174), bd)
new_lookupWithDefaultFM08(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, Succ(wx2820), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(wx2110)), h)
new_lookupWithDefaultFM0291(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, wx12610, wx1948, ca) → new_lookupWithDefaultFM020(wx1209, wx1215, Float(Pos(Zero), Neg(Succ(wx1216))), ca)
new_lookupWithDefaultFM0186(wx1440, wx1441, wx1442, wx1443, wx1444, wx1445, wx1446, wx1447, ha) → new_lookupWithDefaultFM020(wx1440, wx1445, Float(Neg(Zero), Neg(Succ(wx1447))), ha)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0153(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0203(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx8140), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0227(wx1858, wx1859, wx1860, wx1861, wx1862, wx1863, wx1864, wx1865, bad) → new_lookupWithDefaultFM020(wx1858, wx1862, Float(Neg(Succ(wx1864)), Neg(Succ(wx1865))), bad)
new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190600), Succ(wx107300), da) → new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190600, wx107300, da)
new_lookupWithDefaultFM0154(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx655, ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0108(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4970), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM061(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3230), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0409(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Neg(Zero)), fd)
new_lookupWithDefaultFM0316(wx398, wx399, wx4000, wx401, wx402, wx403, wx404, wx405, wx4060, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(wx4060)), da)
new_lookupWithDefaultFM0306(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, cf) → new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, new_primMulNat0(Succ(wx1249), wx1244), cf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Zero), wx206, wx207, wx208, wx209, wx210, Neg(Zero), Zero, h) → new_lookupWithDefaultFM013(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0275(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0274(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(wx263000), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM057(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0294(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0323(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx125900), Succ(Succ(wx195200)), da) → new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195200, wx125900, da)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0379(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM010(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25900)), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0258(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0220(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0163(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6860), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM065(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3330), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0217(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx11350), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Neg(Succ(wx5000)), Pos(Zero)), ba)
new_lookupWithDefaultFM0362(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Zero, Succ(Succ(wx198800)), ed) → new_lookupWithDefaultFM0365(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed)
new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0270(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, bc) → new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, new_primMulNat0(Succ(wx1171), wx1165), bc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0238(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(wx88800), hh) → new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx88800, hh)
new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, Succ(wx19790), gb) → new_lookupWithDefaultFM020(wx1393, wx1398, Float(Neg(Succ(wx1399)), Neg(Succ(wx1400))), gb)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, wx4080, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM046(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0276(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0197(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7970), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0152(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM094(wx1650, wx1651, wx1652, wx1653, wx1654, wx1655, wx1656, wx1657, dc) → new_lookupWithDefaultFM0347(wx1650, wx1651, wx1652, wx1653, wx1654, wx1655, wx1656, wx1657, dc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupWithDefaultFM054(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupWithDefaultFM0430(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, hd) → new_lookupWithDefaultFM0432(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, new_primMulNat0(Succ(wx1463), wx1458), hd)
new_lookupWithDefaultFM093(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx439, ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0345(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Neg(Zero)), da)
new_lookupWithDefaultFM0220(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0495(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM0100(wx1659, wx1660, wx1661, wx1662, wx1663, wx1664, wx1665, wx1666, de) → new_lookupWithDefaultFM0350(wx1659, wx1660, wx1661, wx1662, wx1663, wx1664, wx1665, wx1666, de)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM027(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM064(wx1616, wx1617, wx1618, wx1619, wx1620, wx1621, wx1622, wx1623, cb) → new_lookupWithDefaultFM020(wx1616, wx1621, Float(Pos(Zero), Neg(Succ(wx1623))), cb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0103(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0240(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9630), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0151(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0410(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0429(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh) → new_lookupWithDefaultFM020(wx1430, wx1436, Float(Neg(Zero), Neg(Succ(wx1437))), gh)
new_lookupWithDefaultFM0376(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx10820), fd) → new_lookupWithDefaultFM0402(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx10820, new_primMulNat0(Zero, wx61600), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0137(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0139(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0199(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0433(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM086(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4090), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190400), Zero, da) → new_lookupWithDefaultFM0341(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, da)
new_lookupWithDefaultFM0369(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, fb) → new_lookupWithDefaultFM0371(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, new_primMulNat0(Succ(wx1361), wx1356), fb)
new_lookupWithDefaultFM0274(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, bd) → new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, new_primMulNat0(Succ(wx1180), wx1174), bd)
new_lookupWithDefaultFM0240(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0514(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx199000), Succ(wx192000), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx199000, wx192000, gf)
new_lookupWithDefaultFM0177(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7330), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0142(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5980), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0550(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Zero)), h)
new_lookupWithDefaultFM080(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3800), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0496(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, baf) → new_lookupWithDefaultFM0497(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, new_primMulNat0(Zero, wx1520), baf)
new_lookupWithDefaultFM0405(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Pos(Zero)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM057(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0219(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0492(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0119(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM085(wx398, wx399, Pos(wx4000), wx401, wx402, wx403, wx404, wx405, Pos(wx4060), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(wx4060)), da)
new_lookupWithDefaultFM0419(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx192000), Succ(Succ(wx199000)), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx199000, wx192000, gf)
new_lookupWithDefaultFM0478(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM0114(wx1686, wx1687, wx1688, wx1689, wx1690, wx1691, wx1692, wx1693, ea) → new_lookupWithDefaultFM0353(wx1686, wx1687, wx1688, wx1689, wx1690, wx1691, wx1692, wx1693, ea)
new_lookupWithDefaultFM077(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0307(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0454(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0116(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5170), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Zero, hh) → new_lookupWithDefaultFM0469(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0199(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8090), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0171(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0416(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0191(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Succ(Succ(wx196600)), hh) → new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148000, wx196600, hh)
new_lookupWithDefaultFM0324(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx19530), da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM012(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx11520), h) → new_lookupWithDefaultFM0548(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11520, new_primMulNat0(Zero, wx20500), h)
new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, Succ(wx19410), bbe) → new_lookupWithDefaultFM020(wx1571, wx1576, Float(Neg(Zero), Neg(Succ(wx1577))), bbe)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0310(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM070(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0168(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0366(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, eh) → new_lookupWithDefaultFM0368(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, new_primMulNat0(Succ(wx1353), wx1348), eh)
new_lookupWithDefaultFM0249(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx9900), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0136(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45800)), Succ(wx40800), da) → new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45800, wx40800, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM040(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0168(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7080), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0239(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9580), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM097(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4600), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0233(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0501(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0245(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0101(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx11120), ba) → new_lookupWithDefaultFM020(wx4, wx34, Float(Pos(Succ(wx5000)), Neg(Zero)), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0143(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0120(wx1695, wx1696, wx1697, wx1698, wx1699, wx1700, wx1701, wx1702, ec) → new_lookupWithDefaultFM0360(wx1695, wx1696, wx1697, wx1698, wx1699, wx1700, wx1701, wx1702, ec)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM082(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM062(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3280), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM061(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0363(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx19890), ed) → new_lookupWithDefaultFM020(wx1320, wx1326, Float(Pos(Zero), Neg(Succ(wx1327))), ed)
new_lookupWithDefaultFM081(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3870), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0117(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0144(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx6100), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0290(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Zero, wx1210), ca)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0118(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM075(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM056(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0371(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, Succ(wx19770), fb) → new_lookupWithDefaultFM020(wx1355, wx1360, Float(Pos(Zero), Neg(Succ(wx1361))), fb)
new_lookupWithDefaultFM0125(wx1330, wx1331, wx1332, wx1333, wx1334, wx1335, wx1336, wx1337, ee) → new_lookupWithDefaultFM020(wx1330, wx1335, Float(Pos(Zero), Neg(Succ(wx1337))), ee)
new_lookupWithDefaultFM0117(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0359(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM060(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3160), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM076(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0140(wx1729, wx1730, wx1731, wx1732, wx1733, wx1734, wx1735, fa) → new_lookupWithDefaultFM0370(wx1729, wx1730, wx1731, wx1732, wx1733, wx1734, wx1735, fa)
new_lookupWithDefaultFM0143(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx6050), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0117(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5240), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0123(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0118(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5290), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0294(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0290(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM076(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3720), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0137(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5880), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0116(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM077(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3770), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0122(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5340), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Zero, ed) → new_lookupWithDefaultFM0363(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, new_primMulNat0(Succ(wx1327), wx1322), ed)
new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, Zero, ca) → new_lookupWithDefaultFM0292(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Succ(wx1216), wx1211), ca)
new_lookupWithDefaultFM0123(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5410), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM082(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3920), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0142(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM055(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM078(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, cf) → new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, new_primMulNat0(Succ(wx1249), wx1244), cf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM062(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0119(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx532, ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0138(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5930), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0304(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, cf) → new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, new_primMulNat0(Succ(wx1249), wx1244), cf)
new_lookupWithDefaultFM061(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3230), ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0306(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, cf) → new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, new_primMulNat0(Succ(wx1249), wx1244), cf)
new_lookupWithDefaultFM0293(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM020(wx1209, wx1215, Float(Pos(Zero), Neg(Succ(wx1216))), ca)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM083(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM057(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0294(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM081(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0359(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed) → new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, new_primMulNat0(Zero, wx1321), ed)
new_lookupWithDefaultFM0288(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Zero, wx1210), ca)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0144(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM057(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3130), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0307(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0306(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0305(wx1243, wx1244, wx1245, wx1246, wx1247, wx1248, wx1249, Succ(wx19370), cf) → new_lookupWithDefaultFM020(wx1243, wx1248, Float(Pos(Zero), Neg(Succ(wx1249))), cf)
new_lookupWithDefaultFM055(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0288(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0116(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0359(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0370(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, fb) → new_lookupWithDefaultFM0371(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, new_primMulNat0(Succ(wx1361), wx1356), fb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM080(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM056(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3080), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0145(wx1363, wx1364, wx1365, wx1366, wx1367, wx1368, wx1369, fc) → new_lookupWithDefaultFM020(wx1363, wx1367, Float(Pos(Zero), Neg(Succ(wx1369))), fc)
new_lookupWithDefaultFM075(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3650), ba) → new_lookupWithDefaultFM078(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM083(wx4, wx30100, wx31, wx32, wx33, wx34, wx395, ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0136(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0369(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM064(wx1616, wx1617, wx1618, wx1619, wx1620, wx1621, wx1622, wx1623, cb) → new_lookupWithDefaultFM020(wx1616, wx1621, Float(Pos(Zero), Neg(Succ(wx1623))), cb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM060(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0137(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0136(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5810), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0139(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0118(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0359(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM063(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0137(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0369(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM075(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0304(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0369(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, fb) → new_lookupWithDefaultFM0371(wx1355, wx1356, wx1357, wx1358, wx1359, wx1360, wx1361, new_primMulNat0(Succ(wx1361), wx1356), fb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0142(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5980), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0292(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, Succ(wx19490), ca) → new_lookupWithDefaultFM0293(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca)
new_lookupWithDefaultFM080(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3800), ba) → new_lookupWithDefaultFM084(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM057(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0138(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0369(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0119(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0145(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM084(wx1633, wx1634, wx1635, wx1636, wx1637, wx1638, wx1639, cg) → new_lookupWithDefaultFM020(wx1633, wx1637, Float(Pos(Zero), Neg(Succ(wx1639))), cg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM077(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM077(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0307(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0116(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5170), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0122(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM058(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, ca) → new_lookupWithDefaultFM0289(wx1209, wx1210, wx1211, wx1212, wx1213, wx1214, wx1215, wx1216, new_primMulNat0(Zero, wx1210), ca)
new_lookupWithDefaultFM0360(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, ed) → new_lookupWithDefaultFM0361(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, new_primMulNat0(Zero, wx1321), ed)
new_lookupWithDefaultFM076(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0304(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM063(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx331, ba) → new_lookupWithDefaultFM064(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0120(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0138(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0136(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0139(wx4, wx30100, wx31, wx32, wx33, wx34, wx596, ba) → new_lookupWithDefaultFM0140(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM055(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3010), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM056(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0288(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM058(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0124(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0124(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5460), ba) → new_lookupWithDefaultFM0125(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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



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

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

new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx198800), Succ(wx191100), ed) → new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, wx198800, wx191100, ed)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx198800), Succ(wx191100), ed) → new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, wx198800, wx191100, ed)

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

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

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

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



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

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

new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, Succ(wx198800), Succ(wx191100), ed) → new_lookupWithDefaultFM0364(wx1320, wx1321, wx1322, wx1323, wx1324, wx1325, wx1326, wx1327, wx198800, wx191100, 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_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Succ(wx202000), cc) → new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx199500, wx202000, cc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                          ↳ 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_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Succ(wx202000), cc) → new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx199500, wx202000, cc)

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

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

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

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



↳ 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_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, Succ(wx199500), Succ(wx202000), cc) → new_lookupWithDefaultFM0298(wx1218, wx1219, wx1220, wx1221, wx1222, wx1223, wx1224, wx1225, wx199500, wx202000, 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
                          ↳ 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_lookupWithDefaultFM068(wx4, wx30100, wx31, wx32, wx33, wx34, wx348, ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0127(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0353(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb) → new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, new_primMulNat0(Zero, wx1311), eb)
new_lookupWithDefaultFM0132(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5760), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0112(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5120), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0300(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, ce) → new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, new_primMulNat0(Succ(wx1241), wx1236), ce)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM051(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0285(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, Succ(wx19470), bh) → new_lookupWithDefaultFM0286(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh)
new_lookupWithDefaultFM052(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0287(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM047(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2790), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0283(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Zero, wx1201), bh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0132(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0131(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM046(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM052(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2980), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM066(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3400), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0126(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5490), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Zero, eb) → new_lookupWithDefaultFM0356(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, new_primMulNat0(Succ(wx1317), wx1312), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM051(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2930), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM046(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2740), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0111(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5070), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM047(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0287(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0283(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0131(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5710), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0106(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0367(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, eh) → new_lookupWithDefaultFM0368(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, new_primMulNat0(Succ(wx1353), wx1348), eh)
new_lookupWithDefaultFM0110(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0352(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM072(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0303(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM051(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0281(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0127(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5560), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM049(wx1607, wx1608, wx1609, wx1610, wx1611, wx1612, wx1613, wx1614, bf) → new_lookupWithDefaultFM020(wx1607, wx1612, Float(Pos(Zero), Pos(Succ(wx1614))), bf)
new_lookupWithDefaultFM0130(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5640), ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM071(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM053(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Zero, wx1201), bh)
new_lookupWithDefaultFM0129(wx1339, wx1340, wx1341, wx1342, wx1343, wx1344, wx1345, ef) → new_lookupWithDefaultFM020(wx1339, wx1343, Float(Pos(Zero), Pos(Succ(wx1345))), ef)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0112(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0110(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx5000), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0130(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM068(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM070(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0300(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM048(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx284, ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0108(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4970), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM050(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0281(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0132(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0366(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0133(wx4, wx30100, wx31, wx32, wx33, wx34, wx579, ba) → new_lookupWithDefaultFM0134(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0303(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0302(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, Zero, bh) → new_lookupWithDefaultFM0285(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Succ(wx1207), wx1202), bh)
new_lookupWithDefaultFM0128(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx5610), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0126(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM065(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM071(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0300(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM052(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM072(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3620), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0107(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0133(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0108(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0110(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, Succ(wx19360), ce) → new_lookupWithDefaultFM020(wx1235, wx1240, Float(Pos(Zero), Pos(Succ(wx1241))), ce)
new_lookupWithDefaultFM065(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3330), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0107(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4920), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM045(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM048(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM050(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx2860), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0112(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0352(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM070(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx3500), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0111(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0352(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0106(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx4850), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0109(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM067(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM071(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3570), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0131(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0366(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0134(wx1721, wx1722, wx1723, wx1724, wx1725, wx1726, wx1727, eg) → new_lookupWithDefaultFM0367(wx1721, wx1722, wx1723, wx1724, wx1725, wx1726, wx1727, eg)
new_lookupWithDefaultFM0352(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, eb) → new_lookupWithDefaultFM0354(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, new_primMulNat0(Zero, wx1311), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0128(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0356(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx19870), eb) → new_lookupWithDefaultFM020(wx1310, wx1316, Float(Pos(Zero), Pos(Succ(wx1317))), eb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM073(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0114(wx1686, wx1687, wx1688, wx1689, wx1690, wx1691, wx1692, wx1693, ea) → new_lookupWithDefaultFM0353(wx1686, wx1687, wx1688, wx1689, wx1690, wx1691, wx1692, wx1693, ea)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0111(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0302(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, ce) → new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, new_primMulNat0(Succ(wx1241), wx1236), ce)
new_lookupWithDefaultFM0281(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM0282(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, new_primMulNat0(Zero, wx1201), bh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0113(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0368(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, Succ(wx19760), eh) → new_lookupWithDefaultFM020(wx1347, wx1352, Float(Pos(Zero), Pos(Succ(wx1353))), eh)
new_lookupWithDefaultFM067(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx3450), ba) → new_lookupWithDefaultFM069(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM073(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, ce) → new_lookupWithDefaultFM0301(wx1235, wx1236, wx1237, wx1238, wx1239, wx1240, wx1241, new_primMulNat0(Succ(wx1241), wx1236), ce)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0129(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM070(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0366(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, eh) → new_lookupWithDefaultFM0368(wx1347, wx1348, wx1349, wx1350, wx1351, wx1352, wx1353, new_primMulNat0(Succ(wx1353), wx1348), eh)
new_lookupWithDefaultFM0130(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0366(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0113(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx515, ba) → new_lookupWithDefaultFM0114(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM069(wx1625, wx1626, wx1627, wx1628, wx1629, wx1630, wx1631, cd) → new_lookupWithDefaultFM020(wx1625, wx1629, Float(Pos(Zero), Pos(Succ(wx1631))), cd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM053(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0286(wx1200, wx1201, wx1202, wx1203, wx1204, wx1205, wx1206, wx1207, bh) → new_lookupWithDefaultFM020(wx1200, wx1206, Float(Pos(Zero), Pos(Succ(wx1207))), bh)
new_lookupWithDefaultFM0109(wx1301, wx1302, wx1303, wx1304, wx1305, wx1306, wx1307, wx1308, dh) → new_lookupWithDefaultFM020(wx1301, wx1306, Float(Pos(Zero), Pos(Succ(wx1308))), dh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM066(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM072(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM050(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM045(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx2670), ba) → new_lookupWithDefaultFM049(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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



↳ HASKELL
  ↳ CR
    ↳ HASKELL
      ↳ BR
        ↳ HASKELL
          ↳ COR
            ↳ HASKELL
              ↳ Narrow
                ↳ AND
                  ↳ QDP
                  ↳ QDP
                  ↳ QDP
                    ↳ DependencyGraphProof
                      ↳ AND
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
QDP
                          ↳ 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_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Succ(wx201800), bg) → new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx199400, wx201800, bg)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Succ(wx201800), bg) → new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx199400, wx201800, bg)

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

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

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

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



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

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

new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, Succ(wx199400), Succ(wx201800), bg) → new_lookupWithDefaultFM0279(wx1191, wx1192, wx1193, wx1194, wx1195, wx1196, wx1197, wx1198, wx199400, wx201800, 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
                        ↳ 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_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx198600), Succ(wx191000), eb) → new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, wx198600, wx191000, eb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx198600), Succ(wx191000), eb) → new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, wx198600, wx191000, eb)

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

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

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

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



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

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

new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, Succ(wx198600), Succ(wx191000), eb) → new_lookupWithDefaultFM0357(wx1310, wx1311, wx1312, wx1313, wx1314, wx1315, wx1316, wx1317, wx198600, wx191000, 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
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(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0233(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, Succ(wx19400), bbd) → new_lookupWithDefaultFM020(wx1563, wx1568, Float(Neg(Zero), Pos(Succ(wx1569))), bbd)
new_lookupWithDefaultFM0175(wx1790, wx1791, wx1792, wx1793, wx1794, wx1795, wx1796, wx1797, ge) → new_lookupWithDefaultFM0417(wx1790, wx1791, wx1792, wx1793, wx1794, wx1795, wx1796, wx1797, ge)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0189(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0250(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx9950), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0248(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9830), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0254(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0229(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9260), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0188(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7720), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0255(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0503(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Zero, wx1529), bag)
new_lookupWithDefaultFM0252(wx1885, wx1886, wx1887, wx1888, wx1889, wx1890, wx1891, bbc) → new_lookupWithDefaultFM020(wx1885, wx1889, Float(Neg(Zero), Pos(Succ(wx1891))), bbc)
new_lookupWithDefaultFM0432(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, Succ(wx19800), hd) → new_lookupWithDefaultFM020(wx1457, wx1462, Float(Neg(Zero), Pos(Succ(wx1463))), hd)
new_lookupWithDefaultFM0171(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7160), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0172(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7230), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0522(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, bbd) → new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, new_primMulNat0(Succ(wx1569), wx1564), bbd)
new_lookupWithDefaultFM0190(wx1449, wx1450, wx1451, wx1452, wx1453, wx1454, wx1455, hb) → new_lookupWithDefaultFM020(wx1449, wx1453, Float(Neg(Zero), Pos(Succ(wx1455))), hb)
new_lookupWithDefaultFM0173(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0416(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0230(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0172(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0167(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0250(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0194(wx4, wx30100, wx31, wx32, wx33, wx34, wx795, ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0172(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0416(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0256(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, bbd) → new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, new_primMulNat0(Succ(wx1569), wx1564), bbd)
new_lookupWithDefaultFM0187(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7650), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0251(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0235(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0231(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx934, ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0187(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0254(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0520(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0253(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0169(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7130), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0523(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0522(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0229(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0171(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0236(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Zero, wx1529), bag)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0173(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0173(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7280), ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0505(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, Succ(wx19710), bag) → new_lookupWithDefaultFM0506(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag)
new_lookupWithDefaultFM0507(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0503(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0255(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0523(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0501(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Zero, wx1529), bag)
new_lookupWithDefaultFM0230(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9310), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0193(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0189(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7770), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), 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, wx1421), gf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0228(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0174(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), 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(wx1427), wx1422), gf)
new_lookupWithDefaultFM0506(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, bag) → new_lookupWithDefaultFM020(wx1528, wx1534, Float(Neg(Zero), Pos(Succ(wx1535))), bag)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0231(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0234(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9430), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0431(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, hd) → new_lookupWithDefaultFM0432(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, new_primMulNat0(Succ(wx1463), wx1458), hd)
new_lookupWithDefaultFM0228(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9190), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0253(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx10000), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0169(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0174(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx731, ba) → new_lookupWithDefaultFM0175(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0192(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7870), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0233(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9360), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0430(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, hd) → new_lookupWithDefaultFM0432(wx1457, wx1458, wx1459, wx1460, wx1461, wx1462, wx1463, new_primMulNat0(Succ(wx1463), wx1458), hd)
new_lookupWithDefaultFM0232(wx1867, wx1868, wx1869, wx1870, wx1871, wx1872, wx1873, wx1874, bae) → new_lookupWithDefaultFM020(wx1867, wx1872, Float(Neg(Zero), Pos(Succ(wx1874))), bae)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0188(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0234(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0501(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0190(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0192(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0430(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0235(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0507(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0167(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7010), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0193(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0430(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0232(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0193(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx7920), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0255(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10120), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0249(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0502(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, Zero, bag) → new_lookupWithDefaultFM0505(wx1528, wx1529, wx1530, wx1531, wx1532, wx1533, wx1534, wx1535, new_primMulNat0(Succ(wx1535), wx1530), bag)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0191(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7800), ba) → new_lookupWithDefaultFM0195(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0194(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0420(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx19910), gf) → new_lookupWithDefaultFM020(wx1420, wx1426, Float(Neg(Zero), Pos(Succ(wx1427))), gf)
new_lookupWithDefaultFM0171(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0416(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0235(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9480), ba) → new_lookupWithDefaultFM0236(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0191(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0251(wx4, wx30100, wx31, wx32, wx33, wx34, wx998, ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0168(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0249(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx9900), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0234(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), 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, wx1421), gf)
new_lookupWithDefaultFM0170(wx1411, wx1412, wx1413, wx1414, wx1415, wx1416, wx1417, wx1418, gd) → new_lookupWithDefaultFM020(wx1411, wx1416, Float(Neg(Zero), Pos(Succ(wx1418))), gd)
new_lookupWithDefaultFM0253(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0520(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0195(wx1825, wx1826, wx1827, wx1828, wx1829, wx1830, wx1831, hc) → new_lookupWithDefaultFM0431(wx1825, wx1826, wx1827, wx1828, wx1829, wx1830, wx1831, hc)
new_lookupWithDefaultFM0168(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7080), ba) → new_lookupWithDefaultFM0170(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0254(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10070), ba) → new_lookupWithDefaultFM0256(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0248(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0192(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0233(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0501(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0520(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, bbd) → new_lookupWithDefaultFM0521(wx1563, wx1564, wx1565, wx1566, wx1567, wx1568, wx1569, new_primMulNat0(Succ(wx1569), wx1564), bbd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0252(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0191(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0430(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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



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

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

new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx199000), Succ(wx192000), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx199000, wx192000, gf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx199000), Succ(wx192000), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx199000, wx192000, gf)

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

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

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

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



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

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

new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, Succ(wx199000), Succ(wx192000), gf) → new_lookupWithDefaultFM0421(wx1420, wx1421, wx1422, wx1423, wx1424, wx1425, wx1426, wx1427, wx199000, wx192000, 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_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Succ(wx203000), baf) → new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx200000, wx203000, baf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Succ(wx203000), baf) → new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx200000, wx203000, baf)

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

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

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

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



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

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

new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, Succ(wx200000), Succ(wx203000), baf) → new_lookupWithDefaultFM0499(wx1519, wx1520, wx1521, wx1522, wx1523, wx1524, wx1525, wx1526, wx200000, wx203000, 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
                          ↳ 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_lookupWithDefaultFM0159(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6810), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0446(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0438(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0491(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0490(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67200)), Zero, fd) → new_lookupWithDefaultFM0382(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0492(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, bac) → new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, new_primMulNat0(Succ(wx1508), wx1502), bac)
new_lookupWithDefaultFM0494(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, bac) → new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, new_primMulNat0(Succ(wx1508), wx1502), bac)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Zero, hh) → new_lookupWithDefaultFM0479(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0438(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0448(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0453(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0440(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), Zero, hh) → new_lookupWithDefaultFM0471(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Zero)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0449(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0215(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8700), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, wx6240, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM0471(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx19220), hh) → new_lookupWithDefaultFM0472(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0154(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM0480(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0454(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8860), hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(wx62400), fd) → new_lookupWithDefaultFM0393(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0473(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(wx8320), wx833, wx834, wx835, wx836, wx837, Pos(wx8380), Succ(wx8400), hh) → new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0490(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, bab) → new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, new_primMulNat0(Succ(wx1499), wx1493), bab)
new_lookupWithDefaultFM0374(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6640), fd) → new_lookupWithDefaultFM0380(wx614, wx615, Succ(wx61600), wx617, wx618, wx619, wx620, wx621, Succ(wx62200), fd)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Succ(wx89000)), hh) → new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx89000, hh)
new_lookupWithDefaultFM0439(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0449(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Succ(wx88800)), hh) → new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx88800, hh)
new_lookupWithDefaultFM0224(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx9070), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, Succ(wx19390), bac) → new_lookupWithDefaultFM020(wx1501, wx1506, Float(Neg(Succ(wx1507)), Neg(Succ(wx1508))), bac)
new_lookupWithDefaultFM0401(wx614, wx615, wx6160, wx617, wx618, wx619, wx620, wx621, wx6220, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(wx6220)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0210(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0385(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0377(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0457(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0461(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0455(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0210(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8530), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0219(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67400), Succ(wx62400), fd) → new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67400, wx62400, fd)
new_lookupWithDefaultFM0467(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10910, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Zero)), hh)
new_lookupWithDefaultFM0213(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx8580), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0470(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, Zero, hh) → new_lookupWithDefaultFM0480(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67400), Zero, fd) → new_lookupWithDefaultFM0392(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0226(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0390(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM0397(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(Succ(wx196200)), fd) → new_lookupWithDefaultFM0400(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67400)), Succ(wx62400), fd) → new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67400, wx62400, fd)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM0221(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, bac) → new_lookupWithDefaultFM0493(wx1501, wx1502, wx1503, wx1504, wx1505, wx1506, wx1507, wx1508, new_primMulNat0(Succ(wx1508), wx1502), bac)
new_lookupWithDefaultFM0495(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0494(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67200), Zero, fd) → new_lookupWithDefaultFM0382(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Succ(wx196600), hh) → new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148000, wx196600, hh)
new_lookupWithDefaultFM0147(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6250), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0394(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx13710), fd) → new_lookupWithDefaultFM0387(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx13710, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM0151(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6400), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0215(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0450(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Zero, hh) → new_lookupWithDefaultFM0466(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0475(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(wx8380)), hh)
new_lookupWithDefaultFM0375(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, Succ(wx9120), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(wx8380)), hh)
new_lookupWithDefaultFM0158(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0413(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Zero), wx617, wx618, wx619, wx620, wx621, Pos(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Zero)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0447(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx10900), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, wx6240, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM0448(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx10910), hh) → new_lookupWithDefaultFM0467(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10910, new_primMulNat0(Zero, wx83200), hh)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Zero), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14810, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM0466(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0462(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0225(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0209(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0474(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx19240), hh) → new_lookupWithDefaultFM0475(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0456(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0213(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0488(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0443(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0455(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0224(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0461(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0457(wx830, wx831, wx833, wx834, wx835, wx836, wx837, Succ(wx10950), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Zero)), hh)
new_lookupWithDefaultFM0225(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx9140), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0387(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(Succ(wx196000)), fd) → new_lookupWithDefaultFM0390(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, Succ(wx19380), bab) → new_lookupWithDefaultFM020(wx1492, wx1497, Float(Neg(Succ(wx1498)), Pos(Succ(wx1499))), bab)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0207(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30000), Succ(wx30000)), ba)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(wx89000), hh) → new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx89000, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0218(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0394(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(wx88800), hh) → new_lookupWithDefaultFM0460(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0445(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Zero, hh) → new_lookupWithDefaultFM0459(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0146(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30000), Succ(wx30000)), ba)
new_lookupWithDefaultFM0148(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6320), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(wx89000), hh) → new_lookupWithDefaultFM0478(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0445(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0457(wx830, wx831, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0223(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx9000), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0153(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0410(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), 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(wx1400), wx1394), gb)
new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, Succ(wx9130), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(wx8380)), hh)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Zero), hh) → new_lookupWithDefaultFM0477(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0223(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Zero), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, Zero, hh) → new_lookupWithDefaultFM0462(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0159(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), 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(wx1391), wx1385), fh)
new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196200), Succ(wx137200), fd) → new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196200, wx137200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0214(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Succ(Zero), hh) → new_lookupWithDefaultFM0466(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Succ(wx62400), fd) → new_lookupWithDefaultFM0383(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0463(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx14800), hh) → new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14800, new_primMulNat0(Succ(wx83800), wx83200), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM0166(wx1402, wx1403, wx1404, wx1405, wx1406, wx1407, wx1408, wx1409, gc) → new_lookupWithDefaultFM020(wx1402, wx1406, Float(Neg(Succ(wx1408)), Neg(Succ(wx1409))), gc)
new_lookupWithDefaultFM0216(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, bab) → new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, new_primMulNat0(Succ(wx1499), wx1493), bab)
new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0388(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0149(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196000), Succ(wx137100), fd) → new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196000, wx137100, fd)
new_lookupWithDefaultFM0382(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0385(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0393(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0400(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0218(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0492(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0460(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0215(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0491(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM0161(wx1763, wx1764, wx1765, wx1766, wx1767, wx1768, wx1769, wx1770, ga) → new_lookupWithDefaultFM0414(wx1763, wx1764, wx1765, wx1766, wx1767, wx1768, wx1769, wx1770, ga)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0160(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0155(wx1754, wx1755, wx1756, wx1757, wx1758, wx1759, wx1760, wx1761, fg) → new_lookupWithDefaultFM0411(wx1754, wx1755, wx1756, wx1757, wx1758, wx1759, wx1760, wx1761, fg)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0383(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0152(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6470), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0452(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8840), hh) → new_lookupWithDefaultFM0473(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Succ(wx62400), fd) → new_lookupWithDefaultFM0393(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0212(wx1849, wx1850, wx1851, wx1852, wx1853, wx1854, wx1855, wx1856, baa) → new_lookupWithDefaultFM020(wx1849, wx1853, Float(Neg(Succ(wx1855)), Pos(Succ(wx1856))), baa)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0213(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0444(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0377(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6680), fd) → new_lookupWithDefaultFM0395(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), wx6240, fd)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0437(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0158(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6760), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0159(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0413(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0165(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6980), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0477(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0480(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0151(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0157(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0413(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0441(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), Zero, hh) → new_lookupWithDefaultFM0474(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, fd) → new_lookupWithDefaultFM0398(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Succ(wx89000)), hh) → new_lookupWithDefaultFM0478(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0446(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8800), hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0450(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0218(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx8730), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0153(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6520), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0450(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx8820), hh) → new_lookupWithDefaultFM0470(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0208(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx8410), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Succ(wx62400), fd) → new_lookupWithDefaultFM0383(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0375(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Zero, hh) → new_lookupWithDefaultFM0484(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Zero, fd) → new_lookupWithDefaultFM0384(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0157(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6570), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0451(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0397(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx137200), Succ(Succ(wx196200)), fd) → new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196200, wx137200, fd)
new_lookupWithDefaultFM0391(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Zero, Zero, fd) → new_lookupWithDefaultFM0394(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14800, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Succ(wx83800))), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Succ(wx8400), hh) → new_lookupWithDefaultFM0439(wx830, wx831, wx833, wx834, wx835, wx836, wx837, hh)
new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx67200), Succ(wx62400), fd) → new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67200, wx62400, fd)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(Zero)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0163(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67200)), Succ(wx62400), fd) → new_lookupWithDefaultFM0381(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx67200, wx62400, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0147(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Succ(Zero), hh) → new_lookupWithDefaultFM0484(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Zero), wx617, wx618, wx619, wx620, wx621, Neg(Zero), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(Zero)), fd)
new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, Succ(wx19780), fh) → new_lookupWithDefaultFM020(wx1384, wx1389, Float(Neg(Succ(wx1390)), Pos(Succ(wx1391))), fh)
new_lookupWithDefaultFM0380(wx614, wx615, wx6160, wx617, wx618, wx619, wx620, wx621, wx6220, fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(wx6220)), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0148(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0164(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6930), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0476(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Zero, hh) → new_lookupWithDefaultFM0477(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0372(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Zero), Zero, fd) → new_lookupWithDefaultFM0384(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0384(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0386(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0398(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx19630), fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Neg(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0157(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0472(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(wx8380)), hh)
new_lookupWithDefaultFM0209(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8480), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0452(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0211(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Succ(Succ(wx196800)), hh) → new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148100, wx196800, hh)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Zero), Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Zero, wx833, wx834, wx835, wx836, wx837, Zero, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0153(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0227(wx1858, wx1859, wx1860, wx1861, wx1862, wx1863, wx1864, wx1865, bad) → new_lookupWithDefaultFM020(wx1858, wx1862, Float(Neg(Succ(wx1864)), Neg(Succ(wx1865))), bad)
new_lookupWithDefaultFM0154(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx655, ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0411(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, fh) → new_lookupWithDefaultFM0412(wx1384, wx1385, wx1386, wx1387, wx1388, wx1389, wx1390, wx1391, new_primMulNat0(Succ(wx1391), wx1385), fh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0155(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0437(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0447(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0158(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0150(wx1375, wx1376, wx1377, wx1378, wx1379, wx1380, wx1381, wx1382, ff) → new_lookupWithDefaultFM020(wx1375, wx1379, Float(Neg(Succ(wx1381)), Pos(Succ(wx1382))), ff)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Zero), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0447(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0399(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196200), Zero, fd) → new_lookupWithDefaultFM0400(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0379(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx196000), Zero, fd) → new_lookupWithDefaultFM0390(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0392(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0395(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0220(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0214(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8650), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0459(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0462(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0163(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx6860), ba) → new_lookupWithDefaultFM0166(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0442(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Zero), hh) → new_lookupWithDefaultFM0479(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0146(wx614, wx615, Neg(wx6160), wx617, wx618, wx619, wx620, wx621, Neg(wx6220), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Neg(wx6220)), fd)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(Zero), hh) → new_lookupWithDefaultFM0459(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(wx6160), wx617, wx618, wx619, wx620, wx621, Pos(wx6220), Succ(wx6240), fd) → new_lookupWithDefaultFM020(wx614, wx619, Float(Neg(Succ(wx621)), Pos(wx6220)), fd)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx84000), Succ(wx88800), hh) → new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx84000, wx88800, hh)
new_lookupWithDefaultFM0226(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx917, ba) → new_lookupWithDefaultFM0227(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, 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(wx1400), wx1394), gb)
new_lookupWithDefaultFM0415(wx1393, wx1394, wx1395, wx1396, wx1397, wx1398, wx1399, wx1400, Succ(wx19790), gb) → new_lookupWithDefaultFM020(wx1393, wx1398, Float(Neg(Succ(wx1399)), Neg(Succ(wx1400))), gb)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0152(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0149(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx6370), ba) → new_lookupWithDefaultFM0150(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0375(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6660), fd) → new_lookupWithDefaultFM0385(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0220(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0495(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM0395(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd) → new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primMulNat0(Succ(wx621), wx615), fd)
new_lookupWithDefaultFM0388(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx19610), fd) → new_lookupWithDefaultFM020(wx614, wx620, Float(Neg(Succ(wx621)), Pos(Succ(wx62200))), fd)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0165(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0387(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx137100), Succ(Succ(wx196000)), fd) → new_lookupWithDefaultFM0389(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx196000, wx137100, fd)
new_lookupWithDefaultFM0455(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx10930), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM0485(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10940, Zero, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Zero)), hh)
new_lookupWithDefaultFM0211(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx856, ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0446(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0214(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0488(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0151(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0410(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM0216(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0152(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0410(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0451(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, hh) → new_lookupWithDefaultFM0440(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0160(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx684, ba) → new_lookupWithDefaultFM0161(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Zero), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0443(wx830, wx831, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0488(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, bab) → new_lookupWithDefaultFM0489(wx1492, wx1493, wx1494, wx1495, wx1496, wx1497, wx1498, wx1499, new_primMulNat0(Succ(wx1499), wx1493), bab)
new_lookupWithDefaultFM0220(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8970), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0379(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx6700), fd) → new_lookupWithDefaultFM0401(wx614, wx615, Succ(wx61600), wx617, wx618, wx619, wx620, wx621, Succ(wx62200), fd)
new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Succ(Succ(wx88800)), hh) → new_lookupWithDefaultFM0460(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0458(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, Zero, hh) → new_lookupWithDefaultFM0461(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh)
new_lookupWithDefaultFM0219(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0492(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0164(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0478(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx835, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)
new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx14810), hh) → new_lookupWithDefaultFM0482(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx14810, new_primMulNat0(Succ(wx83800), wx83200), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(wx8320), wx833, wx834, wx835, wx836, wx837, Neg(wx8380), Succ(wx8400), hh) → new_lookupWithDefaultFM0441(wx830, wx831, wx8320, wx833, wx834, wx835, wx836, wx837, wx8380, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0396(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(wx13720), fd) → new_lookupWithDefaultFM0397(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, wx13720, new_primMulNat0(Succ(wx62200), wx61600), fd)
new_lookupWithDefaultFM0454(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Neg(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Neg(Succ(wx83800)), Zero, hh) → new_lookupWithDefaultFM0454(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Zero), Zero, hh) → new_lookupWithDefaultFM0448(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0444(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, hh) → new_lookupWithDefaultFM0456(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0377(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0207(wx830, wx831, Pos(Succ(wx83200)), wx833, wx834, wx835, wx836, wx837, Pos(Succ(wx83800)), Succ(wx8400), hh) → new_lookupWithDefaultFM0436(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx8400, new_primPlusNat0(new_primMulNat0(wx83800, wx83200), Succ(wx83200)), hh)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Pos(Succ(wx62200)), Zero, fd) → new_lookupWithDefaultFM0374(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), fd)
new_lookupWithDefaultFM0452(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Zero, hh) → new_lookupWithDefaultFM0453(wx830, wx831, Succ(wx83200), wx833, wx834, wx835, wx836, wx837, Succ(wx83800), hh)
new_lookupWithDefaultFM0464(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148000), Succ(Succ(wx196600)), hh) → new_lookupWithDefaultFM0465(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148000, wx196600, hh)
new_lookupWithDefaultFM0449(wx830, wx831, wx833, wx834, wx835, wx836, wx837, Succ(wx10920), hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Pos(Zero)), hh)
new_lookupWithDefaultFM0219(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx8920), ba) → new_lookupWithDefaultFM0221(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0212(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0146(wx614, wx615, Pos(Succ(wx61600)), wx617, wx618, wx619, wx620, wx621, Neg(Succ(wx62200)), Succ(wx6240), fd) → new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, new_primPlusNat0(new_primMulNat0(wx62200, wx61600), Succ(wx61600)), wx6240, fd)
new_lookupWithDefaultFM0479(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM0481(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, new_primMulNat0(Succ(wx837), wx831), hh)
new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, Succ(wx148100), Succ(wx196800), hh) → new_lookupWithDefaultFM0483(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, wx148100, wx196800, hh)
new_lookupWithDefaultFM0456(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx10940), hh) → new_lookupWithDefaultFM0485(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx10940, new_primMulNat0(Zero, wx83200), hh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0208(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0373(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, Succ(Succ(wx67400)), Zero, fd) → new_lookupWithDefaultFM0392(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx62200, fd)
new_lookupWithDefaultFM0484(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx83800, hh) → new_lookupWithDefaultFM020(wx830, wx836, Float(Neg(Succ(wx837)), Neg(Succ(wx83800))), hh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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



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

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

new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191400), Succ(wx108200), fd) → new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191400, wx108200, fd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191400), Succ(wx108200), fd) → new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191400, wx108200, fd)

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

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

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

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



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

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

new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191400), Succ(wx108200), fd) → new_lookupWithDefaultFM0404(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191400, wx108200, 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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191600), Succ(wx108500), fd) → new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191600, wx108500, fd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191600), Succ(wx108500), fd) → new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191600, wx108500, fd)

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

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

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

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



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

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

new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, Succ(wx191600), Succ(wx108500), fd) → new_lookupWithDefaultFM0408(wx614, wx615, wx61600, wx617, wx618, wx619, wx620, wx621, wx191600, wx108500, 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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Succ(wx192800), hh) → new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109400, wx192800, hh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Succ(wx192800), hh) → new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109400, wx192800, hh)

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

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

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

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



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

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

new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109400), Succ(wx192800), hh) → new_lookupWithDefaultFM0486(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109400, wx192800, 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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Succ(wx192600), hh) → new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109100, wx192600, hh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Succ(wx192600), hh) → new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109100, wx192600, hh)

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

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

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

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



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

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

new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, Succ(wx109100), Succ(wx192600), hh) → new_lookupWithDefaultFM0468(wx830, wx831, wx83200, wx833, wx834, wx835, wx836, wx837, wx109100, wx192600, 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
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0323(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(Succ(wx195200)), da) → new_lookupWithDefaultFM0326(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0313(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx235, Zero, h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0271(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0270(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM011(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx11510), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM0532(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19300), h) → new_lookupWithDefaultFM0533(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), h)
new_lookupWithDefaultFM0326(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Succ(wx40800), da) → new_lookupWithDefaultFM0319(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0(wx203, wx204, Pos(wx2050), wx206, wx207, wx208, wx209, wx210, Neg(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM02(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM030(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0268(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Neg(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM010(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM026(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx10470), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45800), Succ(wx40800), da) → new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45800, wx40800, da)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45600)), Succ(wx40800), da) → new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45600, wx40800, da)
new_lookupWithDefaultFM0313(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4520), da) → new_lookupWithDefaultFM0331(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0104(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0533(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(wx2110)), h)
new_lookupWithDefaultFM027(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx10530), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Zero, da) → new_lookupWithDefaultFM0330(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0543(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM016(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM06(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM030(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx10600), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM00(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx235, h) → new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx235, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Succ(wx263000))), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM091(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4310), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM043(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0268(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, bc) → new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, new_primMulNat0(Succ(wx1171), wx1165), bc)
new_lookupWithDefaultFM06(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx11490), h) → new_lookupWithDefaultFM0528(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11490, new_primMulNat0(Zero, wx20500), h)
new_lookupWithDefaultFM037(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2390), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx12590), da) → new_lookupWithDefaultFM0323(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx12590, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Succ(wx261000), h) → new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2350, wx261000, h)
new_lookupWithDefaultFM031(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2160), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Zero, h) → new_lookupWithDefaultFM0547(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0334(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx19550), da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM029(wx1587, wx1588, wx1589, wx1590, wx1591, wx1592, wx1593, wx1594, bb) → new_lookupWithDefaultFM020(wx1587, wx1591, Float(Pos(Succ(wx1593)), Pos(Succ(wx1594))), bb)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Zero), wx401, wx402, wx403, wx404, wx405, Pos(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Zero)), da)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Zero), wx206, wx207, wx208, wx209, wx210, Pos(Zero), Zero, h) → new_lookupWithDefaultFM07(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM090(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM04(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, h) → new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM096(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4410), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Zero, h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM017(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM07(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM031(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0268(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM025(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM090(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0346(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM028(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx10570), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM0(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primMulNat0(wx5000, wx30000), ba)
new_lookupWithDefaultFM08(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), Zero, h) → new_lookupWithDefaultFM0532(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM03(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx238, h) → new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx238, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM09(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), Zero, h) → new_lookupWithDefaultFM0535(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0337(wx398, wx399, wx4000, wx401, wx402, wx403, wx404, wx405, wx4060, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(wx4060)), da)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0328(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0331(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195400), Zero, da) → new_lookupWithDefaultFM0336(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM096(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, Succ(wx19350), bd) → new_lookupWithDefaultFM020(wx1173, wx1178, Float(Pos(Succ(wx1179)), Neg(Succ(wx1180))), bd)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, wx4080, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Pos(Zero), Zero, h) → new_lookupWithDefaultFM06(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM010(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19000, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM032(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat1(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), wx30100), ba)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(wx40800), da) → new_lookupWithDefaultFM0319(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM00(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx235, h) → new_lookupWithDefaultFM015(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM088(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM026(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM041(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0104(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4820), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx238, Zero, h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0311(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45600)), Zero, da) → new_lookupWithDefaultFM0318(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195400), Succ(wx126200), da) → new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195400, wx126200, da)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(wx40800), da) → new_lookupWithDefaultFM0329(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0318(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0321(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Succ(wx40800), da) → new_lookupWithDefaultFM0329(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0538(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM011(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0103(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4770), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Succ(wx263000), h) → new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2380, wx263000, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0548(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11520, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Zero)), h)
new_lookupWithDefaultFM0320(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM030(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(wx2050), wx206, wx207, wx208, wx209, wx210, Pos(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM01(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19010), h) → new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19010, new_primMulNat0(Succ(wx21100), wx20500), h)
new_lookupWithDefaultFM04(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM021(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM05(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx11480), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM0528(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11490, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Zero)), h)
new_lookupWithDefaultFM0333(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Succ(Succ(wx195400)), da) → new_lookupWithDefaultFM0336(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx12620), da) → new_lookupWithDefaultFM0333(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx12620, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM098(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0547(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM042(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2540), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0330(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Zero), wx401, wx402, wx403, wx404, wx405, Neg(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Zero)), da)
new_lookupWithDefaultFM0102(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4700), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, Succ(wx19340), bc) → new_lookupWithDefaultFM020(wx1164, wx1169, Float(Pos(Succ(wx1170)), Pos(Succ(wx1171))), bc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM00(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Zero, wx235, h) → new_lookupWithDefaultFM017(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0347(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, dd) → new_lookupWithDefaultFM0348(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, new_primMulNat0(Succ(wx1281), wx1275), dd)
new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195200), Zero, da) → new_lookupWithDefaultFM0326(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45600), Succ(wx40800), da) → new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45600, wx40800, da)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Succ(wx261000))), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0102(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Zero, h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Succ(Succ(wx198400)), h) → new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190100, wx198400, h)
new_lookupWithDefaultFM033(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, bc) → new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, new_primMulNat0(Succ(wx1171), wx1165), bc)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0330(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM092(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM0531(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM08(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0321(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM0540(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM013(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM097(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM087(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM035(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx2230), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM015(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM05(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Succ(wx198400), h) → new_lookupWithDefaultFM0546(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190100, wx198400, h)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Zero)), da)
new_lookupWithDefaultFM0350(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, df) → new_lookupWithDefaultFM0351(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, new_primMulNat0(Succ(wx1290), wx1284), df)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM036(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Pos(wx2050), wx206, wx207, wx208, wx209, wx210, Pos(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM00(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0351(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, Succ(wx19750), df) → new_lookupWithDefaultFM020(wx1283, wx1288, Float(Pos(Succ(wx1289)), Neg(Succ(wx1290))), df)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Pos(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM04(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primPlusNat0(new_primMulNat0(wx21100, wx20500), Succ(wx20500)), h)
new_lookupWithDefaultFM0319(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM03(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Zero, wx238, h) → new_lookupWithDefaultFM0539(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM0349(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, df) → new_lookupWithDefaultFM0351(wx1283, wx1284, wx1285, wx1286, wx1287, wx1288, wx1289, wx1290, new_primMulNat0(Succ(wx1290), wx1284), df)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM091(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx235, Succ(Zero), h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Succ(Succ(Zero)), h) → new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45800), Zero, da) → new_lookupWithDefaultFM0328(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM021(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM010(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, h) → new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0272(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, bd) → new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, new_primMulNat0(Succ(wx1180), wx1174), bd)
new_lookupWithDefaultFM036(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0272(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, Zero, da) → new_lookupWithDefaultFM0320(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM099(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx468, ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Zero, h) → new_lookupWithDefaultFM025(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Zero), Zero, da) → new_lookupWithDefaultFM0320(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM02(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, wx237, h) → new_lookupWithDefaultFM0534(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h)
new_lookupWithDefaultFM09(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, Succ(wx2830), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(wx2110)), h)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(wx261000), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM0329(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Succ(wx20500)), wx206, wx207, wx208, wx209, wx210, Neg(Zero), Zero, h) → new_lookupWithDefaultFM012(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM032(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2210), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM097(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0349(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0334(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Succ(Succ(wx198200)), h) → new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190000, wx198200, h)
new_lookupWithDefaultFM085(wx398, wx399, Neg(wx4000), wx401, wx402, wx403, wx404, wx405, Neg(wx4060), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(wx4060)), da)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx238, Succ(Zero), h) → new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Zero), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM0(wx203, wx204, Neg(wx2050), wx206, wx207, wx208, wx209, wx210, Neg(wx2110), Succ(wx2120), h) → new_lookupWithDefaultFM03(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primPlusNat0(wx2120, wx204), h)
new_lookupWithDefaultFM0348(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, Succ(wx19740), dd) → new_lookupWithDefaultFM020(wx1274, wx1279, Float(Pos(Succ(wx1280)), Pos(Succ(wx1281))), dd)
new_lookupWithDefaultFM0315(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4540), da) → new_lookupWithDefaultFM0337(wx398, wx399, Succ(wx40000), wx401, wx402, wx403, wx404, wx405, Succ(wx40600), da)
new_lookupWithDefaultFM0346(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, dd) → new_lookupWithDefaultFM0348(wx1274, wx1275, wx1276, wx1277, wx1278, wx1279, wx1280, wx1281, new_primMulNat0(Succ(wx1281), wx1275), dd)
new_lookupWithDefaultFM0535(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19320), h) → new_lookupWithDefaultFM0536(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Succ(wx21100), h)
new_lookupWithDefaultFM0311(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx195200), Succ(wx125900), da) → new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195200, wx125900, da)
new_lookupWithDefaultFM07(wx203, wx204, wx206, wx207, wx208, wx209, wx210, Succ(wx11500), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(Zero)), h)
new_lookupWithDefaultFM035(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0272(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM037(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0275(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM035(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM038(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, bd) → new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, new_primMulNat0(Succ(wx1180), wx1174), bd)
new_lookupWithDefaultFM08(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, Succ(wx2820), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Pos(wx2110)), h)
new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Succ(wx198200), h) → new_lookupWithDefaultFM024(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx190000, wx198200, h)
new_lookupWithDefaultFM032(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0271(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba)
new_lookupWithDefaultFM098(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4650), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0313(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM0316(wx398, wx399, wx4000, wx401, wx402, wx403, wx404, wx405, wx4060, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(wx4060)), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0331(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM0332(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx405), wx399), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM088(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4210), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM031(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Zero), wx206, wx207, wx208, wx209, wx210, Neg(Zero), Zero, h) → new_lookupWithDefaultFM013(wx203, wx204, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM036(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2300), ba) → new_lookupWithDefaultFM038(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0275(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, ba) → new_lookupWithDefaultFM0274(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(wx263000), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM092(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4360), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0323(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx125900), Succ(Succ(wx195200)), da) → new_lookupWithDefaultFM0325(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195200, wx125900, da)
new_lookupWithDefaultFM010(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25900)), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx19000), h) → new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19000, new_primMulNat0(Succ(wx21100), wx20500), h)
new_lookupWithDefaultFM010(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM0543(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM021(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM023(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190000), Succ(Zero), h) → new_lookupWithDefaultFM025(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0105(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM091(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0346(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Zero, h) → new_lookupWithDefaultFM021(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM044(wx1596, wx1597, wx1598, wx1599, wx1600, wx1601, wx1602, wx1603, be) → new_lookupWithDefaultFM020(wx1596, wx1600, Float(Pos(Succ(wx1602)), Neg(Succ(wx1603))), be)
new_lookupWithDefaultFM00(wx203, wx204, Succ(wx20500), wx206, wx207, wx208, wx209, wx210, Zero, wx235, h) → new_lookupWithDefaultFM016(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM0333(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx126200), Succ(Succ(wx195400)), da) → new_lookupWithDefaultFM0335(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx195400, wx126200, da)
new_lookupWithDefaultFM0542(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM0544(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM01(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, wx236, h) → new_lookupWithDefaultFM0531(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h)
new_lookupWithDefaultFM0270(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, bc) → new_lookupWithDefaultFM0269(wx1164, wx1165, wx1166, wx1167, wx1168, wx1169, wx1170, wx1171, new_primMulNat0(Succ(wx1171), wx1165), bc)
new_lookupWithDefaultFM096(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Zero, ba) → new_lookupWithDefaultFM0349(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM099(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM093(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, wx4080, da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM089(wx1265, wx1266, wx1267, wx1268, wx1269, wx1270, wx1271, wx1272, db) → new_lookupWithDefaultFM020(wx1265, wx1269, Float(Pos(Succ(wx1271)), Pos(Succ(wx1272))), db)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Zero), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Zero)), da)
new_lookupWithDefaultFM094(wx1650, wx1651, wx1652, wx1653, wx1654, wx1655, wx1656, wx1657, dc) → new_lookupWithDefaultFM0347(wx1650, wx1651, wx1652, wx1653, wx1654, wx1655, wx1656, wx1657, dc)
new_lookupWithDefaultFM0(wx203, wx204, Neg(wx2050), wx206, wx207, wx208, wx209, wx210, Pos(wx2110), Zero, h) → new_lookupWithDefaultFM08(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0311(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4500), da) → new_lookupWithDefaultFM0321(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM093(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx439, ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0317(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx45600), Zero, da) → new_lookupWithDefaultFM0318(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0100(wx1659, wx1660, wx1661, wx1662, wx1663, wx1664, wx1665, wx1666, de) → new_lookupWithDefaultFM0350(wx1659, wx1660, wx1661, wx1662, wx1663, wx1664, wx1665, wx1666, de)
new_lookupWithDefaultFM03(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Succ(wx21100), wx238, h) → new_lookupWithDefaultFM0538(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), wx51), ba) → new_lookupWithDefaultFM085(wx4, wx30000, wx301, wx31, wx32, wx33, wx34, wx5000, wx51, new_primPlusNat0(new_primMulNat0(wx5000, wx30000), Succ(wx30000)), ba)
new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx190100), Succ(Zero), h) → new_lookupWithDefaultFM0547(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM019(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h) → new_lookupWithDefaultFM022(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM04(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25700)), h) → new_lookupWithDefaultFM018(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2040, wx25700, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM027(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM043(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx265, ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0(wx203, wx204, Neg(Zero), wx206, wx207, wx208, wx209, wx210, Neg(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM011(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Succ(Succ(Zero)), h) → new_lookupWithDefaultFM0543(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0103(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM086(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0534(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM09(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM04(wx203, Zero, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25700)), h) → new_lookupWithDefaultFM020(wx203, wx208, Float(Pos(Succ(wx210)), Pos(Succ(wx21100))), h)
new_lookupWithDefaultFM0(wx203, wx204, Pos(Zero), wx206, wx207, wx208, wx209, wx210, Pos(Succ(wx21100)), Zero, h) → new_lookupWithDefaultFM05(wx203, wx204, wx206, wx207, wx208, wx209, wx210, wx21100, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0(wx203, wx204, Pos(wx2050), wx206, wx207, wx208, wx209, wx210, Neg(wx2110), Zero, h) → new_lookupWithDefaultFM09(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM029(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM086(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4090), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0536(wx203, wx204, wx2050, wx206, wx207, wx208, wx209, wx210, wx2110, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(wx2110)), h)
new_lookupWithDefaultFM0274(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, bd) → new_lookupWithDefaultFM0273(wx1173, wx1174, wx1175, wx1176, wx1177, wx1178, wx1179, wx1180, new_primMulNat0(Succ(wx1180), wx1174), bd)
new_lookupWithDefaultFM092(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0346(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), wx4080, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM028(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM098(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba) → new_lookupWithDefaultFM0349(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0545(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx19010, Zero, h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Succ(wx21100))), h)
new_lookupWithDefaultFM085(wx398, wx399, Pos(wx4000), wx401, wx402, wx403, wx404, wx405, Pos(wx4060), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(wx4060)), da)
new_lookupWithDefaultFM0537(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2380), Succ(Succ(Succ(wx263000))), h) → new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2380, wx263000, h)
new_lookupWithDefaultFM090(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx4240), ba) → new_lookupWithDefaultFM094(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM014(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(wx2350), Succ(Succ(Succ(wx261000))), h) → new_lookupWithDefaultFM018(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2350, wx261000, h)
new_lookupWithDefaultFM013(wx203, wx204, wx206, wx207, wx208, wx209, wx210, Succ(wx11530), h) → new_lookupWithDefaultFM020(wx203, wx209, Float(Pos(Succ(wx210)), Neg(Zero)), h)
new_lookupWithDefaultFM0322(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Zero, da) → new_lookupWithDefaultFM0324(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primMulNat0(Succ(wx40600), wx40000), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM042(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0539(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, h) → new_lookupWithDefaultFM012(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, new_primMulNat0(Succ(wx210), wx204), h)
new_lookupWithDefaultFM0324(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx19530), da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Zero))), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Zero, ba)
new_lookupWithDefaultFM012(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx11520), h) → new_lookupWithDefaultFM0548(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx11520, new_primMulNat0(Zero, wx20500), h)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM0308(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), wx4080, da)
new_lookupWithDefaultFM085(wx398, wx399, Pos(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0310(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM040(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, Succ(wx2420), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Succ(wx40000)), wx401, wx402, wx403, wx404, wx405, Neg(Succ(wx40600)), Zero, da) → new_lookupWithDefaultFM0315(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, new_primPlusNat0(new_primMulNat0(wx40600, wx40000), Succ(wx40000)), da)
new_lookupWithDefaultFM04(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Zero), h) → new_lookupWithDefaultFM019(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM033(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Zero), ba)
new_lookupWithDefaultFM03(wx203, wx204, Zero, wx206, wx207, wx208, wx209, wx210, Zero, wx238, h) → new_lookupWithDefaultFM0540(wx203, wx204, wx206, wx207, wx208, wx209, wx210, h)
new_lookupWithDefaultFM041(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx2490), ba) → new_lookupWithDefaultFM044(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM087(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4160), ba) → new_lookupWithDefaultFM089(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM010(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Succ(Succ(wx25900)), h) → new_lookupWithDefaultFM0541(wx203, Succ(wx2040), wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, wx2040, wx25900, h)
new_lookupWithDefaultFM0310(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(wx4480), da) → new_lookupWithDefaultFM0316(wx398, wx399, Succ(wx40000), wx401, wx402, wx403, wx404, wx405, Succ(wx40600), da)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45800)), Zero, da) → new_lookupWithDefaultFM0328(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da)
new_lookupWithDefaultFM0105(wx1292, wx1293, wx1294, wx1295, wx1296, wx1297, wx1298, wx1299, dg) → new_lookupWithDefaultFM020(wx1292, wx1296, Float(Pos(Succ(wx1298)), Neg(Succ(wx1299))), dg)
new_lookupWithDefaultFM0309(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, Succ(Succ(wx45800)), Succ(wx40800), da) → new_lookupWithDefaultFM0327(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, wx45800, wx40800, da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM040(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM085(wx398, wx399, Neg(Zero), wx401, wx402, wx403, wx404, wx405, Pos(Succ(wx40600)), Succ(wx4080), da) → new_lookupWithDefaultFM020(wx398, wx403, Float(Pos(Succ(wx405)), Pos(Succ(wx40600))), da)
new_lookupWithDefaultFM097(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(wx4600), ba) → new_lookupWithDefaultFM0100(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0336(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx40600, da) → new_lookupWithDefaultFM020(wx398, wx404, Float(Pos(Succ(wx405)), Neg(Succ(wx40600))), da)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx5000)), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM037(wx4, wx30100, wx31, wx32, wx33, wx34, wx5000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0541(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, Zero, Zero, h) → new_lookupWithDefaultFM0543(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx21100, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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



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

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

new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Succ(wx194400), h) → new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx115200, wx194400, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Succ(wx194400), h) → new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx115200, wx194400, h)

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

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

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

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



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

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

new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx115200), Succ(wx194400), h) → new_lookupWithDefaultFM0549(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx115200, wx194400, 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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190600), Succ(wx107300), da) → new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190600, wx107300, da)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190600), Succ(wx107300), da) → new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190600, wx107300, da)

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

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

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

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



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

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

new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190600), Succ(wx107300), da) → new_lookupWithDefaultFM0344(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190600, wx107300, 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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Succ(wx194200), h) → new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx114900, wx194200, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Succ(wx194200), h) → new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx114900, wx194200, h)

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

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

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

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



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

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

new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, Succ(wx114900), Succ(wx194200), h) → new_lookupWithDefaultFM0529(wx203, wx204, wx20500, wx206, wx207, wx208, wx209, wx210, wx114900, wx194200, 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
                          ↳ UsableRulesProof
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190400), Succ(wx107000), da) → new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190400, wx107000, da)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190400), Succ(wx107000), da) → new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190400, wx107000, da)

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

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

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

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



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

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

new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, Succ(wx190400), Succ(wx107000), da) → new_lookupWithDefaultFM0340(wx398, wx399, wx40000, wx401, wx402, wx403, wx404, wx405, wx190400, wx107000, 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
                          ↳ QDPSizeChangeProof
                        ↳ QDP
                        ↳ QDP

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

new_lookupWithDefaultFM0508(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Zero, wx1538), bah)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0198(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0263(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0239(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0184(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0246(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx981, ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0201(wx1833, wx1834, wx1835, wx1836, wx1837, wx1838, wx1839, he) → new_lookupWithDefaultFM0434(wx1833, wx1834, wx1835, wx1836, wx1837, wx1838, wx1839, he)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0510(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Zero, wx1538), bah)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0265(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0514(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0510(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0184(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7570), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0427(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx19930), gh) → new_lookupWithDefaultFM020(wx1430, wx1436, Float(Neg(Zero), Neg(Succ(wx1437))), gh)
new_lookupWithDefaultFM0512(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, Succ(wx19730), bah) → new_lookupWithDefaultFM0513(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah)
new_lookupWithDefaultFM0266(wx4, wx30100, wx31, wx32, wx33, wx34, wx1045, ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0424(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh) → new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0260(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0203(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0200(wx4, wx30100, wx31, wx32, wx33, wx34, wx812, ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0198(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0433(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0423(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, gh) → new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, new_primMulNat0(Zero, wx1431), gh)
new_lookupWithDefaultFM0527(wx4, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupWithDefaultFM0526(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0241(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Zero, wx1538), bah)
new_lookupWithDefaultFM0177(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0423(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0204(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8210), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0179(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0423(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0183(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0267(wx1893, wx1894, wx1895, wx1896, wx1897, wx1898, wx1899, bbf) → new_lookupWithDefaultFM020(wx1893, wx1897, Float(Neg(Zero), Neg(Succ(wx1899))), bbf)
new_lookupWithDefaultFM0245(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9780), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0197(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0186(wx1440, wx1441, wx1442, wx1443, wx1444, wx1445, wx1446, wx1447, ha) → new_lookupWithDefaultFM020(wx1440, wx1445, Float(Neg(Zero), Neg(Succ(wx1447))), ha)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0243(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0259(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0425(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Zero, gh) → new_lookupWithDefaultFM0427(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, new_primMulNat0(Succ(wx1437), wx1432), gh)
new_lookupWithDefaultFM0203(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx8140), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0513(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, bah) → new_lookupWithDefaultFM020(wx1537, wx1543, Float(Neg(Zero), Neg(Succ(wx1544))), bah)
new_lookupWithDefaultFM0435(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, Succ(wx19810), hf) → new_lookupWithDefaultFM020(wx1465, wx1470, Float(Neg(Zero), Neg(Succ(wx1471))), hf)
new_lookupWithDefaultFM0244(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9730), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0181(wx1799, wx1800, wx1801, wx1802, wx1803, wx1804, wx1805, wx1806, gg) → new_lookupWithDefaultFM0424(wx1799, wx1800, wx1801, wx1802, wx1803, wx1804, wx1805, wx1806, gg)
new_lookupWithDefaultFM0178(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0423(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0264(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10370), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0185(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7620), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0178(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7400), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0526(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, bbe) → new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, new_primMulNat0(Succ(wx1577), wx1572), bbe)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0258(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0197(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0433(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0198(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8040), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0177(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM0433(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, hf) → new_lookupWithDefaultFM0435(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, new_primMulNat0(Succ(wx1471), wx1466), hf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0264(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0260(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0527(wx4, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0259(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10220), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Succ(wx510000000)))))))), ba) → new_lookupWithDefaultFM0238(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx510000000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0263(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx10300), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Zero), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0260(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10270), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0239(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0508(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0197(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7970), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0266(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0238(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0508(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0509(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, Zero, bah) → new_lookupWithDefaultFM0512(wx1537, wx1538, wx1539, wx1540, wx1541, wx1542, wx1543, wx1544, new_primMulNat0(Succ(wx1544), wx1539), bah)
new_lookupWithDefaultFM0240(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9630), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0265(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx10420), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0206(wx1473, wx1474, wx1475, wx1476, wx1477, wx1478, wx1479, hg) → new_lookupWithDefaultFM020(wx1473, wx1477, Float(Neg(Zero), Neg(Succ(wx1479))), hg)
new_lookupWithDefaultFM0199(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0433(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0185(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0258(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx10150), ba) → new_lookupWithDefaultFM0261(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0240(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0514(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupWithDefaultFM0177(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7330), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0180(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx748, ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0267(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM0259(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupWithDefaultFM0524(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM0434(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, hf) → new_lookupWithDefaultFM0435(wx1465, wx1466, wx1467, wx1468, wx1469, wx1470, wx1471, new_primMulNat0(Succ(wx1471), wx1466), hf)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0200(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0258(wx4, wx30100, wx31, wx32, wx33, wx34, wx510000000, Zero, ba) → new_lookupWithDefaultFM0524(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0240(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM0205(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8260), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0199(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(wx8090), ba) → new_lookupWithDefaultFM0201(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM0179(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7450), ba) → new_lookupWithDefaultFM0181(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Zero))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0180(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM0247(wx1876, wx1877, wx1878, wx1879, wx1880, wx1881, wx1882, wx1883, bba) → new_lookupWithDefaultFM020(wx1876, wx1881, Float(Neg(Zero), Neg(Succ(wx1883))), bba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0246(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(Succ(new_primPlusNat0(wx30100, wx30100)), wx30100), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0205(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0524(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, bbe) → new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, new_primMulNat0(Succ(wx1577), wx1572), bbe)
new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, Succ(wx19410), bbe) → new_lookupWithDefaultFM020(wx1571, wx1576, Float(Neg(Zero), Neg(Succ(wx1577))), bbe)
new_lookupWithDefaultFM0261(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, bbe) → new_lookupWithDefaultFM0525(wx1571, wx1572, wx1573, wx1574, wx1575, wx1576, wx1577, new_primMulNat0(Succ(wx1577), wx1572), bbe)
new_lookupWithDefaultFM0183(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx7500), ba) → new_lookupWithDefaultFM0186(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0244(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0238(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9510), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0199(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0204(wx4, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM0243(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, wx510000000, Succ(wx9660), ba) → new_lookupWithDefaultFM0247(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Succ(wx510000000))))), ba)
new_lookupWithDefaultFM0239(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx9580), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Succ(Succ(Zero)))), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0245(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Succ(Zero))))))), ba) → new_lookupWithDefaultFM0178(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0241(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Succ(Zero)))))), ba) → new_lookupWithDefaultFM0179(wx4, wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupWithDefaultFM020(wx4, Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(Zero))))), ba) → new_lookupWithDefaultFM0206(wx4, wx30100, wx31, wx32, wx33, wx34, Succ(Succ(Zero)), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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



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

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

new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx199200), Succ(wx192100), gh) → new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, wx199200, wx192100, gh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx199200), Succ(wx192100), gh) → new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, wx199200, wx192100, gh)

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

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

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

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



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

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

new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, Succ(wx199200), Succ(wx192100), gh) → new_lookupWithDefaultFM0428(wx1430, wx1431, wx1432, wx1433, wx1434, wx1435, wx1436, wx1437, wx199200, wx192100, 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
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
                        ↳ QDP
QDP
                          ↳ UsableRulesProof

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

new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Succ(wx203200), bbb) → new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx200100, wx203200, bbb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat1(Succ(wx2150), wx30000) → Succ(Succ(new_primPlusNat0(wx2150, wx30000)))
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat0(Succ(wx21500), Zero) → Succ(wx21500)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx21500), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx21500, wx300000)))
new_primMulNat0(Succ(wx50000), wx30000) → new_primPlusNat1(new_primMulNat0(wx50000, wx30000), wx30000)

The set Q consists of the following terms:

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

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

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

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

new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Succ(wx203200), bbb) → new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx200100, wx203200, bbb)

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

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

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

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



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

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

new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, Succ(wx200100), Succ(wx203200), bbb) → new_lookupWithDefaultFM0518(wx1546, wx1547, wx1548, wx1549, wx1550, wx1551, wx1552, wx1553, wx200100, wx203200, 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: