YES 152.468 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
  ↳ BR

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ BR
HASKELL
      ↳ COR

mainModule FiniteMap
  ((lookupFM :: FiniteMap Float a  ->  Float  ->  Maybe a) :: FiniteMap Float a  ->  Float  ->  Maybe a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude

  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a


  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 

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


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

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

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)

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
  ↳ BR
    ↳ HASKELL
      ↳ COR
HASKELL
          ↳ Narrow

mainModule FiniteMap
  (lookupFM :: FiniteMap Float a  ->  Float  ->  Maybe 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


module Maybe where
  import qualified FiniteMap
import qualified Prelude



Haskell To QDPs


↳ 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(wx7800), Succ(wx300000)) → new_primPlusNat(wx7800, 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
  ↳ BR
    ↳ HASKELL
      ↳ COR
        ↳ HASKELL
          ↳ Narrow
            ↳ AND
              ↳ QDP
QDP
                ↳ QDPSizeChangeProof
              ↳ QDP

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

new_primMulNat(Succ(wx40000), wx30000) → new_primMulNat(wx40000, 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
  ↳ BR
    ↳ HASKELL
      ↳ COR
        ↳ HASKELL
          ↳ Narrow
            ↳ AND
              ↳ QDP
              ↳ QDP
QDP
                ↳ DependencyGraphProof

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

new_lookupFM2195(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM240(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2130(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Pos(Zero)), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM227(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM243(wx37, Pos(wx380), wx39, wx40, wx41, wx42, wx43, Pos(wx440), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(wx440)), bd)
new_lookupFM269(wx56, Pos(wx570), wx58, wx59, wx60, wx61, wx62, Pos(wx630), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(wx630)), bf)
new_lookupFM148(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6040), ba) → new_lookupFM1313(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6040, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2146(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM274(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2710), ba) → new_lookupFM2178(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM1326(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx88400)), ba) → new_lookupFM1329(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77800), Succ(wx60400), ba) → new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77800, wx60400, ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Succ(wx38200)), bh) → new_lookupFM2203(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1278(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8020), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1309(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx87600)), ba) → new_lookupFM1312(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Zero, bd) → new_lookupFM2141(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1173(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx53900), Succ(Succ(wx75400)), be) → new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx75400, wx53900, be)
new_lookupFM155(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7230), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20200), Zero, bd) → new_lookupFM2139(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Zero, ba) → new_lookupFM1169(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1413(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1394(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2154(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Zero, ba) → new_lookupFM1430(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM119(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM241(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1162(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Succ(Zero), be) → new_lookupFM1182(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), wx41), ba) → new_lookupFM2(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat1(new_primMulNat0(wx4000, wx30000), wx30000), ba)
new_lookupFM1131(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6590, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, Succ(wx58500), Succ(wx47200), ba) → new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, wx58500, wx47200, ba)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Zero, bf) → new_lookupFM2160(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM2217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6820), ba) → new_lookupFM1235(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6820, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM1359(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Succ(Zero), bh) → new_lookupFM1361(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM149(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1318(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1210(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx76200)), ba) → new_lookupFM1213(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2116(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2163(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2890), bf) → new_lookupFM2175(wx56, Succ(wx5700), wx58, wx59, wx60, wx61, wx62, Succ(wx6300), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM235(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69000), Zero, bf) → new_lookupFM1265(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM140(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Zero, bf) → new_lookupFM2173(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1245(wx30100, wx31, wx32, wx33, wx34, Succ(wx7670), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1340(wx30100, wx31, wx32, wx33, wx34, Succ(wx71100), Succ(Succ(wx88800)), ba) → new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, wx88800, wx71100, ba)
new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Succ(wx82800), ba) → new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx65800, wx82800, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM148(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77200), Zero, bf) → new_lookupFM1261(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM249(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1860), ba) → new_lookupFM2151(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1127(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6580, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2223(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM126(wx30100, wx31, wx32, wx33, wx34, Succ(wx6640), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM110(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx5320), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Zero)), ba)
new_lookupFM117(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4570), ba) → new_lookupFM1109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4570, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1414(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM264(wx30100, wx31, wx32, wx33, wx34, Succ(wx2400), ba) → new_lookupFM2155(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1223(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx68000), Succ(Succ(wx85800)), ba) → new_lookupFM186(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, wx410000, wx85800, wx68000, ba)
new_lookupFM1417(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx9050), ba) → new_lookupFM1418(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1214(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx58300)), ba) → new_lookupFM1217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM13(wx28, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1377(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx76200), Succ(wx58200), ba) → new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, wx76200, wx58200, ba)
new_lookupFM111(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx6510), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM259(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2240), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Zero, be) → new_lookupFM1179(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, new_primMulNat0(wx2610, wx21), be)
new_lookupFM290(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3310), ba) → new_lookupFM2186(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, wx53000, wx72200, bh)
new_lookupFM258(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2220), ba) → new_lookupFM2153(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1184(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Succ(Succ(wx75200)), bd) → new_lookupFM1187(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, Succ(wx7110), ba) → new_lookupFM1340(wx30100, wx31, wx32, wx33, wx34, wx7110, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM289(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM127(wx30100, wx31, wx32, wx33, wx34, Succ(wx5350), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM1290(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5620, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM233(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1126(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM282(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1244(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx76600)), ba) → new_lookupFM1247(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM146(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM27(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1344(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx78200)), ba) → new_lookupFM1347(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1404(wx30000, wx31, wx32, wx33, wx34, wx4960, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM27(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1030), h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM1259(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx7730), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM1424(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Succ(Succ(wx90800)), ba) → new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, wx73400, wx90800, ba)
new_lookupFM225(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx970), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7050), ba) → new_lookupFM1309(wx30000, wx30100, wx31, wx32, wx33, wx34, wx7050, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), wx41), ba) → new_lookupFM294(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat0(new_primMulNat0(wx4000, wx30000), Succ(wx30000)), ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM2197(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM258(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Succ(Succ(wx78400)), bh) → new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx61500, wx78400, bh)
new_lookupFM1401(wx30000, wx31, wx32, wx33, wx34, wx4940, wx624, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Succ(wx57000), ba) → new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, wx46300, wx57000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM290(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1348(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), Zero, bh) → new_lookupFM1179(wx65, wx6600, wx67, wx68, wx69, wx70, Succ(wx71), Succ(wx7200), new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM2103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3860), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1189(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx6730), bd) → new_lookupFM(wx42, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM189(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6530, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1173(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Zero, Succ(Succ(wx75400)), be) → new_lookupFM1176(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM1249(wx56, wx58, wx59, wx60, wx61, wx62, Zero, bf) → new_lookupFM1267(wx56, wx58, wx59, wx60, wx61, wx62, new_primMulNat1, bf)
new_lookupFM2120(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM175(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1169(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1247(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2129(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1406(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM232(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1171(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Zero, be) → new_lookupFM1174(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, new_primMulNat0(wx2610, wx21), be)
new_lookupFM2177(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1279(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1111(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM287(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM2221(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Zero, bd) → new_lookupFM2134(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM1140(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6600), ba) → new_lookupFM1141(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6600, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Zero)), bd)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1341(wx30100, wx31, wx32, wx33, wx34, Succ(wx8890), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Zero, bf) → new_lookupFM2163(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20200)), Succ(wx16300), bd) → new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20200, wx16300, bd)
new_lookupFM2108(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1115(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM2200(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM1304(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx70400), Succ(Succ(wx87400)), ba) → new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87400, wx70400, ba)
new_lookupFM1371(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8110), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1288(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8730), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(wx4100))), ba) → new_lookupFM168(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1238(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM252(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2133(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx1940), bd) → new_lookupFM2137(wx37, Succ(wx3800), wx39, wx40, wx41, wx42, wx43, Succ(wx4400), bd)
new_lookupFM189(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Succ(Zero), ba) → new_lookupFM191(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2105(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3920), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1277(wx56, wx58, wx59, wx60, wx61, wx62, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM1206(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx67700), Succ(Succ(wx85200)), ba) → new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, wx85200, wx67700, ba)
new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx76200), Zero, ba) → new_lookupFM1213(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM294(wx65, Neg(wx660), wx67, wx68, wx69, wx70, wx71, Pos(wx720), Succ(wx3430), bh) → new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM161(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Zero, ba) → new_lookupFM1380(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(wx4100))), ba) → new_lookupFM165(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1113(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6560, wx824, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM282(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1417(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1149(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1330(wx30100, wx31, wx32, wx33, wx34, Succ(wx61300), Succ(Succ(wx78000)), ba) → new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, wx78000, wx61300, ba)
new_lookupFM240(wx30100, wx31, wx32, wx33, wx34, Succ(wx1550), ba) → new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Succ(wx790), h) → new_lookupFM26(Float(Pos(Succ(wx28)), Neg(Succ(wx2900))), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1345(wx30100, wx31, wx32, wx33, wx34, Succ(wx7830), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM29(wx28, Zero, wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM1179(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx7600), be) → new_lookupFM(wx25, Float(Neg(wx2600), Pos(wx2610)), be)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1426(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM268(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM28(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM29(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM2152(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM221(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM148(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1314(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1206(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx85200)), ba) → new_lookupFM1209(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Succ(wx790), h) → new_lookupFM26(Float(Pos(Succ(wx28)), Neg(Zero)), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1244(wx30100, wx31, wx32, wx33, wx34, Succ(wx59000), Succ(Succ(wx76600)), ba) → new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, wx76600, wx59000, ba)
new_lookupFM18(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM1248(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Zero, bf) → new_lookupFM1263(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, new_primMulNat0(Zero, wx5700), bf)
new_lookupFM1331(wx30100, wx31, wx32, wx33, wx34, Succ(wx7810), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1279(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8030), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Zero, bf) → new_lookupFM2173(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM115(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1299(wx30000, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx60200)), ba) → new_lookupFM1302(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Zero, ba) → new_lookupFM191(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1170(wx37, wx39, wx40, wx41, wx42, wx43, Zero, bd) → new_lookupFM1189(wx37, wx39, wx40, wx41, wx42, wx43, new_primMulNat1, bd)
new_lookupFM2126(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM152(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1159(wx30100, wx31, wx32, wx33, wx34, wx6660, wx840, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1349(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), Zero, bh) → new_lookupFM1365(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM231(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1270), ba) → new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx58300), Zero, ba) → new_lookupFM1217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Succ(wx62600), ba) → new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, wx49600, wx62600, ba)
new_lookupFM1378(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Succ(Succ(wx61600)), ba) → new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, wx48800, wx61600, ba)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Zero, bh) → new_lookupFM2204(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM299(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1317(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx60500)), ba) → new_lookupFM1320(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM192(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Succ(Zero), ba) → new_lookupFM194(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM215(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM218(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Succ(wx11100)), h) → new_lookupFM216(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM280(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM162(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4900), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(wx4100))), ba)
new_lookupFM2139(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Zero, bh) → new_lookupFM2209(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2105(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1215(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5840), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx85200), Zero, ba) → new_lookupFM1209(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2213(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1371(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1227(wx30100, wx31, wx32, wx33, wx34, Succ(wx8610), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM255(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2160), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1199(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM249(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1195(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM244(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM121(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1250(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Zero, bf) → new_lookupFM1271(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, new_primMulNat0(Zero, wx5700), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM114(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Succ(wx11100)), h) → new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11100, h)
new_lookupFM1404(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Succ(Zero), ba) → new_lookupFM1406(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM2175(wx56, wx570, wx58, wx59, wx60, wx61, wx62, wx630, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(wx630)), bf)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Succ(wx3430), bh) → new_lookupFM2190(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx37)), Neg(Succ(wx3800))), wx39, wx40, wx41, wx42, wx43, bd)
new_lookupFM192(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4540, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM1156(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8390), ba) → new_lookupFM1157(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, Succ(wx78000), Succ(wx61300), ba) → new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, wx78000, wx61300, ba)
new_lookupFM1362(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Succ(Succ(wx72000)), bh) → new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, wx52800, wx72000, bh)
new_lookupFM2199(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM280(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3010), ba) → new_lookupFM2180(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM128(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM147(wx30000, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1300(wx30000, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1233(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM223(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM210(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM211(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM1431(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx5040, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Zero)), h)
new_lookupFM146(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4790), ba) → new_lookupFM1295(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4790, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM211(wx28, Zero, wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM1350(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx5260), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Zero, bh) → new_lookupFM1369(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM296(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1224(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8590), ba) → new_lookupFM185(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, wx410000, wx8590, Zero, ba)
new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6570), ba) → new_lookupFM1117(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6570, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1430(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM12(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx5040), h) → new_lookupFM1431(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx5040, new_primMulNat0(Zero, wx2900), h)
new_lookupFM276(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2770), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1404(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Succ(Succ(wx62600)), ba) → new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, wx49600, wx62600, ba)
new_lookupFM1397(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1241(wx30100, wx31, wx32, wx33, wx34, Succ(wx8650), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx56, Neg(Zero), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM274(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69600), Succ(wx52200), bf) → new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, wx69600, wx52200, bf)
new_lookupFM1285(wx498100, wx499, wx500, wx501, wx502, Succ(wx9470), bg) → new_lookupFM(wx502, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM1226(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx86000)), ba) → new_lookupFM1229(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1362(wx65, wx67, wx68, wx69, wx70, wx71, wx5280, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Zero)), bh)
new_lookupFM13(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx5050), h) → new_lookupFM1434(wx28, wx30, wx31, wx32, wx33, wx34, wx5050, new_primMulNat1, h)
new_lookupFM1253(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx59200), Succ(Succ(wx77000)), bf) → new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77000, wx59200, bf)
new_lookupFM151(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1331(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2156(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1424(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7340, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2189(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1350(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1418(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM135(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4710), ba) → new_lookupFM1214(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4710, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM163(wx30000, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1385(wx30000, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM242(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx86200), Zero, ba) → new_lookupFM1238(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM236(wx30100, wx31, wx32, wx33, wx34, Succ(wx1430), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM257(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2180), ba) → new_lookupFM2152(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1374(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7250), ba) → new_lookupFM1375(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx7250, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Succ(wx74600), h) → new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56200, wx74600, h)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Zero, bh) → new_lookupFM2202(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5620), h) → new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5620, new_primMulNat0(Succ(wx3500), wx2900), h)
new_lookupFM174(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7860), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM289(wx30100, wx31, wx32, wx33, wx34, Succ(wx3290), ba) → new_lookupFM2185(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM21(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM11(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM121(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4600), ba) → new_lookupFM1123(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4600, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Succ(Zero), h) → new_lookupFM18(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM291(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69000), Succ(wx51800), bf) → new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69000, wx51800, bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM225(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1177(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, wx758, be) → new_lookupFM1180(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM217(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1321(wx30000, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx60700)), ba) → new_lookupFM1324(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1166(wx30100, wx31, wx32, wx33, wx34, Succ(wx6690), ba) → new_lookupFM1167(wx30100, wx31, wx32, wx33, wx34, wx6690, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(wx4100))), ba) → new_lookupFM116(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM155(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1420(wx30100, wx31, wx32, wx33, wx34, wx7320, wx906, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), wx2540, bf)
new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60000), Zero, ba) → new_lookupFM1298(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, Succ(wx7320), ba) → new_lookupFM1420(wx30100, wx31, wx32, wx33, wx34, wx7320, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1326(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx70900), Succ(Succ(wx88400)), ba) → new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88400, wx70900, ba)
new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Zero, ba) → new_lookupFM1410(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60500), Succ(wx48200), ba) → new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60500, wx48200, ba)
new_lookupFM1282(Float(Pos(Succ(wx498000)), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1283(wx498000, wx498100, wx499, wx500, wx501, wx502, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM1375(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx7250, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2104(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Succ(Succ(wx74600)), h) → new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56200, wx74600, h)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Zero, bf) → new_lookupFM2168(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1209(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM153(wx30100, wx31, wx32, wx33, wx34, Succ(wx6140), ba) → new_lookupFM1344(wx30100, wx31, wx32, wx33, wx34, wx6140, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1254(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx85200), Succ(wx67700), ba) → new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, wx85200, wx67700, ba)
new_lookupFM2162(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM252(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2060), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, Succ(wx76400), Succ(wx58900), ba) → new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, wx76400, wx58900, ba)
new_lookupFM1258(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx59300), Succ(Succ(wx77200)), bf) → new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77200, wx59300, bf)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM170(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Zero)), ba) → new_lookupFM156(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2106(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2100(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3660), ba) → new_lookupFM1373(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM2198(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM1280(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8040), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM228(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1190), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Zero, bd) → new_lookupFM2135(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1156(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM269(wx56, Neg(wx570), wx58, wx59, wx60, wx61, wx62, Neg(wx630), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(wx630)), bf)
new_lookupFM2127(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Neg(wx2610), Succ(wx5400), be) → new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, new_primMulNat0(wx2610, wx21), be)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM266(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Zero), bh) → new_lookupFM2209(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1219(wx30000, wx31, wx32, wx33, wx34, Succ(wx5860), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1167(wx30100, wx31, wx32, wx33, wx34, wx6690, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM145(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4040), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM216(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Succ(wx89400), ba) → new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx72500, wx89400, ba)
new_lookupFM213(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1283(wx498000, wx498100, wx499, wx500, wx501, wx502, Succ(wx9370), bg) → new_lookupFM(wx502, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(wx25400), bf) → new_lookupFM2172(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM221(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx850), ba) → new_lookupFM174(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM197(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM243(wx37, Neg(Zero), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Zero, bd) → new_lookupFM1170(wx37, wx39, wx40, wx41, wx42, wx43, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM288(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3250), ba) → new_lookupFM2184(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2116(wx30100, wx31, wx32, wx33, wx34, Succ(wx4260), ba) → new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx87600), Zero, ba) → new_lookupFM1312(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Zero), bh) → new_lookupFM2202(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1262(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx51800), Succ(Succ(wx69000)), bf) → new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69000, wx51800, bf)
new_lookupFM2187(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2169(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87200), Zero, ba) → new_lookupFM1290(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1352(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx5280), bh) → new_lookupFM1362(wx65, wx67, wx68, wx69, wx70, wx71, wx5280, new_primMulNat1, bh)
new_lookupFM1262(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Zero, Succ(Succ(wx69000)), bf) → new_lookupFM1265(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM166(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1399(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(wx11300), h) → new_lookupFM2226(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM10(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), Zero, h) → new_lookupFM182(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM2194(wx65, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM1354(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2186(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Succ(wx3430), bh) → new_lookupFM2191(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, Succ(wx86400), Zero, ba) → new_lookupFM1243(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1180(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be) → new_lookupFM(wx25, Float(Neg(wx2600), Pos(wx2610)), be)
new_lookupFM286(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3190), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx86200), Succ(wx68200), ba) → new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, wx86200, wx68200, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM234(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2207(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM133(wx30000, wx31, wx32, wx33, wx34, Succ(wx4690), ba) → new_lookupFM1196(wx30000, wx31, wx32, wx33, wx34, wx4690, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM249(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM227(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM183(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2113(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4160), ba) → new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1141(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6600, wx832, ba) → new_lookupFM185(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, wx410000, wx6600, wx832, ba)
new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Zero, h) → new_lookupFM18(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM273(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2690), ba) → new_lookupFM2177(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM139(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1245(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2171(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM2174(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2135(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM118(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1423(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7340), ba) → new_lookupFM1424(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7340, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM233(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1330), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx67200), Zero, bd) → new_lookupFM1191(wx37, wx39, wx40, wx41, wx42, wx43, bd)
new_lookupFM166(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4930), ba) → new_lookupFM1398(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4930, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM2100(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2215(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1378(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Succ(Zero), ba) → new_lookupFM1380(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1229(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6550, wx822, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1137(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Succ(Zero), ba) → new_lookupFM1139(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1428(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Succ(Succ(wx91000)), ba) → new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, wx73500, wx91000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM231(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1187(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM(wx42, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM167(wx30000, wx31, wx32, wx33, wx34, Succ(wx4940), ba) → new_lookupFM1401(wx30000, wx31, wx32, wx33, wx34, wx4940, new_primMulNat1, ba)
new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Zero, ba) → new_lookupFM1426(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM125(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM163(wx30000, wx31, wx32, wx33, wx34, Succ(wx4910), ba) → new_lookupFM1384(wx30000, wx31, wx32, wx33, wx34, wx4910, new_primMulNat1, ba)
new_lookupFM1250(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx5210), bf) → new_lookupFM1270(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx5210, new_primMulNat0(Zero, wx5700), bf)
new_lookupFM1136(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1408(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Succ(Succ(wx90000)), ba) → new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, wx72800, wx90000, ba)
new_lookupFM295(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3500), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM138(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM164(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1344(wx30100, wx31, wx32, wx33, wx34, Succ(wx61400), Succ(Succ(wx78200)), ba) → new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, wx78200, wx61400, ba)
new_lookupFM138(wx30100, wx31, wx32, wx33, wx34, Succ(wx5420), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM2161(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2850), bf) → new_lookupFM2169(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1307(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1362(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Succ(Zero), bh) → new_lookupFM1364(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Succ(wx16300), bd) → new_lookupFM2140(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Zero), Zero, bf) → new_lookupFM1248(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM2166(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM2169(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, Succ(wx58500), Zero, ba) → new_lookupFM1221(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1163(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Succ(Succ(wx84200)), ba) → new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, wx66800, wx84200, ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Neg(Succ(wx2900))), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM287(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1273(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM1292(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7770), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2107(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1145(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Zero), bh) → new_lookupFM2211(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1385(wx30000, wx31, wx32, wx33, wx34, Succ(wx6210), ba) → new_lookupFM1386(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7260), ba) → new_lookupFM1388(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx7260, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Succ(wx3430), bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM2115(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4220), ba) → new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1221(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1370(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8100), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM125(wx30000, wx31, wx32, wx33, wx34, Succ(wx4640), ba) → new_lookupFM1137(wx30000, wx31, wx32, wx33, wx34, wx4640, new_primMulNat1, ba)
new_lookupFM2108(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4020), ba) → new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2101(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1129(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM119(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5340), ba) → new_lookupFM1120(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5340, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1254(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx7710), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Succ(wx5400), be) → new_lookupFM1177(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, new_primMulNat0(wx2610, wx21), be)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM2203(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20400)), Zero, bd) → new_lookupFM2143(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20200), Succ(wx16300), bd) → new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20200, wx16300, bd)
new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Succ(wx78400), bh) → new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx61500, wx78400, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2115(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1270(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx52100), Succ(Succ(wx69400)), bf) → new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69400, wx52100, bf)
new_lookupFM1412(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7290, wx902, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM277(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29100)), Succ(wx25400), bf) → new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29100, wx25400, bf)
new_lookupFM11(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5030), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88600), Zero, ba) → new_lookupFM1338(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29300), Zero, bf) → new_lookupFM2171(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM23(wx28, wx30, wx31, wx32, wx33, wx34, h) → new_lookupFM13(wx28, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2191(wx65, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM1352(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2184(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2148(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1192(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2108(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1424(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Succ(Zero), ba) → new_lookupFM1426(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM19(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx6500), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM254(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1375(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Succ(Succ(wx89400)), ba) → new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx72500, wx89400, ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Succ(wx790), h) → new_lookupFM21(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1256(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM1333(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1226(wx30100, wx31, wx32, wx33, wx34, Succ(wx68100), Succ(Succ(wx86000)), ba) → new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, wx86000, wx68100, ba)
new_lookupFM273(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1279(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69400), Zero, bf) → new_lookupFM1273(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM1295(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx47900), Succ(Succ(wx60000)), ba) → new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60000, wx47900, ba)
new_lookupFM2228(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM298(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1223(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx85800)), ba) → new_lookupFM187(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM220(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2111(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1407(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, Succ(wx60200), Zero, ba) → new_lookupFM1302(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Succ(wx56400), ba) → new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, wx45400, wx56400, ba)
new_lookupFM1369(wx65, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM1352(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM29(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx75200), Zero, bd) → new_lookupFM1187(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM218(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM232(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1310), ba) → new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Succ(wx790), h) → new_lookupFM25(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2210(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM1433(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Zero)), h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(wx4100))), ba) → new_lookupFM120(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM285(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2119(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM174(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM228(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(wx38400), bh) → new_lookupFM2210(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM228(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM188(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2227(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Succ(Succ(wx74800)), h) → new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56300, wx74800, h)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM2199(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Succ(wx61800), ba) → new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, wx48900, wx61800, ba)
new_lookupFM1265(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM1367(wx65, wx67, wx68, wx69, wx70, wx71, wx5300, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM2102(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3720), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM168(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4950), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(wx4100))), ba)
new_lookupFM269(wx56, Neg(Zero), wx58, wx59, wx60, wx61, wx62, Pos(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM185(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Succ(Succ(wx92000)), bc) → new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, wx9190, wx92000, bc)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(wx4100))), ba) → new_lookupFM162(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), wx2540, bf)
new_lookupFM2150(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1194(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1201(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx67600), Succ(Succ(wx85000)), ba) → new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx85000, wx67600, ba)
new_lookupFM149(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4820), ba) → new_lookupFM1317(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4820, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, Succ(wx60700), Succ(wx48300), ba) → new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, wx60700, wx48300, ba)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), wx1630, bd)
new_lookupFM1358(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM192(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Succ(Succ(wx56400)), ba) → new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, wx45400, wx56400, ba)
new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60500), Zero, ba) → new_lookupFM1320(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Zero)), ba) → new_lookupFM110(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, Succ(wx76600), Zero, ba) → new_lookupFM1247(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29100), Succ(wx25400), bf) → new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29100, wx25400, bf)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Succ(wx3430), bh) → new_lookupFM2194(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM132(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM281(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM238(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2128(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM213(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1309(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx70500), Succ(Succ(wx87600)), ba) → new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, wx87600, wx70500, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM163(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1282(Float(Neg(Succ(wx498000)), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1179(wx498000, wx498100, wx499, wx500, wx501, wx502, Zero, Succ(Succ(Zero)), new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM161(wx30000, wx31, wx32, wx33, wx34, Succ(wx4890), ba) → new_lookupFM1381(wx30000, wx31, wx32, wx33, wx34, wx4890, new_primMulNat1, ba)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, Succ(wx76400), Zero, ba) → new_lookupFM1233(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM229(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1210), ba) → new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1416(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7310, wx904, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(wx11100), h) → new_lookupFM216(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM273(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM113(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4540), ba) → new_lookupFM192(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4540, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Succ(wx11300)), h) → new_lookupFM2226(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM289(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6760), ba) → new_lookupFM1201(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6760, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1374(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1122(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1442(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM128(wx30100, wx31, wx32, wx33, wx34, Succ(wx6670), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM248(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM274(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1280(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM260(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77600), Succ(wx59900), ba) → new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77600, wx59900, ba)
new_lookupFM182(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx6440), h) → new_lookupFM181(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM224(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2122(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM2226(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM1170(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx5110), bd) → new_lookupFM1188(wx37, wx39, wx40, wx41, wx42, wx43, wx5110, new_primMulNat1, bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM154(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM248(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1194(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1143(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Succ(Succ(wx83300)), ba) → new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, wx66100, wx83300, ba)
new_lookupFM134(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1211(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Succ(Zero), bh) → new_lookupFM1358(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, Succ(wx86000), Zero, ba) → new_lookupFM1229(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM170(wx30100, wx31, wx32, wx33, wx34, Succ(wx7300), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1126(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6580), ba) → new_lookupFM1127(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6580, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM173(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM127(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM243(wx37, Neg(Zero), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, Succ(wx78200), Succ(wx61400), ba) → new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, wx78200, wx61400, ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Neg(Zero)), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM245(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM210(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1431(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Succ(Succ(wx64600)), h) → new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx50400, wx64600, h)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM2195(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM251(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1920), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx56, Pos(Zero), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM147(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2130(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2125(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1105(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1163(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Succ(Zero), ba) → new_lookupFM1165(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM229(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2123(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2167(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Succ(wx790), h) → new_lookupFM23(wx28, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM211(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2190(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM1351(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM135(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM280(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2112(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Zero, bd) → new_lookupFM2145(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM224(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM279(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2110(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4080), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM288(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2197(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1305(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8750), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1153(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Zero, bd) → new_lookupFM2136(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM290(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2118(wx30100, wx31, wx32, wx33, wx34, Succ(wx4320), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2198(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM2199(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM257(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM164(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5570), ba) → new_lookupFM1395(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5570, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69400, wx52100, bf)
new_lookupFM283(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3110), ba) → new_lookupFM2183(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2116(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2221(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM189(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Succ(Succ(wx81800)), ba) → new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65300, wx81800, ba)
new_lookupFM2182(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2172(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM117(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1110(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Succ(wx11300)), h) → new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11300, h)
new_lookupFM165(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4920), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(wx4100))), ba)
new_lookupFM1143(wx30100, wx31, wx32, wx33, wx34, wx6610, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(wx4100))), ba) → new_lookupFM123(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1393(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2106(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1335(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx88600)), ba) → new_lookupFM1338(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM250(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM167(wx30000, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1402(wx30000, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM263(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Succ(wx38400)), bh) → new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38400, bh)
new_lookupFM298(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2213(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2104(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1389(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8970), ba) → new_lookupFM1390(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2222(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM242(wx30100, wx31, wx32, wx33, wx34, Succ(wx1610), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1152(wx30100, wx31, wx32, wx33, wx34, Succ(wx8370), ba) → new_lookupFM1153(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, wx2540, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Zero, h) → new_lookupFM2227(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1437(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx6410), h) → new_lookupFM1438(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM1304(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx87400)), ba) → new_lookupFM1307(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, Succ(wx4520), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(wx720)), bh)
new_lookupFM116(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4560), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(wx4100))), ba)
new_lookupFM144(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx5470), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Zero)), ba)
new_lookupFM129(wx30100, wx31, wx32, wx33, wx34, Succ(wx5360), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM2196(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM136(wx30000, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1219(wx30000, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx6150), bh) → new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx6150, new_primMulNat0(Succ(wx7200), wx6600), bh)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(wx11100), h) → new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11100, h)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Zero, h) → new_lookupFM2225(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2189(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1182(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be) → new_lookupFM(wx25, Float(Neg(wx2600), Neg(wx2610)), be)
new_lookupFM158(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx5550), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2110(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1365(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx7160), bh) → new_lookupFM1366(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM2196(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM2197(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, Succ(wx58000), Succ(wx46900), ba) → new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, wx58000, wx46900, ba)
new_lookupFM1388(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx7260, wx896, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM14(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1347(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM239(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2129(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM297(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, Zero, h) → new_lookupFM2228(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Zero, ba) → new_lookupFM1129(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77000), Zero, bf) → new_lookupFM1256(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM275(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2128(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1148(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2113(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2218(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM167(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Zero, bd) → new_lookupFM2133(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29300), Succ(wx25400), bf) → new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29300, wx25400, bf)
new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Zero, h) → new_lookupFM1436(wx28, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM287(wx30100, wx31, wx32, wx33, wx34, Succ(wx3230), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM120(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4590), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(wx4100))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1114(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8250), ba) → new_lookupFM1115(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM213(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1090), h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM277(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2810), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1381(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Succ(Zero), ba) → new_lookupFM1383(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM220(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx830), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1378(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4880, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1395(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5570, wx744, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1298(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5630), h) → new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5630, new_primMulNat0(Succ(wx3500), wx2900), h)
new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7310), ba) → new_lookupFM1416(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7310, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM257(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM137(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1155(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6650, wx838, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1131(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Succ(Succ(wx83000)), ba) → new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65900, wx83000, ba)
new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1114(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, Succ(wx76600), Succ(wx59000), ba) → new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, wx76600, wx59000, ba)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29300)), Zero, bf) → new_lookupFM2171(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29100)), Zero, bf) → new_lookupFM2166(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM169(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6620), ba) → new_lookupFM1147(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6620, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM262(wx30100, wx31, wx32, wx33, wx34, Succ(wx2340), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1403(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2111(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4100), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, Succ(wx6810), ba) → new_lookupFM1226(wx30100, wx31, wx32, wx33, wx34, wx6810, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1438(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(wx350)), h)
new_lookupFM1194(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7960), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1139(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1295(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx60000)), ba) → new_lookupFM1298(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2147(wx37, wx380, wx39, wx40, wx41, wx42, wx43, wx440, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(wx440)), bd)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Zero), bh) → new_lookupFM2204(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM236(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1142(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM224(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx950), ba) → new_lookupFM177(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM122(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx75400), Zero, be) → new_lookupFM1176(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM1335(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx71000), Succ(Succ(wx88600)), ba) → new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88600, wx71000, ba)
new_lookupFM1108(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Succ(wx38400)), bh) → new_lookupFM2210(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1322(wx30000, wx31, wx32, wx33, wx34, Succ(wx6080), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM253(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1372(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8120), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2206(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Zero, bd) → new_lookupFM2141(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM26(Float(Pos(Succ(wx13000)), wx131), wx14, wx15, wx16, wx17, wx18, bb) → new_lookupFM178(wx13000, wx131, wx14, wx15, wx16, wx17, wx18, new_primPlusNat0(new_primMulNat0(wx18, wx13000), Succ(wx13000)), bb)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM144(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM247(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1193(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2178(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1280(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87200), Succ(wx70300), ba) → new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87200, wx70300, ba)
new_lookupFM119(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1121(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, Succ(wx88800), Zero, ba) → new_lookupFM1343(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1312(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Zero, ba) → new_lookupFM1139(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM2173(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM272(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2650), ba) → new_lookupFM2176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM133(wx30000, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1197(wx30000, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM265(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM188(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6530), ba) → new_lookupFM189(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6530, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1240(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx86400)), ba) → new_lookupFM1243(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Zero, ba) → new_lookupFM1383(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM296(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3540), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM239(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Succ(wx790), h) → new_lookupFM22(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1421(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1351(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx5270), bh) → new_lookupFM1359(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx5270, new_primMulNat0(Zero, wx6600), bh)
new_lookupFM1336(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8870), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM282(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3070), ba) → new_lookupFM2182(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM141(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1218(wx30000, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx58500)), ba) → new_lookupFM1221(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1227(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Zero, bh) → new_lookupFM1364(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM2162(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2870), bf) → new_lookupFM2174(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2135(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx1980), bd) → new_lookupFM2146(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Zero, ba) → new_lookupFM1377(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM283(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1259(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Succ(wx91000), ba) → new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, wx73500, wx91000, ba)
new_lookupFM266(wx30100, wx31, wx32, wx33, wx34, Succ(wx2460), ba) → new_lookupFM2157(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM29(wx28, Zero, wx30, wx31, wx32, wx33, wx34, Zero, h)
new_lookupFM1195(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7970), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM259(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1133(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1117(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6570, wx826, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM244(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1700), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM221(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2119(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM151(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Zero, be) → new_lookupFM1182(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Zero, ba) → new_lookupFM194(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1167(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Succ(Zero), ba) → new_lookupFM1169(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1383(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1359(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx5270, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Zero)), bh)
new_lookupFM2141(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29300)), Succ(wx25400), bf) → new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29300, wx25400, bf)
new_lookupFM2101(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3680), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, Succ(wx88800), Succ(wx71100), ba) → new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, wx88800, wx71100, ba)
new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, Succ(wx58000), Zero, ba) → new_lookupFM1199(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Zero)), ba) → new_lookupFM131(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Zero, bh) → new_lookupFM1361(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM1160(wx30100, wx31, wx32, wx33, wx34, Succ(wx8410), ba) → new_lookupFM1161(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM261(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM265(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1165(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1317(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48200), Succ(Succ(wx60500)), ba) → new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60500, wx48200, ba)
new_lookupFM130(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7400), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM2198(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3780), bh) → new_lookupFM2207(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM146(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1296(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Zero, h) → new_lookupFM217(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6540), ba) → new_lookupFM199(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6540, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1163(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6680, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM28(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM1185(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx4400), wx3800), bd)
new_lookupFM156(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx5540), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Zero)), ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM2197(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM1275(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx6970), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, Zero, h) → new_lookupFM218(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2145(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM1373(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8130), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69600), Zero, bf) → new_lookupFM1277(wx56, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM227(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1150), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2200(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3800), bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM11(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1184(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx57400), Succ(Succ(wx75200)), bd) → new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx75200, wx57400, bd)
new_lookupFM2112(wx30100, wx31, wx32, wx33, wx34, Succ(wx4140), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM153(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1345(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM160(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM22(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h) → new_lookupFM12(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM152(wx30100, wx31, wx32, wx33, wx34, Succ(wx5500), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1134(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Succ(Succ(wx57000)), ba) → new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, wx46300, wx57000, ba)
new_lookupFM177(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7890), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Succ(wx38200)), bh) → new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38200, bh)
new_lookupFM281(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3050), ba) → new_lookupFM2181(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM158(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Succ(wx16300), bd) → new_lookupFM2140(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM2104(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3900), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1211(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7630), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1287(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx87200)), ba) → new_lookupFM1290(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, Succ(wx86000), Succ(wx68100), ba) → new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, wx86000, wx68100, ba)
new_lookupFM299(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3620), ba) → new_lookupFM1372(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1336(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM264(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1235(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx86200)), ba) → new_lookupFM1238(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1353(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx5290), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM243(wx37, Pos(Zero), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Zero)), bd)
new_lookupFM1119(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, Succ(wx78000), Zero, ba) → new_lookupFM1333(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1396(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7450), ba) → new_lookupFM1397(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM265(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2420), ba) → new_lookupFM2156(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Succ(wx90000), ba) → new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, wx72800, wx90000, ba)
new_lookupFM1393(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8990), ba) → new_lookupFM1394(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1348(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Zero, Zero, bh) → new_lookupFM1179(wx65, wx6600, wx67, wx68, wx69, wx70, Succ(wx71), Zero, Zero, bh)
new_lookupFM122(wx30000, wx31, wx32, wx33, wx34, Succ(wx4610), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), wx1630, bd)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM233(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM191(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1118(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM134(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Succ(wx16300), bd) → new_lookupFM2144(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM172(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1398(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4930, wx622, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2140(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM2179(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1281(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Zero), Zero, bf) → new_lookupFM1250(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM246(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1760), ba) → new_lookupFM2148(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(wx38400), bh) → new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38400, bh)
new_lookupFM270(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2590), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Zero, ba) → new_lookupFM1165(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1366(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(wx720)), bh)
new_lookupFM275(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1281(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1197(wx30000, wx31, wx32, wx33, wx34, Succ(wx5810), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM246(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1192(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Zero), h) → new_lookupFM2227(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Zero, bh) → new_lookupFM1358(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1210(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx58200), Succ(Succ(wx76200)), ba) → new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, wx76200, wx58200, ba)
new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1241(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7090), ba) → new_lookupFM1326(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7090, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1202(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1267(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx6930), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69200), Zero, bf) → new_lookupFM1269(wx56, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx75200), Succ(wx57400), bd) → new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx75200, wx57400, bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM241(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1152(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM259(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM134(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5820), ba) → new_lookupFM1210(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5820, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1235(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx68200), Succ(Succ(wx86200)), ba) → new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, wx86200, wx68200, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2105(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1236(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1224(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2113(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM279(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM297(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2212(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM1201(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, Succ(Succ(wx85000)), ba) → new_lookupFM1204(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM278(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2950), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM145(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5990), ba) → new_lookupFM1291(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5990, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1266(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx51900), Succ(Succ(wx69200)), bf) → new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, wx69200, wx51900, bf)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Succ(wx25400), bf) → new_lookupFM2167(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1271(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx6950), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM1313(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx77800)), ba) → new_lookupFM1316(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM181(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(wx350)), h)
new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, Succ(wx6830), ba) → new_lookupFM1240(wx30100, wx31, wx32, wx33, wx34, wx6830, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2225(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM2228(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6800), ba) → new_lookupFM1223(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6800, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1110(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5670), ba) → new_lookupFM1111(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1123(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4600, wx568, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1207(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8530), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM250(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1880), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM149(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM236(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1266(wx56, wx58, wx59, wx60, wx61, wx62, Zero, Succ(Succ(wx69200)), bf) → new_lookupFM1269(wx56, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), wx41), ba) → new_lookupFM243(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat0(new_primMulNat0(wx4000, wx30000), Succ(wx30000)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM130(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM271(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2630), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM2199(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM2110(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM283(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Zero, bf) → new_lookupFM2161(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2107(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM12(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, Succ(wx86400), Succ(wx68300), ba) → new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, wx86400, wx68300, ba)
new_lookupFM1121(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7390), ba) → new_lookupFM1122(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM269(wx56, Neg(Zero), wx58, wx59, wx60, wx61, wx62, Pos(Zero), Zero, bf) → new_lookupFM1249(wx56, wx58, wx59, wx60, wx61, wx62, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM195(wx30000, wx31, wx32, wx33, wx34, wx4550, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM178(wx13000, Pos(wx1310), wx14, wx15, wx16, wx17, wx18, Succ(wx6280), bb) → new_lookupFM179(wx13000, wx1310, wx14, wx15, wx16, wx17, wx18, Zero, wx6280, bb)
new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6550), ba) → new_lookupFM1103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6550, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, Succ(wx60200), Succ(wx48000), ba) → new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, wx60200, wx48000, ba)
new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Succ(wx63200), ba) → new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, wx45500, wx63200, ba)
new_lookupFM219(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx800), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2121(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, Zero, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7270), ba) → new_lookupFM1392(wx30000, wx30100, wx31, wx32, wx33, wx34, wx7270, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2(wx28, Neg(wx290), wx30, wx31, wx32, wx33, wx34, Pos(wx350), Succ(wx790), h) → new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1130(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6590), ba) → new_lookupFM1131(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6590, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1407(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7280), ba) → new_lookupFM1408(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7280, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1134(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Succ(Zero), ba) → new_lookupFM1136(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2136(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx2000), bd) → new_lookupFM2147(wx37, Succ(wx3800), wx39, wx40, wx41, wx42, wx43, Succ(wx4400), bd)
new_lookupFM1384(wx30000, wx31, wx32, wx33, wx34, wx4910, wx620, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1390(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM230(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1250), ba) → new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Pos(Zero)), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM2157(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM219(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM230(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2124(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM114(wx30000, wx31, wx32, wx33, wx34, Succ(wx4550), ba) → new_lookupFM195(wx30000, wx31, wx32, wx33, wx34, wx4550, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2117(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1196(wx30000, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx58000)), ba) → new_lookupFM1199(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM247(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1800), ba) → new_lookupFM2149(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77200), Succ(wx59300), bf) → new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77200, wx59300, bf)
new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, Succ(wx4490), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(wx350)), h)
new_lookupFM234(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1130(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Succ(wx64800), h) → new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, wx50500, wx64800, h)
new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1341(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1310(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8770), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2117(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1423(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1434(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Succ(Zero), h) → new_lookupFM1436(wx28, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1127(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Succ(Succ(wx82800)), ba) → new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx65800, wx82800, ba)
new_lookupFM1386(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM237(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2127(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1270(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Zero, Succ(Succ(wx69400)), bf) → new_lookupFM1273(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Succ(Zero), h) → new_lookupFM1442(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM278(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29100), Zero, bf) → new_lookupFM2166(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1243(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1202(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8510), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1399(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6230), ba) → new_lookupFM1400(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1191(wx37, wx39, wx40, wx41, wx42, wx43, bd) → new_lookupFM(wx42, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM1324(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM124(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4630), ba) → new_lookupFM1134(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4630, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1367(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Succ(Zero), bh) → new_lookupFM1369(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1450), ba) → new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM150(wx30000, wx31, wx32, wx33, wx34, Succ(wx4830), ba) → new_lookupFM1321(wx30000, wx31, wx32, wx33, wx34, wx4830, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Zero)), ba) → new_lookupFM142(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM254(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1258(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(Succ(wx77200)), bf) → new_lookupFM1261(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, wx2540, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM1236(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8630), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1381(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Succ(Succ(wx61800)), ba) → new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, wx48900, wx61800, ba)
new_lookupFM137(wx30100, wx31, wx32, wx33, wx34, Succ(wx5890), ba) → new_lookupFM1230(wx30100, wx31, wx32, wx33, wx34, wx5890, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM243(wx37, Pos(Zero), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx37)), Pos(Zero)), wx39, wx40, wx41, wx42, wx43, bd)
new_lookupFM194(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM1100(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8210), ba) → new_lookupFM1101(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2160(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2830), bf) → new_lookupFM2164(wx56, Succ(wx5700), wx58, wx59, wx60, wx61, wx62, Succ(wx6300), bf)
new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, Succ(wx4500), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(wx350)), h)
new_lookupFM140(wx30100, wx31, wx32, wx33, wx34, Succ(wx5430), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM297(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3560), ba) → new_lookupFM1370(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Zero, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM112(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4530), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(wx4100))), ba)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(wx38200), bh) → new_lookupFM2203(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM298(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3600), ba) → new_lookupFM1371(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM129(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1253(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(Succ(wx77000)), bf) → new_lookupFM1256(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2115(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2220(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1287(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx70300), Succ(Succ(wx87200)), ba) → new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87200, wx70300, ba)
new_lookupFM226(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1010), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM28(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1050), h) → new_lookupFM2222(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM248(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1820), ba) → new_lookupFM2150(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Zero, ba) → new_lookupFM1406(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1381(wx30000, wx31, wx32, wx33, wx34, wx4890, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx85000), Zero, ba) → new_lookupFM1204(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1434(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Succ(Succ(wx64800)), h) → new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, wx50500, wx64800, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM262(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7100), ba) → new_lookupFM1335(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7100, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM269(wx56, Pos(Zero), wx58, wx59, wx60, wx61, wx62, Neg(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM230(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2136(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Zero, bf) → new_lookupFM2168(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1354(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx5300), bh) → new_lookupFM1367(wx65, wx67, wx68, wx69, wx70, wx71, wx5300, new_primMulNat1, bh)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM19(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1124(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5690), ba) → new_lookupFM1125(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM272(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1278(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM269(wx56, Pos(Zero), wx58, wx59, wx60, wx61, wx62, Neg(Zero), Zero, bf) → new_lookupFM1251(wx56, wx58, wx59, wx60, wx61, wx62, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM260(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2280), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1125(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM285(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3170), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1151(wx30100, wx31, wx32, wx33, wx34, wx6630, wx836, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1299(wx30000, wx31, wx32, wx33, wx34, Succ(wx48000), Succ(Succ(wx60200)), ba) → new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, wx60200, wx48000, ba)
new_lookupFM2134(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM1340(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx88800)), ba) → new_lookupFM1343(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM157(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM195(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Succ(Succ(wx63200)), ba) → new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, wx45500, wx63200, ba)
new_lookupFM1127(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Succ(Zero), ba) → new_lookupFM1129(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Succ(wx90800), ba) → new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, wx73400, wx90800, ba)
new_lookupFM14(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5060), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Succ(wx84200), ba) → new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, wx66800, wx84200, ba)
new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1327(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Succ(wx75900), be) → new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx54000, wx75900, be)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM111(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Succ(wx61600), ba) → new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, wx48800, wx61600, ba)
new_lookupFM2164(wx56, wx570, wx58, wx59, wx60, wx61, wx62, wx630, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(wx630)), bf)
new_lookupFM1(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), Zero, h) → new_lookupFM1437(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM243(wx37, Neg(Zero), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM1428(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Succ(Zero), ba) → new_lookupFM1430(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM132(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7410), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM1137(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Succ(Succ(wx63300)), ba) → new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, wx46400, wx63300, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Neg(Zero)), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM243(wx37, Neg(wx380), wx39, wx40, wx41, wx42, wx43, Neg(wx440), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(wx440)), bd)
new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx6150, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2112(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1375(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Succ(Zero), ba) → new_lookupFM1377(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM1353(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM241(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1570), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1213(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Succ(wx74800), h) → new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56300, wx74800, h)
new_lookupFM173(wx30100, wx31, wx32, wx33, wx34, Succ(wx5600), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2180(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM160(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4880), ba) → new_lookupFM1378(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4880, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM2122(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM177(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1147(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6620, wx834, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1134(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4630, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Zero, ba) → new_lookupFM1145(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2212(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1370(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM142(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx5460), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Zero)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM286(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20200)), Zero, bd) → new_lookupFM2139(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM235(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1140(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1118(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8270), ba) → new_lookupFM1119(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM115(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1107(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM143(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7430), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM281(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx58300), Succ(wx47100), ba) → new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx58300, wx47100, ba)
new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69200), Succ(wx51900), bf) → new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, wx69200, wx51900, bf)
new_lookupFM2202(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM2205(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM266(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, Zero, bh) → new_lookupFM2205(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Zero, ba) → new_lookupFM1133(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM178(wx13000, Neg(Zero), wx14, wx15, wx16, wx17, wx18, Succ(wx6280), bb) → new_lookupFM(wx17, Float(Pos(Succ(wx18)), Neg(Zero)), bb)
new_lookupFM2123(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM242(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1166(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(wx4100))), ba) → new_lookupFM159(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1302(wx30000, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM1350(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1330(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx78000)), ba) → new_lookupFM1333(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1408(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Succ(Zero), ba) → new_lookupFM1410(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2193(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1353(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Zero, h) → new_lookupFM1433(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(wx4100))), ba) → new_lookupFM112(wx30000, wx31, wx32, wx33, wx34, wx4100, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1305(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1100(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1107(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7370), ba) → new_lookupFM1108(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1240(wx30100, wx31, wx32, wx33, wx34, Succ(wx68300), Succ(Succ(wx86400)), ba) → new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, wx86400, wx68300, ba)
new_lookupFM1313(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60400), Succ(Succ(wx77800)), ba) → new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77800, wx60400, ba)
new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7030), ba) → new_lookupFM1287(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx7030, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Zero, bf) → new_lookupFM2162(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM1188(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx51100), Succ(Succ(wx67200)), bd) → new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, wx67200, wx51100, bd)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Succ(wx16300), bd) → new_lookupFM2144(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7040), ba) → new_lookupFM1304(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx7040, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM115(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx5330), ba) → new_lookupFM1106(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5330, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, Succ(wx6660), ba) → new_lookupFM1159(wx30100, wx31, wx32, wx33, wx34, wx6660, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM195(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Succ(Zero), ba) → new_lookupFM197(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM2211(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Zero), h) → new_lookupFM217(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM27(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, wx1630, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM294(wx65, Pos(wx660), wx67, wx68, wx69, wx70, wx71, Neg(wx720), Succ(wx3430), bh) → new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Zero, h) → new_lookupFM215(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6770), ba) → new_lookupFM1206(wx30000, wx30100, wx31, wx32, wx33, wx34, wx6770, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM293(wx30100, wx31, wx32, wx33, wx34, Succ(wx3410), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM240(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2151(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1195(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM175(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7870), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1294(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1413(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx9030), ba) → new_lookupFM1414(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM268(wx30100, wx31, wx32, wx33, wx34, Succ(wx2520), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1284(wx498100, wx499, wx500, wx501, wx502, Succ(wx9410), bg) → new_lookupFM(wx502, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM2155(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2118(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx5740), bd) → new_lookupFM1184(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx5740, new_primMulNat0(Succ(wx4400), wx3800), bd)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(wx25400), bf) → new_lookupFM2167(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1161(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx37)), Pos(Succ(wx3800))), wx39, wx40, wx41, wx42, wx43, bd)
new_lookupFM1400(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1364(wx65, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Zero)), bh)
new_lookupFM1316(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx75400), Succ(wx53900), be) → new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx75400, wx53900, be)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2193(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1436(wx28, wx30, wx31, wx32, wx33, wx34, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Zero)), h)
new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Zero, ba) → new_lookupFM197(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM2124(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1320(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM166(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM178(wx13000, Pos(wx1310), wx14, wx15, wx16, wx17, wx18, Zero, bb) → new_lookupFM180(wx13000, wx1310, wx14, wx15, wx16, wx17, wx18, Zero, bb)
new_lookupFM25(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM14(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1231(wx30100, wx31, wx32, wx33, wx34, Succ(wx7650), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1101(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1251(wx56, wx58, wx59, wx60, wx61, wx62, Zero, bf) → new_lookupFM1275(wx56, wx58, wx59, wx60, wx61, wx62, new_primMulNat1, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), wx41), ba) → new_lookupFM269(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat0(new_primMulNat0(wx4000, wx30000), Succ(wx30000)), ba)
new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1310(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1367(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Succ(Succ(wx72200)), bh) → new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, wx53000, wx72200, bh)
new_lookupFM1431(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Succ(Zero), h) → new_lookupFM1433(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, Zero, be) → new_lookupFM(wx25, Float(Neg(wx2600), Neg(wx2610)), be)
new_lookupFM2220(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2106(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3960), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77600), Zero, ba) → new_lookupFM1294(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2215(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1373(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM253(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2100), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1296(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6010), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM2195(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3740), bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM2219(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM1291(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx59900), Succ(Succ(wx77600)), ba) → new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77600, wx59900, ba)
new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77800), Zero, ba) → new_lookupFM1316(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM223(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx910), ba) → new_lookupFM176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2209(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM247(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1321(wx30000, wx31, wx32, wx33, wx34, Succ(wx48300), Succ(Succ(wx60700)), ba) → new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, wx60700, wx48300, ba)
new_lookupFM1157(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2181(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1282(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM226(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM232(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2126(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM180(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h) → new_lookupFM182(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1230(wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx76400)), ba) → new_lookupFM1233(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM136(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1421(wx30100, wx31, wx32, wx33, wx34, Succ(wx9070), ba) → new_lookupFM1422(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2204(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM1351(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1171(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Succ(wx5390), be) → new_lookupFM1173(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5390, new_primMulNat0(wx2610, wx21), be)
new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx5930), bf) → new_lookupFM1258(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx5930, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM164(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1396(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1142(wx30100, wx31, wx32, wx33, wx34, Succ(wx6610), ba) → new_lookupFM1143(wx30100, wx31, wx32, wx33, wx34, wx6610, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Succ(wx790), h) → new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM299(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2214(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM113(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1167(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Succ(Succ(wx84400)), ba) → new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, wx66900, wx84400, ba)
new_lookupFM1338(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1380(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1410(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1300(wx30000, wx31, wx32, wx33, wx34, Succ(wx6030), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM1329(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM255(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM139(wx30100, wx31, wx32, wx33, wx34, Succ(wx5900), ba) → new_lookupFM1244(wx30100, wx31, wx32, wx33, wx34, wx5900, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7880), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Zero), h) → new_lookupFM2225(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1192(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7940), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM29(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Zero, h)
new_lookupFM1131(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Succ(Zero), ba) → new_lookupFM1133(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM172(wx30100, wx31, wx32, wx33, wx34, Succ(wx7330), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM121(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1124(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM258(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Succ(wx71800), bh) → new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx52700, wx71800, bh)
new_lookupFM185(wx913, wx914, wx915, wx916, wx917, wx918, wx919, Zero, bc) → new_lookupFM(wx917, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx918))))), bc)
new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5630, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM1120(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5340, wx738, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2205(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2100(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1196(wx30000, wx31, wx32, wx33, wx34, Succ(wx46900), Succ(Succ(wx58000)), ba) → new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, wx58000, wx46900, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM251(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1285(wx498100, wx499, wx500, wx501, wx502, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Succ(wx81800), ba) → new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65300, wx81800, ba)
new_lookupFM118(wx30000, wx31, wx32, wx33, wx34, Succ(wx4580), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM2161(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM123(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4620), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(wx4100))), ba)
new_lookupFM184(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6520, wx816, ba) → new_lookupFM185(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, wx410000, wx6520, wx816, ba)
new_lookupFM1204(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM263(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2360), ba) → new_lookupFM2154(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM237(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Succ(wx83300), ba) → new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, wx66100, wx83300, ba)
new_lookupFM231(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2125(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1389(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM2197(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6650), ba) → new_lookupFM1155(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6650, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM239(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1510), ba) → new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, wx1630, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM139(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1278(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2111(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1174(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx7560), be) → new_lookupFM(wx25, Float(Pos(wx2600), Pos(wx2610)), be)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM238(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM141(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7420), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM292(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3370), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, Succ(wx6630), ba) → new_lookupFM1151(wx30100, wx31, wx32, wx33, wx34, wx6630, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM288(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Zero, bh) → new_lookupFM2211(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2214(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1372(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM234(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1370), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Succ(wx72000), bh) → new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, wx52800, wx72000, bh)
new_lookupFM1402(wx30000, wx31, wx32, wx33, wx34, Succ(wx6250), ba) → new_lookupFM1403(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM2117(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4280), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM137(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1231(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2118(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1427(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2114(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM187(wx913, wx914, wx915, wx916, wx917, wx918, bc) → new_lookupFM(wx917, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx918))))), bc)
new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88400), Zero, ba) → new_lookupFM1329(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1176(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be) → new_lookupFM(wx25, Float(Pos(wx2600), Pos(wx2610)), be)
new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx7290), ba) → new_lookupFM1412(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7290, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1160(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM222(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2120(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Zero), h) → new_lookupFM215(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1281(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8050), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx87600), Succ(wx70500), ba) → new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, wx87600, wx70500, ba)
new_lookupFM2143(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM2146(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM256(wx20, wx21, wx22, wx23, wx24, wx25, Float(Neg(wx2600), wx261), be) → new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx261, new_primMulNat0(wx2600, wx20), be)
new_lookupFM1162(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6680), ba) → new_lookupFM1163(wx30100, wx31, wx32, wx33, wx34, wx410000, wx6680, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1185(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx7530), bd) → new_lookupFM(wx42, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM147(wx30000, wx31, wx32, wx33, wx34, Succ(wx4800), ba) → new_lookupFM1299(wx30000, wx31, wx32, wx33, wx34, wx4800, new_primMulNat1, ba)
new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88600), Succ(wx71000), ba) → new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88600, wx71000, ba)
new_lookupFM1428(wx30100, wx31, wx32, wx33, wx34, wx7350, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM261(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2300), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1314(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7790), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1327(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8850), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM271(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM210(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1070), h) → new_lookupFM2223(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM246(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM2199(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM1354(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM159(wx30000, wx31, wx32, wx33, wx34, wx4100, Succ(wx4870), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(wx4100))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM295(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM264(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(wx11300), h) → new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11300, h)
new_lookupFM223(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2121(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM267(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2480), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1104(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Neg(Zero), Pos(Zero)), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Neg(Zero)), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM291(wx30100, wx31, wx32, wx33, wx34, Succ(wx3350), ba) → new_lookupFM2187(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM267(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM185(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Succ(Zero), bc) → new_lookupFM187(wx913, wx914, wx915, wx916, wx917, wx918, bc)
new_lookupFM1361(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Zero)), bh)
new_lookupFM263(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM238(wx30100, wx31, wx32, wx33, wx34, Succ(wx1490), ba) → new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM284(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3130), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1214(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx47100), Succ(Succ(wx58300)), ba) → new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx58300, wx47100, ba)
new_lookupFM199(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6540, wx820, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1106(wx30000, wx30100, wx31, wx32, wx33, wx34, wx5330, wx736, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM291(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Zero, bd) → new_lookupFM2145(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20400)), Succ(wx16300), bd) → new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20400, wx16300, bd)
new_lookupFM2114(wx30100, wx31, wx32, wx33, wx34, Succ(wx4200), ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM2153(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60000), Succ(wx47900), ba) → new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60000, wx47900, ba)
new_lookupFM254(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2120), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1193(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7950), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1284(wx498100, wx499, wx500, wx501, wx502, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87400), Zero, ba) → new_lookupFM1307(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1148(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8350), ba) → new_lookupFM1149(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM284(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM235(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1390), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Succ(wx83000), ba) → new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65900, wx83000, ba)
new_lookupFM1269(wx56, wx58, wx59, wx60, wx61, wx62, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Zero, h) → new_lookupFM1442(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1251(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx5220), bf) → new_lookupFM1274(wx56, wx58, wx59, wx60, wx61, wx62, wx5220, new_primMulNat1, bf)
new_lookupFM243(wx37, Neg(Zero), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Zero, bd) → new_lookupFM212(Float(Neg(Succ(wx37)), Neg(Zero)), wx39, wx40, wx41, wx42, wx43, bd)
new_lookupFM1143(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Succ(Zero), ba) → new_lookupFM1145(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2137(wx37, wx380, wx39, wx40, wx41, wx42, wx43, wx440, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(wx440)), bd)
new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, Succ(wx60700), Zero, ba) → new_lookupFM1324(wx30000, wx31, wx32, wx33, wx34, ba)
new_lookupFM1434(wx28, wx30, wx31, wx32, wx33, wx34, wx5050, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Zero)), h)
new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, Succ(wx4510), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(wx720)), bh)
new_lookupFM1109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx4570, wx566, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM117(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Zero, ba) → new_lookupFM1136(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, Succ(wx78200), Zero, ba) → new_lookupFM1347(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM243(wx37, Pos(Zero), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Zero)), ba) → new_lookupFM212(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM279(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2990), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2168(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM2185(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2102(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1291(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, Succ(Succ(wx77600)), ba) → new_lookupFM1294(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM293(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1343(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1274(wx56, wx58, wx59, wx60, wx61, wx62, Zero, Succ(Succ(wx69600)), bf) → new_lookupFM1277(wx56, wx58, wx59, wx60, wx61, wx62, bf)
new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1288(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77000), Succ(wx59200), bf) → new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77000, wx59200, bf)
new_lookupFM260(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2144(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM153(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM135(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1215(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM1218(wx30000, wx31, wx32, wx33, wx34, Succ(wx47200), Succ(Succ(wx58500)), ba) → new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, wx58500, wx47200, ba)
new_lookupFM145(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1292(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM171(wx30100, wx31, wx32, wx33, wx34, Succ(wx5590), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM151(wx30100, wx31, wx32, wx33, wx34, Succ(wx6130), ba) → new_lookupFM1330(wx30100, wx31, wx32, wx33, wx34, wx6130, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Succ(wx63300), ba) → new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, wx46400, wx63300, ba)
new_lookupFM1263(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx6910), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Zero)), ba) → new_lookupFM124(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1249(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx5190), bf) → new_lookupFM1266(wx56, wx58, wx59, wx60, wx61, wx62, wx5190, new_primMulNat1, bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM212(Float(Pos(Succ(wx13000)), wx131), wx14, wx15, wx16, wx17, wx18, bb) → new_lookupFM178(wx13000, wx131, wx14, wx15, wx16, wx17, wx18, new_primPlusNat0(new_primMulNat0(wx18, wx13000), Succ(wx13000)), bb)
new_lookupFM178(wx13000, Neg(Succ(wx13100)), wx14, wx15, wx16, wx17, wx18, Succ(wx6280), bb) → new_lookupFM(wx17, Float(Pos(Succ(wx18)), Neg(Zero)), bb)
new_lookupFM183(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6520), ba) → new_lookupFM184(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6520, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1318(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx6060), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1422(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM229(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM256(wx20, wx21, wx22, wx23, wx24, wx25, Float(Pos(wx2600), wx261), be) → new_lookupFM1171(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx261, new_primMulNat0(wx2600, wx20), be)
new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Succ(wx92000), bc) → new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, wx9190, wx92000, bc)
new_lookupFM2174(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM1392(wx30000, wx30100, wx31, wx32, wx33, wx34, wx7270, wx898, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2218(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1427(wx30100, wx31, wx32, wx33, wx34, Succ(wx7350), ba) → new_lookupFM1428(wx30100, wx31, wx32, wx33, wx34, wx7350, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM154(wx30100, wx31, wx32, wx33, wx34, Succ(wx5510), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Succ(wx64600), h) → new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx50400, wx64600, h)
new_lookupFM1248(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx5180), bf) → new_lookupFM1262(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx5180, new_primMulNat0(Zero, wx5700), bf)
new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Zero, bc) → new_lookupFM187(wx913, wx914, wx915, wx916, wx917, wx918, bc)
new_lookupFM2200(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20400), Zero, bd) → new_lookupFM2143(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM157(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7240), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM270(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2134(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx1960), bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM276(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1274(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx52200), Succ(Succ(wx69600)), bf) → new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, wx69600, wx52200, bf)
new_lookupFM2183(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM150(wx30000, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1322(wx30000, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM136(wx30000, wx31, wx32, wx33, wx34, Succ(wx4720), ba) → new_lookupFM1218(wx30000, wx31, wx32, wx33, wx34, wx4720, new_primMulNat1, ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Succ(wx790), h) → new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20400), Succ(wx16300), bd) → new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20400, wx16300, bd)
new_lookupFM1104(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8230), ba) → new_lookupFM1105(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM222(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM292(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1359(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Succ(Succ(wx71800)), bh) → new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx52700, wx71800, bh)
new_lookupFM2114(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2219(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM171(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM272(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM255(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM126(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1137(wx30000, wx31, wx32, wx33, wx34, wx4640, Zero, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Zero)), ba)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(wx38200), bh) → new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38200, bh)
new_lookupFM1230(wx30100, wx31, wx32, wx33, wx34, Succ(wx58900), Succ(Succ(wx76400)), ba) → new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, wx76400, wx58900, ba)
new_lookupFM222(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx890), ba) → new_lookupFM175(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Succ(wx25400), bf) → new_lookupFM2172(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM131(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx5380), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Zero)), ba)
new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Succ(Succ(wx75900)), be) → new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx54000, wx75900, be)
new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx67200), Succ(wx51100), bd) → new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, wx67200, wx51100, bd)
new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Succ(wx84400), ba) → new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, wx66900, wx84400, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM143(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx85000), Succ(wx67600), ba) → new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx85000, wx67600, ba)
new_lookupFM1261(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM2196(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3760), bh) → new_lookupFM2206(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Zero)), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM133(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87400), Succ(wx70400), ba) → new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87400, wx70400, ba)
new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx6560), ba) → new_lookupFM1113(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx6560, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM275(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2750), ba) → new_lookupFM2179(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx5920), bf) → new_lookupFM1253(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx5920, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Pos(Succ(wx2900))), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM2149(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1193(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM179(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, wx4500, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(wx350)), h)
new_lookupFM1408(wx30100, wx31, wx32, wx33, wx34, wx410000, wx7280, Zero, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Pos(wx290), wx30, wx31, wx32, wx33, wx34, Neg(wx350), Succ(wx790), h) → new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Zero)), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM150(wx30000, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1207(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2107(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3980), ba) → new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88400), Succ(wx70900), ba) → new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88400, wx70900, ba)
new_lookupFM169(wx30000, wx31, wx32, wx33, wx34, Succ(wx4960), ba) → new_lookupFM1404(wx30000, wx31, wx32, wx33, wx34, wx4960, new_primMulNat1, ba)
new_lookupFM245(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1740), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1188(wx37, wx39, wx40, wx41, wx42, wx43, Zero, Succ(Succ(wx67200)), bd) → new_lookupFM1191(wx37, wx39, wx40, wx41, wx42, wx43, bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM148(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1314(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM172(wx30100, wx31, wx32, wx33, wx34, Succ(wx7330), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM164(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1397(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM153(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1345(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1396(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7450), ba) → new_lookupFM1397(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM148(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM164(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1396(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1314(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7790), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1345(wx30100, wx31, wx32, wx33, wx34, Succ(wx7830), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM172(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Zero))), ba) → new_lookupFM153(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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



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

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

new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, Succ(wx78200), Succ(wx61400), ba) → new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, wx78200, wx61400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, Succ(wx78200), Succ(wx61400), ba) → new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, wx78200, wx61400, ba)

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

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

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

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



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

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

new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, Succ(wx78200), Succ(wx61400), ba) → new_lookupFM1346(wx30100, wx31, wx32, wx33, wx34, wx78200, wx61400, ba)

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

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



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

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

new_lookupFM1121(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7390), ba) → new_lookupFM1122(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM119(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM1245(wx30100, wx31, wx32, wx33, wx34, Succ(wx7670), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM128(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM119(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1121(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM139(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1245(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM134(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1211(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM139(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1122(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM134(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1211(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7630), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM128(wx30100, wx31, wx32, wx33, wx34, Succ(wx6670), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Zero))), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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



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

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

new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx76200), Succ(wx58200), ba) → new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, wx76200, wx58200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx76200), Succ(wx58200), ba) → new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, wx76200, wx58200, ba)

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

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

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

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



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

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

new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx76200), Succ(wx58200), ba) → new_lookupFM1212(wx30000, wx30100, wx31, wx32, wx33, wx34, wx76200, wx58200, ba)

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

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



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

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

new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, Succ(wx76600), Succ(wx59000), ba) → new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, wx76600, wx59000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, Succ(wx76600), Succ(wx59000), ba) → new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, wx76600, wx59000, ba)

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

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

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

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



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

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

new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, Succ(wx76600), Succ(wx59000), ba) → new_lookupFM1246(wx30100, wx31, wx32, wx33, wx34, wx76600, wx59000, ba)

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

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



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

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

new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77800), Succ(wx60400), ba) → new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77800, wx60400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77800), Succ(wx60400), ba) → new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77800, wx60400, ba)

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

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

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

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



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

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

new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77800), Succ(wx60400), ba) → new_lookupFM1315(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77800, wx60400, ba)

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

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



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

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

new_lookupFM213(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Pos(Zero)), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM221(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx850), ba) → new_lookupFM174(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM262(wx30100, wx31, wx32, wx33, wx34, Succ(wx2340), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM227(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM243(wx37, Pos(wx380), wx39, wx40, wx41, wx42, wx43, Pos(wx440), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(wx440)), bd)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20200)), Zero, bd) → new_lookupFM2139(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM2146(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM1438(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(wx350)), h)
new_lookupFM1194(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7960), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM115(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1107(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2147(wx37, wx380, wx39, wx40, wx41, wx42, wx43, wx440, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(wx440)), bd)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(wx11300), h) → new_lookupFM2226(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx75400), Zero, be) → new_lookupFM1176(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM224(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx950), ba) → new_lookupFM177(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1108(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Zero, bd) → new_lookupFM2141(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM10(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), Zero, h) → new_lookupFM182(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1173(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx53900), Succ(Succ(wx75400)), be) → new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx75400, wx53900, be)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20200), Zero, bd) → new_lookupFM2139(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM178(wx13000, Neg(Zero), wx14, wx15, wx16, wx17, wx18, Succ(wx6280), bb) → new_lookupFM(wx17, Float(Pos(Succ(wx18)), Neg(Zero)), bb)
new_lookupFM2123(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM253(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2154(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM249(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Zero, bd) → new_lookupFM2141(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1100(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), wx41), ba) → new_lookupFM2(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat1(new_primMulNat0(wx4000, wx30000), wx30000), ba)
new_lookupFM26(Float(Pos(Succ(wx13000)), wx131), wx14, wx15, wx16, wx17, wx18, bb) → new_lookupFM178(wx13000, wx131, wx14, wx15, wx16, wx17, wx18, new_primPlusNat0(new_primMulNat0(wx18, wx13000), Succ(wx13000)), bb)
new_lookupFM247(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1193(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1107(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7370), ba) → new_lookupFM1108(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Zero, h) → new_lookupFM18(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Succ(wx16300), bd) → new_lookupFM2144(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM2135(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM235(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Succ(wx790), h) → new_lookupFM22(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Zero), h) → new_lookupFM217(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM27(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1227(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, wx1630, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM1187(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM(wx42, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM2135(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx1980), bd) → new_lookupFM2146(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Zero, h) → new_lookupFM215(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM249(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1860), ba) → new_lookupFM2151(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM2223(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM29(wx28, Zero, wx30, wx31, wx32, wx33, wx34, Zero, h)
new_lookupFM126(wx30100, wx31, wx32, wx33, wx34, Succ(wx6640), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2151(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1195(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1195(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7970), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM175(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7870), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM244(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1700), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM264(wx30100, wx31, wx32, wx33, wx34, Succ(wx2400), ba) → new_lookupFM2155(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM221(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2119(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM2155(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM13(wx28, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx5740), bd) → new_lookupFM1184(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx5740, new_primMulNat0(Succ(wx4400), wx3800), bd)
new_lookupFM111(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx6510), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx75400), Succ(wx53900), be) → new_lookupFM1175(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx75400, wx53900, be)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Succ(wx16300), bd) → new_lookupFM2140(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1184(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Succ(Succ(wx75200)), bd) → new_lookupFM1187(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM2141(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM2124(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM261(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM25(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM14(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5620, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM1231(wx30100, wx31, wx32, wx33, wx34, Succ(wx7650), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Neg(Succ(wx2900))), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1101(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM130(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7400), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM27(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1030), h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM27(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Zero, h) → new_lookupFM217(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM28(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM1185(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx4400), wx3800), bd)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, Zero, h) → new_lookupFM218(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2145(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM1183(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primMulNat0(Succ(wx43), wx37), bd)
new_lookupFM225(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx970), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM227(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1150), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM11(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1184(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx57400), Succ(Succ(wx75200)), bd) → new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx75200, wx57400, bd)
new_lookupFM253(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2100), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM223(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx910), ba) → new_lookupFM176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM22(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, h) → new_lookupFM12(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM247(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM226(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM177(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7890), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Succ(wx16300), bd) → new_lookupFM2140(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20400)), Zero, bd) → new_lookupFM2143(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1173(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Zero, Succ(Succ(wx75400)), be) → new_lookupFM1176(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20200), Succ(wx16300), bd) → new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20200, wx16300, bd)
new_lookupFM2120(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM175(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM264(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1171(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Succ(wx5390), be) → new_lookupFM1173(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5390, new_primMulNat0(wx2610, wx21), be)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM11(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5030), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM243(wx37, Pos(Zero), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Zero)), bd)
new_lookupFM23(wx28, wx30, wx31, wx32, wx33, wx34, h) → new_lookupFM13(wx28, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2148(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1192(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1171(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Zero, be) → new_lookupFM1174(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, new_primMulNat0(wx2610, wx21), be)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Succ(wx790), h) → new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), wx1630, bd)
new_lookupFM19(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx6500), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM254(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Succ(wx790), h) → new_lookupFM21(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM255(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Succ(wx16300), bd) → new_lookupFM2144(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7880), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Zero), h) → new_lookupFM2225(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1192(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7940), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM29(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Zero, h)
new_lookupFM2140(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM246(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1760), ba) → new_lookupFM2148(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM2228(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Zero, bd) → new_lookupFM2134(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Zero)), bd)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM220(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM185(wx913, wx914, wx915, wx916, wx917, wx918, wx919, Zero, bc) → new_lookupFM(wx917, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx918))))), bc)
new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5630, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20200)), Succ(wx16300), bd) → new_lookupFM2138(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20200, wx16300, bd)
new_lookupFM29(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx75200), Zero, bd) → new_lookupFM1187(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM218(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM246(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1192(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Zero), h) → new_lookupFM2227(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Succ(wx790), h) → new_lookupFM25(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2133(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx1940), bd) → new_lookupFM2137(wx37, Succ(wx3800), wx39, wx40, wx41, wx42, wx43, Succ(wx4400), bd)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM252(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM251(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM228(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2119(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM174(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2227(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Succ(Succ(wx74800)), h) → new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56300, wx74800, h)
new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx75200), Succ(wx57400), bd) → new_lookupFM1186(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx75200, wx57400, bd)
new_lookupFM263(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2360), ba) → new_lookupFM2154(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM237(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1152(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM2150(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1194(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1149(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1224(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, wx1630, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Succ(wx790), h) → new_lookupFM26(Float(Pos(Succ(wx28)), Neg(Succ(wx2900))), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM2131(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), wx1630, bd)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Succ(wx3500)), Zero, h) → new_lookupFM29(wx28, Zero, wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM1174(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx7560), be) → new_lookupFM(wx25, Float(Pos(wx2600), Pos(wx2610)), be)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM238(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM28(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM29(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM221(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM132(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM238(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2128(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM213(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM229(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1210), ba) → new_lookupFM198(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM181(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(wx350)), h)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Succ(wx790), h) → new_lookupFM26(Float(Pos(Succ(wx28)), Neg(Zero)), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(wx11100), h) → new_lookupFM216(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2225(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM2228(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM18(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM137(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1231(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Succ(wx11300)), h) → new_lookupFM2226(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM250(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1880), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM115(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM236(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1442(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), wx41), ba) → new_lookupFM243(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat0(new_primMulNat0(wx4000, wx30000), Succ(wx30000)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM130(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM248(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1176(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be) → new_lookupFM(wx25, Float(Pos(wx2600), Pos(wx2610)), be)
new_lookupFM182(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx6440), h) → new_lookupFM181(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM222(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2120(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Zero), h) → new_lookupFM215(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM224(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2122(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM2226(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM248(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1194(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2143(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM2146(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM1185(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx7530), bd) → new_lookupFM(wx42, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM261(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2300), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Zero, h) → new_lookupFM12(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM210(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1070), h) → new_lookupFM2223(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM243(wx37, Neg(Zero), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM246(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Neg(Zero)), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM245(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM210(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM215(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM218(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(wx11300), h) → new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11300, h)
new_lookupFM264(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1225(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM223(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2121(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1104(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM251(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1920), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Succ(Succ(wx11100)), h) → new_lookupFM216(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2139(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM263(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1222(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM178(wx13000, Pos(wx1310), wx14, wx15, wx16, wx17, wx18, Succ(wx6280), bb) → new_lookupFM179(wx13000, wx1310, wx14, wx15, wx16, wx17, wx18, Zero, wx6280, bb)
new_lookupFM238(wx30100, wx31, wx32, wx33, wx34, Succ(wx1490), ba) → new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Zero), Zero, bd) → new_lookupFM2145(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM2132(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(Succ(wx20400)), Succ(wx16300), bd) → new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20400, wx16300, bd)
new_lookupFM1105(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1227(wx30100, wx31, wx32, wx33, wx34, Succ(wx8610), ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM229(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2123(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM254(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2120), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM219(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx800), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1193(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7950), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2121(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM255(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2160), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1148(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8350), ba) → new_lookupFM1149(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2(wx28, Neg(wx290), wx30, wx31, wx32, wx33, wx34, Pos(wx350), Succ(wx790), h) → new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM235(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1390), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM249(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1195(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Pos(Zero), Succ(wx790), h) → new_lookupFM23(wx28, wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Zero, h) → new_lookupFM1442(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM244(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM211(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2136(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx2000), bd) → new_lookupFM2147(wx37, Succ(wx3800), wx39, wx40, wx41, wx42, wx43, Succ(wx4400), bd)
new_lookupFM230(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1250), ba) → new_lookupFM1102(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM20(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Succ(wx11100)), h) → new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11100, h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM219(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM230(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2124(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2137(wx37, wx380, wx39, wx40, wx41, wx42, wx43, wx440, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(wx440)), bd)
new_lookupFM1434(wx28, wx30, wx31, wx32, wx33, wx34, wx5050, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Zero)), h)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, Zero, bd) → new_lookupFM2145(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM247(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1800), ba) → new_lookupFM2149(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, Succ(wx4490), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(wx350)), h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM224(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1153(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Zero, bd) → new_lookupFM2136(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM243(wx37, Pos(Zero), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM210(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, h) → new_lookupFM211(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM223(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1431(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx5040, Zero, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Pos(Zero)), h)
new_lookupFM237(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2127(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Succ(Zero), h) → new_lookupFM1442(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM2(wx28, Pos(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM211(wx28, Zero, wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM2144(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM1224(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8590), ba) → new_lookupFM185(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, wx410000, wx8590, Zero, ba)
new_lookupFM12(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx5040), h) → new_lookupFM1431(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx5040, new_primMulNat0(Zero, wx2900), h)
new_lookupFM237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1450), ba) → new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM254(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(Succ(wx11300)), h) → new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11300, h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM250(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM212(Float(Pos(Succ(wx13000)), wx131), wx14, wx15, wx16, wx17, wx18, bb) → new_lookupFM178(wx13000, wx131, wx14, wx15, wx16, wx17, wx18, new_primPlusNat0(new_primMulNat0(wx18, wx13000), Succ(wx13000)), bb)
new_lookupFM178(wx13000, Neg(Succ(wx13100)), wx14, wx15, wx16, wx17, wx18, Succ(wx6280), bb) → new_lookupFM(wx17, Float(Pos(Succ(wx18)), Neg(Zero)), bb)
new_lookupFM13(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx5050), h) → new_lookupFM1434(wx28, wx30, wx31, wx32, wx33, wx34, wx5050, new_primMulNat1, h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM263(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM229(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM256(wx20, wx21, wx22, wx23, wx24, wx25, Float(Pos(wx2600), wx261), be) → new_lookupFM1171(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx261, new_primMulNat0(wx2600, wx20), be)
new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, Succ(wx4500), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(wx350)), h)
new_lookupFM1100(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8210), ba) → new_lookupFM1101(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2222(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, h) → new_lookupFM1(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM243(wx37, Neg(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Zero, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM1152(wx30100, wx31, wx32, wx33, wx34, Succ(wx8370), ba) → new_lookupFM1153(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM236(wx30100, wx31, wx32, wx33, wx34, Succ(wx1430), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Zero, Zero, h) → new_lookupFM2227(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM1437(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx6410), h) → new_lookupFM1438(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Succ(wx74600), h) → new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56200, wx74600, h)
new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5620), h) → new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5620, new_primMulNat0(Succ(wx3500), wx2900), h)
new_lookupFM174(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx7860), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM21(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM11(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20400), Zero, bd) → new_lookupFM2143(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, bd)
new_lookupFM226(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1010), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM28(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1050), h) → new_lookupFM2222(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), h)
new_lookupFM248(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx1820), ba) → new_lookupFM2150(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Pos(Zero), Pos(Zero)), ba)
new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Succ(Zero), h) → new_lookupFM18(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM262(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Succ(wx11100), h) → new_lookupFM214(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx7900, wx11100, h)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM230(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2134(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx1960), bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM225(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2224(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx7900), Zero, h) → new_lookupFM2225(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM217(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM15(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM2136(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Neg(Succ(wx4400))), bd)
new_lookupFM2(wx28, Neg(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Succ(wx790), h) → new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Succ(wx20400), Succ(wx16300), bd) → new_lookupFM2142(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, wx20400, wx16300, bd)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM19(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1104(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8230), ba) → new_lookupFM1105(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2(wx28, Neg(Zero), wx30, wx31, wx32, wx33, wx34, Neg(Succ(wx3500)), Zero, h) → new_lookupFM14(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM222(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM24(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx790, Zero, h) → new_lookupFM2228(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM126(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM255(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM16(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56200), Succ(Succ(wx74600)), h) → new_lookupFM17(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56200, wx74600, h)
new_lookupFM2134(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, Zero, bd) → new_lookupFM256(wx37, wx3800, wx39, wx40, wx41, wx42, Float(Pos(Succ(wx43)), Pos(Succ(wx4400))), bd)
new_lookupFM14(wx28, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5060), h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM222(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx890), ba) → new_lookupFM175(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2128(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1150(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM111(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1148(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Pos(Succ(wx4400)), Zero, bd) → new_lookupFM2133(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM252(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2060), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1(wx28, Succ(wx2900), wx30, wx31, wx32, wx33, wx34, Succ(wx3500), Zero, h) → new_lookupFM1437(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, new_primPlusNat0(new_primMulNat0(wx3500, wx2900), Succ(wx2900)), h)
new_lookupFM243(wx37, Neg(Zero), wx39, wx40, wx41, wx42, wx43, Pos(Zero), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Pos(Zero)), bd)
new_lookupFM132(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7410), ba) → new_lookupFM(wx34, Float(Pos(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM243(wx37, Neg(wx380), wx39, wx40, wx41, wx42, wx43, Neg(wx440), Succ(wx1630), bd) → new_lookupFM(wx41, Float(Pos(Succ(wx43)), Neg(wx440)), bd)
new_lookupFM2(wx28, Pos(Succ(wx2900)), wx30, wx31, wx32, wx33, wx34, Neg(Zero), Zero, h) → new_lookupFM212(Float(Pos(Succ(wx28)), Pos(Succ(wx2900))), wx30, wx31, wx32, wx33, wx34, h)
new_lookupFM213(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx1090), h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Neg(Succ(wx3500))), h)
new_lookupFM2149(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1193(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM179(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, wx4500, h) → new_lookupFM(wx33, Float(Pos(Succ(wx34)), Neg(wx350)), h)
new_lookupFM228(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1190), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Pos(Zero), Pos(Succ(Zero))), ba)
new_lookupFM220(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx830), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM243(wx37, Pos(Succ(wx3800)), wx39, wx40, wx41, wx42, wx43, Neg(Succ(wx4400)), Zero, bd) → new_lookupFM2135(wx37, wx3800, wx39, wx40, wx41, wx42, wx43, wx4400, new_primPlusNat0(new_primMulNat0(wx4400, wx3800), Succ(wx3800)), bd)
new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx56300), Succ(wx74800), h) → new_lookupFM1441(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx56300, wx74800, h)
new_lookupFM2127(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1146(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2(wx28, Pos(wx290), wx30, wx31, wx32, wx33, wx34, Neg(wx350), Succ(wx790), h) → new_lookupFM10(wx28, wx290, wx30, wx31, wx32, wx33, wx34, wx350, new_primMulNat0(Succ(wx34), wx28), h)
new_lookupFM1439(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, Succ(wx5630), h) → new_lookupFM1440(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, wx5630, new_primMulNat0(Succ(wx3500), wx2900), h)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Pos(Succ(Zero))), ba) → new_lookupFM137(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM245(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx1740), ba) → new_lookupFM(wx33, Float(Pos(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM216(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx3500, h) → new_lookupFM(wx32, Float(Pos(Succ(wx34)), Pos(Succ(wx3500))), h)
new_lookupFM2122(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM177(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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



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

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

new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Succ(wx64800), h) → new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, wx50500, wx64800, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Succ(wx64800), h) → new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, wx50500, wx64800, h)

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

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

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

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



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

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

new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, Succ(wx50500), Succ(wx64800), h) → new_lookupFM1435(wx28, wx30, wx31, wx32, wx33, wx34, wx50500, wx64800, h)

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

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



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

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

new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx67200), Succ(wx51100), bd) → new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, wx67200, wx51100, bd)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx67200), Succ(wx51100), bd) → new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, wx67200, wx51100, bd)

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

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

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

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



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

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

new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, Succ(wx67200), Succ(wx51100), bd) → new_lookupFM1190(wx37, wx39, wx40, wx41, wx42, wx43, wx67200, wx51100, bd)

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

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



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

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

new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Succ(wx64600), h) → new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx50400, wx64600, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Succ(wx64600), h) → new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx50400, wx64600, h)

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

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

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

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



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

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

new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, Succ(wx50400), Succ(wx64600), h) → new_lookupFM1432(wx28, wx2900, wx30, wx31, wx32, wx33, wx34, wx50400, wx64600, 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
  ↳ BR
    ↳ HASKELL
      ↳ COR
        ↳ HASKELL
          ↳ Narrow
            ↳ AND
              ↳ QDP
              ↳ QDP
              ↳ QDP
                ↳ DependencyGraphProof
                  ↳ AND
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
QDP
                      ↳ UsableRulesProof
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP
                    ↳ QDP

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

new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, Succ(wx76400), Succ(wx58900), ba) → new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, wx76400, wx58900, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, Succ(wx76400), Succ(wx58900), ba) → new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, wx76400, wx58900, ba)

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

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

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

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



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

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

new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, Succ(wx76400), Succ(wx58900), ba) → new_lookupFM1232(wx30100, wx31, wx32, wx33, wx34, wx76400, wx58900, ba)

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

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



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

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

new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx58300), Succ(wx47100), ba) → new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx58300, wx47100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx58300), Succ(wx47100), ba) → new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx58300, wx47100, ba)

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

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

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

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



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

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

new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx58300), Succ(wx47100), ba) → new_lookupFM1216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx58300, wx47100, ba)

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

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



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

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

new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Succ(wx63300), ba) → new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, wx46400, wx63300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Succ(wx63300), ba) → new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, wx46400, wx63300, ba)

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

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

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

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



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

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

new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, Succ(wx46400), Succ(wx63300), ba) → new_lookupFM1138(wx30000, wx31, wx32, wx33, wx34, wx46400, wx63300, ba)

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

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



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

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

new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, Succ(wx58500), Succ(wx47200), ba) → new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, wx58500, wx47200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, Succ(wx58500), Succ(wx47200), ba) → new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, wx58500, wx47200, ba)

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

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

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

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



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

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

new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, Succ(wx58500), Succ(wx47200), ba) → new_lookupFM1220(wx30000, wx31, wx32, wx33, wx34, wx58500, wx47200, ba)

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

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



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

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

new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Succ(wx57000), ba) → new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, wx46300, wx57000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Succ(wx57000), ba) → new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, wx46300, wx57000, ba)

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

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

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

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



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

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

new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx46300), Succ(wx57000), ba) → new_lookupFM1135(wx30000, wx30100, wx31, wx32, wx33, wx34, wx46300, wx57000, ba)

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

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



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

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

new_lookupFM1202(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8510), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM233(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1330), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM267(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2480), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM239(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM267(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM239(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2129(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2125(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1236(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8630), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM231(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1115(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1157(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2156(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1202(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM257(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2180), ba) → new_lookupFM2152(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1156(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8390), ba) → new_lookupFM1157(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM241(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM259(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2240), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM231(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2125(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM259(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM231(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1270), ba) → new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1114(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8250), ba) → new_lookupFM1115(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1236(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2129(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM241(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1570), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM265(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2420), ba) → new_lookupFM2156(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM239(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx1510), ba) → new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM265(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1234(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM1154(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1156(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM257(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM257(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM233(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1112(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1114(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM265(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2152(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1200(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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



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

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

new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx85000), Succ(wx67600), ba) → new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx85000, wx67600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx85000), Succ(wx67600), ba) → new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx85000, wx67600, ba)

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

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

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

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



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

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

new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx85000), Succ(wx67600), ba) → new_lookupFM1203(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx85000, wx67600, ba)

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

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



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

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

new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Succ(wx84200), ba) → new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, wx66800, wx84200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Succ(wx84200), ba) → new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, wx66800, wx84200, ba)

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

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

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

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



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

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

new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx66800), Succ(wx84200), ba) → new_lookupFM1164(wx30100, wx31, wx32, wx33, wx34, wx410000, wx66800, wx84200, ba)

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

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



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

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

new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Succ(wx82800), ba) → new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx65800, wx82800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Succ(wx82800), ba) → new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx65800, wx82800, ba)

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

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

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

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



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

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

new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx65800), Succ(wx82800), ba) → new_lookupFM1128(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx65800, wx82800, ba)

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

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



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

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

new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx86200), Succ(wx68200), ba) → new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, wx86200, wx68200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx86200), Succ(wx68200), ba) → new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, wx86200, wx68200, ba)

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

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

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

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



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

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

new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx86200), Succ(wx68200), ba) → new_lookupFM1237(wx30100, wx31, wx32, wx33, wx34, wx410000, wx86200, wx68200, ba)

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

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



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

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

new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Succ(wx56400), ba) → new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, wx45400, wx56400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Succ(wx56400), ba) → new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, wx45400, wx56400, ba)

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

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

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

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



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

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

new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx45400), Succ(wx56400), ba) → new_lookupFM193(wx30000, wx30100, wx31, wx32, wx33, wx34, wx45400, wx56400, ba)

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

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



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

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

new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Succ(wx63200), ba) → new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, wx45500, wx63200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Succ(wx63200), ba) → new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, wx45500, wx63200, ba)

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

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

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

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



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

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

new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, Succ(wx45500), Succ(wx63200), ba) → new_lookupFM196(wx30000, wx31, wx32, wx33, wx34, wx45500, wx63200, ba)

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

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



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

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

new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, Succ(wx58000), Succ(wx46900), ba) → new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, wx58000, wx46900, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, Succ(wx58000), Succ(wx46900), ba) → new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, wx58000, wx46900, ba)

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

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

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

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



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

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

new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, Succ(wx58000), Succ(wx46900), ba) → new_lookupFM1198(wx30000, wx31, wx32, wx33, wx34, wx58000, wx46900, ba)

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

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



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

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

new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Succ(wx92000), bc) → new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, wx9190, wx92000, bc)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Succ(wx92000), bc) → new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, wx9190, wx92000, bc)

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

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

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

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



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

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

new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, Succ(wx9190), Succ(wx92000), bc) → new_lookupFM186(wx913, wx914, wx915, wx916, wx917, wx918, wx9190, wx92000, bc)

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

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



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

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

new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Succ(wx81800), ba) → new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65300, wx81800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Succ(wx81800), ba) → new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65300, wx81800, ba)

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

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

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

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



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

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

new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65300), Succ(wx81800), ba) → new_lookupFM190(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65300, wx81800, ba)

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

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



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

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

new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Succ(wx83300), ba) → new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, wx66100, wx83300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Succ(wx83300), ba) → new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, wx66100, wx83300, ba)

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

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

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

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



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

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

new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, Succ(wx66100), Succ(wx83300), ba) → new_lookupFM1144(wx30100, wx31, wx32, wx33, wx34, wx66100, wx83300, ba)

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

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



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

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

new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, Succ(wx86000), Succ(wx68100), ba) → new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, wx86000, wx68100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, Succ(wx86000), Succ(wx68100), ba) → new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, wx86000, wx68100, ba)

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

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

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

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



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

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

new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, Succ(wx86000), Succ(wx68100), ba) → new_lookupFM1228(wx30100, wx31, wx32, wx33, wx34, wx86000, wx68100, ba)

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

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



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

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

new_lookupFM240(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2130(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2130(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM258(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1241(wx30100, wx31, wx32, wx33, wx34, Succ(wx8650), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM260(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2280), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM2153(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1118(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8270), ba) → new_lookupFM1119(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM258(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM232(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1310), ba) → new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM234(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx1370), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1207(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8530), ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM240(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM266(wx30100, wx31, wx32, wx33, wx34, Succ(wx2460), ba) → new_lookupFM2157(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM232(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2126(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM266(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM268(wx30100, wx31, wx32, wx33, wx34, Succ(wx2520), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1241(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2157(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1239(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM242(wx30100, wx31, wx32, wx33, wx34, Succ(wx1610), ba) → new_lookupFM(wx33, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM260(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2126(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM242(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM234(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1161(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1160(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM258(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2220), ba) → new_lookupFM2153(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1119(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1160(wx30100, wx31, wx32, wx33, wx34, Succ(wx8410), ba) → new_lookupFM1161(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM240(wx30100, wx31, wx32, wx33, wx34, Succ(wx1550), ba) → new_lookupFM1158(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM232(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM266(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1205(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1207(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Pos(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM268(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1116(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1118(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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



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

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

new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, Succ(wx86400), Succ(wx68300), ba) → new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, wx86400, wx68300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, Succ(wx86400), Succ(wx68300), ba) → new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, wx86400, wx68300, ba)

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

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

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

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



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

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

new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, Succ(wx86400), Succ(wx68300), ba) → new_lookupFM1242(wx30100, wx31, wx32, wx33, wx34, wx86400, wx68300, ba)

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

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



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

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

new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Succ(wx83000), ba) → new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65900, wx83000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Succ(wx83000), ba) → new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65900, wx83000, ba)

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

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

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

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



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

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

new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx65900), Succ(wx83000), ba) → new_lookupFM1132(wx30000, wx30100, wx31, wx32, wx33, wx34, wx65900, wx83000, ba)

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

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



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

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

new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx85200), Succ(wx67700), ba) → new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, wx85200, wx67700, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx85200), Succ(wx67700), ba) → new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, wx85200, wx67700, ba)

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

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

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

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



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

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

new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx85200), Succ(wx67700), ba) → new_lookupFM1208(wx30000, wx30100, wx31, wx32, wx33, wx34, wx85200, wx67700, ba)

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

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



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

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

new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Succ(wx84400), ba) → new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, wx66900, wx84400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Succ(wx84400), ba) → new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, wx66900, wx84400, ba)

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

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

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

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



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

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

new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, Succ(wx66900), Succ(wx84400), ba) → new_lookupFM1168(wx30100, wx31, wx32, wx33, wx34, wx66900, wx84400, ba)

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

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



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

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

new_lookupFM2195(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29100)), Zero, bf) → new_lookupFM2166(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1283(wx498000, wx498100, wx499, wx500, wx501, wx502, Succ(wx9370), bg) → new_lookupFM(wx502, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(wx25400), bf) → new_lookupFM2172(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2212(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1370(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2116(wx30100, wx31, wx32, wx33, wx34, Succ(wx4260), ba) → new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM288(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3250), ba) → new_lookupFM2184(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM286(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM269(wx56, Pos(wx570), wx58, wx59, wx60, wx61, wx62, Pos(wx630), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(wx630)), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Neg(Zero)), ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Zero), bh) → new_lookupFM2202(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM274(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2710), ba) → new_lookupFM2178(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM2111(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4100), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Succ(wx38200)), bh) → new_lookupFM2203(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2187(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM1352(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx5280), bh) → new_lookupFM1362(wx65, wx67, wx68, wx69, wx70, wx71, wx5280, new_primMulNat1, bh)
new_lookupFM2169(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM281(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM143(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7430), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Zero), bh) → new_lookupFM2204(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1278(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8020), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2194(wx65, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM1354(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2202(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM2205(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Succ(wx38400)), bh) → new_lookupFM2210(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2186(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Succ(wx3430), bh) → new_lookupFM2191(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM155(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7230), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, Zero, bh) → new_lookupFM2205(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1180(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be) → new_lookupFM(wx25, Float(Neg(wx2600), Pos(wx2610)), be)
new_lookupFM286(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3190), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1413(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1394(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM1350(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2207(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2193(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1353(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2206(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1372(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8120), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Succ(Zero), be) → new_lookupFM1182(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1305(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2113(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4160), ba) → new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2178(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1280(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM273(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2690), ba) → new_lookupFM2177(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Zero, bf) → new_lookupFM2160(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM2217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2171(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM2174(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Zero, bf) → new_lookupFM2162(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM2173(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM272(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2650), ba) → new_lookupFM2176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2116(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2163(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2890), bf) → new_lookupFM2175(wx56, Succ(wx5700), wx58, wx59, wx60, wx61, wx62, Succ(wx6300), bf)
new_lookupFM296(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3540), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2100(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2215(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1421(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Zero, bf) → new_lookupFM2173(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1351(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx5270), bh) → new_lookupFM1359(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx5270, new_primMulNat0(Zero, wx6600), bh)
new_lookupFM1336(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8870), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2211(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM282(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3070), ba) → new_lookupFM2182(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM141(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM294(wx65, Pos(wx660), wx67, wx68, wx69, wx70, wx71, Neg(wx720), Succ(wx3430), bh) → new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2162(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2870), bf) → new_lookupFM2174(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77200), Zero, bf) → new_lookupFM1261(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM283(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM293(wx30100, wx31, wx32, wx33, wx34, Succ(wx3410), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1259(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM1413(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx9030), ba) → new_lookupFM1414(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM295(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3500), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1414(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1417(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx9050), ba) → new_lookupFM1418(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1284(wx498100, wx499, wx500, wx501, wx502, Succ(wx9410), bg) → new_lookupFM(wx502, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2118(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM151(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(wx25400), bf) → new_lookupFM2167(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Zero, be) → new_lookupFM1182(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM2161(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2850), bf) → new_lookupFM2169(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Zero, be) → new_lookupFM1179(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, new_primMulNat0(wx2610, wx21), be)
new_lookupFM290(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3310), ba) → new_lookupFM2186(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2193(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1359(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx5270, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Zero)), bh)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29300)), Succ(wx25400), bf) → new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29300, wx25400, bf)
new_lookupFM2101(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3680), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM289(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2166(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM2169(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM282(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM287(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2198(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3780), bh) → new_lookupFM2207(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM1292(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx7770), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM2107(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1310(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), wx41), ba) → new_lookupFM269(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat0(new_primMulNat0(wx4000, wx30000), Succ(wx30000)), ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM2197(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM1259(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx7730), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, Zero, be) → new_lookupFM(wx25, Float(Neg(wx2600), Neg(wx2610)), be)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(Zero), bh) → new_lookupFM2211(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2220(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2106(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3960), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1373(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8130), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Succ(wx3430), bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM2200(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3800), bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM2215(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1373(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2115(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4220), ba) → new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2195(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3740), bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM2219(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM2197(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), wx301), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), wx41), ba) → new_lookupFM294(wx30000, wx301, wx31, wx32, wx33, wx34, wx4000, wx41, new_primPlusNat0(new_primMulNat0(wx4000, wx30000), Succ(wx30000)), ba)
new_lookupFM2112(wx30100, wx31, wx32, wx33, wx34, Succ(wx4140), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1370(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8100), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2209(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM2108(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4020), ba) → new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Succ(Succ(wx78400)), bh) → new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx61500, wx78400, bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2101(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1348(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), Zero, bh) → new_lookupFM1179(wx65, wx6600, wx67, wx68, wx69, wx70, Succ(wx71), Succ(wx7200), new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM290(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1254(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx7710), bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM2181(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1282(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM2103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3860), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Pos(wx2610), Succ(wx5400), be) → new_lookupFM1177(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, new_primMulNat0(wx2610, wx21), be)
new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Succ(wx38200)), bh) → new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38200, bh)
new_lookupFM281(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3050), ba) → new_lookupFM2181(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2104(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3900), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2203(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM1421(wx30100, wx31, wx32, wx33, wx34, Succ(wx9070), ba) → new_lookupFM1422(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2115(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Succ(wx78400), bh) → new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx61500, wx78400, bh)
new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1336(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM299(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3620), ba) → new_lookupFM1372(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2204(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM1351(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM277(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Zero)), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Zero)), ba)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29100)), Succ(wx25400), bf) → new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29100, wx25400, bf)
new_lookupFM1353(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx5290), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM2216(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29300), Zero, bf) → new_lookupFM2171(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx5930), bf) → new_lookupFM1258(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx5930, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM2191(wx65, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM1352(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM1393(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8990), ba) → new_lookupFM1394(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2184(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM299(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2214(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2108(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2177(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1279(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM1256(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM273(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1279(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2179(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1281(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2221(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1419(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM298(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(wx38400), bh) → new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38400, bh)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM270(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2590), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1341(wx30100, wx31, wx32, wx33, wx34, Succ(wx8890), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM1352(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1366(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(wx720)), bh)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Zero, bf) → new_lookupFM2163(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM2205(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM275(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM1281(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2108(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2217(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2100(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM2200(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM1371(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8110), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1288(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8730), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1357(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Zero, bh) → new_lookupFM1358(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2210(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM(wx69, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM285(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1285(wx498100, wx499, wx500, wx501, wx502, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(wx38400), bh) → new_lookupFM2210(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2161(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM2105(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3920), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM2199(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM1367(wx65, wx67, wx68, wx69, wx70, wx71, wx5300, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(Zero)), bh)
new_lookupFM294(wx65, Neg(wx660), wx67, wx68, wx69, wx70, wx71, Pos(wx720), Succ(wx3430), bh) → new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM2102(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3720), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM269(wx56, Neg(Zero), wx58, wx59, wx60, wx61, wx62, Pos(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1389(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), wx2540, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM282(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1415(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1417(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Zero, bh) → new_lookupFM2197(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2105(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2113(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2176(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1278(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2111(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1179(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx7600), be) → new_lookupFM(wx25, Float(Neg(wx2600), Pos(wx2610)), be)
new_lookupFM297(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM2212(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba)
new_lookupFM278(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx2950), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2103(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1358(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29100), Succ(wx25400), bf) → new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29100, wx25400, bf)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Succ(wx3430), bh) → new_lookupFM2194(wx65, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM141(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7420), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM292(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3370), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Succ(wx25400), bf) → new_lookupFM2167(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM281(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM288(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Zero, bh) → new_lookupFM2211(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM273(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2214(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, ba) → new_lookupFM1372(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM1331(wx30100, wx31, wx32, wx33, wx34, Succ(wx7810), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM1279(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8030), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2117(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4280), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM289(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2114(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Zero, bf) → new_lookupFM2173(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM274(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1280(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM2199(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM271(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2630), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2110(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1281(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx8050), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM283(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1349(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), Zero, bh) → new_lookupFM1365(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Zero, bf) → new_lookupFM2161(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba)
new_lookupFM256(wx20, wx21, wx22, wx23, wx24, wx25, Float(Neg(wx2600), wx261), be) → new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx261, new_primMulNat0(wx2600, wx20), be)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2107(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Zero, bh) → new_lookupFM2204(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx61500), Succ(Zero), bh) → new_lookupFM1358(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1327(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8850), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM299(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM170(wx30100, wx31, wx32, wx33, wx34, Succ(wx7300), ba) → new_lookupFM(wx34, Float(Neg(Zero), Pos(Succ(Zero))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM271(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM2199(wx65, Zero, wx67, wx68, wx69, wx70, wx71, Zero, bh)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Zero), Zero, bh) → new_lookupFM1354(wx65, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM269(wx56, Neg(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Pos(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Zero)), bf)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM295(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM2195(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM269(wx56, Pos(Zero), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM280(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM291(wx30100, wx31, wx32, wx33, wx34, Succ(wx3350), ba) → new_lookupFM2187(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Zero, bh) → new_lookupFM2209(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM284(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3130), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM291(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, new_primMulNat1, ba)
new_lookupFM2105(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2213(wx30100, wx31, wx32, wx33, wx34, wx4000, ba) → new_lookupFM1371(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2114(wx30100, wx31, wx32, wx33, wx34, Succ(wx4200), ba) → new_lookupFM1282(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1284(wx498100, wx499, wx500, wx501, wx502, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, Zero, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM284(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2167(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM1390(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2190(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh) → new_lookupFM1351(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Zero), Succ(wx3430), bh) → new_lookupFM2190(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, bh)
new_lookupFM2175(wx56, wx570, wx58, wx59, wx60, wx61, wx62, wx630, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(wx630)), bf)
new_lookupFM280(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2117(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, Succ(wx4510), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(wx720)), bh)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM279(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77200), Succ(wx59300), bf) → new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77200, wx59300, bf)
new_lookupFM2110(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx4080), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM288(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2199(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM1339(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1341(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2197(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, bh) → new_lookupFM1348(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM280(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3010), ba) → new_lookupFM2180(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM1305(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8750), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM1310(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx8770), ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM290(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1334(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM2198(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM2199(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM2118(wx30100, wx31, wx32, wx33, wx34, Succ(wx4320), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM279(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx2990), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM2185(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1282(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34, ba)
new_lookupFM2168(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2102(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM278(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM293(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1350(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx5260), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29100), Zero, bf) → new_lookupFM2166(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1288(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM283(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3110), ba) → new_lookupFM2183(wx30000, wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77000), Succ(wx59200), bf) → new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77000, wx59200, bf)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM296(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2116(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2221(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM276(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx2770), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM2182(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1303(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM145(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1292(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM274(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM269(wx56, Neg(Zero), wx58, wx59, wx60, wx61, wx62, Pos(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM1258(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(Succ(wx77200)), bf) → new_lookupFM1261(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2172(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, wx2540, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM1391(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1393(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2106(wx30000, wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM256(wx30000, wx30100, wx31, wx32, wx33, wx34, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM1285(wx498100, wx499, wx500, wx501, wx502, Succ(wx9470), bg) → new_lookupFM(wx502, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), bg)
new_lookupFM1362(wx65, wx67, wx68, wx69, wx70, wx71, wx5280, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Zero)), bh)
new_lookupFM1253(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx59200), Succ(Succ(wx77000)), bf) → new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77000, wx59200, bf)
new_lookupFM1422(wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM151(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM1331(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Succ(wx38400)), bh) → new_lookupFM2208(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38400, bh)
new_lookupFM298(wx30100, wx31, wx32, wx33, wx34, wx4000, Zero, ba) → new_lookupFM2213(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM2174(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM2218(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1411(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat1, ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2104(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2160(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx2830), bf) → new_lookupFM2164(wx56, Succ(wx5700), wx58, wx59, wx60, wx61, wx62, Succ(wx6300), bf)
new_lookupFM1389(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx8970), ba) → new_lookupFM1390(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2189(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh) → new_lookupFM1350(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM297(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx3560), ba) → new_lookupFM1370(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, Succ(wx38200), bh) → new_lookupFM2203(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1418(wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM(wx34, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM298(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3600), ba) → new_lookupFM1371(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, wx2540, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(Succ(wx6300))), bf)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Zero, bh) → new_lookupFM2202(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM1253(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Succ(Succ(wx77000)), bf) → new_lookupFM1256(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2115(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2220(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM289(wx30100, wx31, wx32, wx33, wx34, Succ(wx3290), ba) → new_lookupFM2185(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM2200(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM256(wx65, wx6600, wx67, wx68, wx69, wx70, Float(Neg(Succ(wx71)), Neg(Succ(wx7200))), bh)
new_lookupFM1349(wx65, wx660, wx67, wx68, wx69, wx70, wx71, wx720, Succ(wx4520), bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Neg(wx720)), bh)
new_lookupFM157(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx7240), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM294(wx65, Neg(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Zero, bh) → new_lookupFM2196(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM270(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM291(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1355(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx6150), bh) → new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx6150, new_primMulNat0(Succ(wx7200), wx6600), bh)
new_lookupFM269(wx56, Pos(Zero), wx58, wx59, wx60, wx61, wx62, Neg(Zero), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(Zero)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM276(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1177(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, wx758, be) → new_lookupFM1180(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be)
new_lookupFM294(wx65, Pos(Zero), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2189(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2183(wx30000, wx30100, wx31, wx32, wx33, wx34, ba) → new_lookupFM1308(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM1182(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, be) → new_lookupFM(wx25, Float(Neg(wx2600), Neg(wx2610)), be)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM2110(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2158(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Zero, bf) → new_lookupFM2168(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1365(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx7160), bh) → new_lookupFM1366(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Zero))), ba) → new_lookupFM155(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1354(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx5300), bh) → new_lookupFM1367(wx65, wx67, wx68, wx69, wx70, wx71, wx5300, new_primMulNat1, bh)
new_lookupFM269(wx56, Pos(Succ(wx5700)), wx58, wx59, wx60, wx61, wx62, Neg(Succ(wx6300)), Succ(wx2540), bf) → new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primPlusNat0(new_primMulNat0(wx6300, wx5700), Succ(wx5700)), wx2540, bf)
new_lookupFM2196(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Zero, bh) → new_lookupFM2197(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba)
new_lookupFM272(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Zero, ba) → new_lookupFM1278(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM292(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM297(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2114(wx30100, wx31, wx32, wx33, wx34, Zero, ba) → new_lookupFM2219(wx30100, wx31, wx32, wx33, wx34, ba)
new_lookupFM1282(Float(Pos(Succ(wx498000)), Neg(Succ(wx498100))), wx499, wx500, wx501, wx502, bg) → new_lookupFM1283(wx498000, wx498100, wx499, wx500, wx501, wx502, new_primPlusNat0(new_primMulNat0(Succ(Zero), wx498100), Succ(wx498100)), bg)
new_lookupFM285(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx3170), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1255(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx77000), Zero, bf) → new_lookupFM1256(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM(Branch(Float(Pos(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Pos(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM272(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba) → new_lookupFM275(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(wx38200), bh) → new_lookupFM2201(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx34300, wx38200, bh)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Pos(Succ(wx7200)), Succ(wx3430), bh) → new_lookupFM2188(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx3430, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM157(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2165(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, Zero, bf) → new_lookupFM2168(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1325(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM1327(wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Succ(Succ(Succ(wx410000))), wx30100), ba)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Zero), Succ(wx25400), bf) → new_lookupFM2172(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Succ(wx75900), be) → new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx54000, wx75900, be)
new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, Succ(wx54000), Succ(Succ(wx75900)), be) → new_lookupFM1181(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx54000, wx75900, be)
new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1254(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM2162(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Zero, bf) → new_lookupFM1257(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, new_primMulNat0(Succ(wx62), wx56), bf)
new_lookupFM2113(wx30100, wx31, wx32, wx33, wx34, wx410000, Zero, ba) → new_lookupFM2218(wx30100, wx31, wx32, wx33, wx34, wx410000, ba)
new_lookupFM2164(wx56, wx570, wx58, wx59, wx60, wx61, wx62, wx630, bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Pos(wx630)), bf)
new_lookupFM(Branch(Float(Pos(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Succ(wx4000)), Neg(Succ(Zero))), ba) → new_lookupFM143(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM1258(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx59300), Succ(Succ(wx77200)), bf) → new_lookupFM1260(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx77200, wx59300, bf)
new_lookupFM(Branch(Float(Neg(Zero), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM170(wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Succ(Zero), wx30100), ba)
new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx29300), Succ(wx25400), bf) → new_lookupFM2170(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx29300, wx25400, bf)
new_lookupFM2196(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx3760), bh) → new_lookupFM2206(wx65, Succ(wx6600), wx67, wx68, wx69, wx70, wx71, Succ(wx7200), bh)
new_lookupFM1261(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf) → new_lookupFM(wx61, Float(Neg(Succ(wx62)), Neg(Succ(wx6300))), bf)
new_lookupFM287(wx30100, wx31, wx32, wx33, wx34, Succ(wx3230), ba) → new_lookupFM(wx33, Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba) → new_lookupFM2109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat0(wx410000, wx30100), Succ(wx30100)), Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM1356(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, wx6150, Zero, bh) → new_lookupFM(wx70, Float(Neg(Succ(wx71)), Pos(Succ(wx7200))), bh)
new_lookupFM(Branch(Float(Neg(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2106(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM(Branch(Float(Neg(Zero), Pos(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Succ(Zero)))), ba) → new_lookupFM2112(wx30100, wx31, wx32, wx33, wx34, new_primPlusNat0(new_primPlusNat0(Zero, Succ(wx30100)), Succ(wx30100)), ba)
new_lookupFM2100(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx3660), ba) → new_lookupFM1373(wx30100, wx31, wx32, wx33, wx34, wx4000, new_primMulNat0(Succ(Succ(Zero)), wx30100), ba)
new_lookupFM275(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2750), ba) → new_lookupFM2179(wx30100, wx31, wx32, wx33, wx34, wx4000, ba)
new_lookupFM294(wx65, Neg(Zero), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM1353(wx65, wx67, wx68, wx69, wx70, wx71, wx7200, new_primMulNat0(Succ(wx71), wx65), bh)
new_lookupFM294(wx65, Pos(Succ(wx6600)), wx67, wx68, wx69, wx70, wx71, Neg(Succ(wx7200)), Zero, bh) → new_lookupFM2198(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, new_primPlusNat0(new_primMulNat0(wx7200, wx6600), Succ(wx6600)), bh)
new_lookupFM1252(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(wx5920), bf) → new_lookupFM1253(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, wx5920, new_primMulNat0(Succ(wx6300), wx5700), bf)
new_lookupFM277(wx30100, wx31, wx32, wx33, wx34, wx4000, Succ(wx2810), ba) → new_lookupFM(wx33, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Zero)))), ba)
new_lookupFM1280(wx30100, wx31, wx32, wx33, wx34, wx4000, wx410000, Succ(wx8040), ba) → new_lookupFM(wx34, Float(Neg(Succ(wx4000)), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM269(wx56, Neg(wx570), wx58, wx59, wx60, wx61, wx62, Neg(wx630), Succ(wx2540), bf) → new_lookupFM(wx60, Float(Neg(Succ(wx62)), Neg(wx630)), bf)
new_lookupFM1172(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, Neg(wx2610), Succ(wx5400), be) → new_lookupFM1178(wx20, wx21, wx22, wx23, wx24, wx25, wx2600, wx2610, wx5400, new_primMulNat0(wx2610, wx21), be)
new_lookupFM2192(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, Succ(wx34300), Succ(Zero), bh) → new_lookupFM2209(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx7200, bh)
new_lookupFM2107(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx3980), ba) → new_lookupFM1387(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2109(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx4040), ba) → new_lookupFM(wx33, Float(Neg(Zero), Neg(Succ(Succ(Succ(wx410000))))), ba)
new_lookupFM(Branch(Float(Pos(Succ(wx30000)), Neg(Succ(wx30100))), wx31, wx32, wx33, wx34), Float(Neg(Zero), Pos(Succ(Zero))), ba) → new_lookupFM145(wx30000, wx30100, wx31, wx32, wx33, wx34, new_primMulNat0(Zero, wx30000), ba)
new_lookupFM2159(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, Succ(Succ(wx29300)), Zero, bf) → new_lookupFM2171(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx6300, bf)
new_lookupFM2180(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, ba) → new_lookupFM1286(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, new_primMulNat0(Zero, wx30000), ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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



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

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

new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69200), Succ(wx51900), bf) → new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, wx69200, wx51900, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69200), Succ(wx51900), bf) → new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, wx69200, wx51900, bf)

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

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

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

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



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

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

new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69200), Succ(wx51900), bf) → new_lookupFM1268(wx56, wx58, wx59, wx60, wx61, wx62, wx69200, wx51900, bf)

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

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



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

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

new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Succ(wx71800), bh) → new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx52700, wx71800, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Succ(wx71800), bh) → new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx52700, wx71800, bh)

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

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

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

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



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

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

new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, Succ(wx52700), Succ(wx71800), bh) → new_lookupFM1360(wx65, wx6600, wx67, wx68, wx69, wx70, wx71, wx52700, wx71800, bh)

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

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



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

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

new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Succ(wx72000), bh) → new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, wx52800, wx72000, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Succ(wx72000), bh) → new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, wx52800, wx72000, bh)

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

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

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

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



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

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

new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx52800), Succ(wx72000), bh) → new_lookupFM1363(wx65, wx67, wx68, wx69, wx70, wx71, wx52800, wx72000, bh)

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

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



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

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

new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69000), Succ(wx51800), bf) → new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69000, wx51800, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69000), Succ(wx51800), bf) → new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69000, wx51800, bf)

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

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

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

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



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

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

new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69000), Succ(wx51800), bf) → new_lookupFM1264(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69000, wx51800, bf)

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

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



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

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

new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, wx53000, wx72200, bh)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, wx53000, wx72200, bh)

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

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

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

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



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

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

new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, Succ(wx53000), Succ(wx72200), bh) → new_lookupFM1368(wx65, wx67, wx68, wx69, wx70, wx71, wx53000, wx72200, bh)

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

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



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

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

new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69400, wx52100, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69400, wx52100, bf)

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

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

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

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



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

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

new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, Succ(wx69400), Succ(wx52100), bf) → new_lookupFM1272(wx56, wx5700, wx58, wx59, wx60, wx61, wx62, wx69400, wx52100, bf)

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

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



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

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

new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69600), Succ(wx52200), bf) → new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, wx69600, wx52200, bf)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69600), Succ(wx52200), bf) → new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, wx69600, wx52200, bf)

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

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

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

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



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

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

new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, Succ(wx69600), Succ(wx52200), bf) → new_lookupFM1276(wx56, wx58, wx59, wx60, wx61, wx62, wx69600, wx52200, bf)

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

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



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

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

new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, Succ(wx88800), Succ(wx71100), ba) → new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, wx88800, wx71100, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, Succ(wx88800), Succ(wx71100), ba) → new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, wx88800, wx71100, ba)

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

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

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

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



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

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

new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, Succ(wx88800), Succ(wx71100), ba) → new_lookupFM1342(wx30100, wx31, wx32, wx33, wx34, wx88800, wx71100, ba)

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

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



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

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

new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx87600), Succ(wx70500), ba) → new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, wx87600, wx70500, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx87600), Succ(wx70500), ba) → new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, wx87600, wx70500, ba)

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

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

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

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



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

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

new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx87600), Succ(wx70500), ba) → new_lookupFM1311(wx30000, wx30100, wx31, wx32, wx33, wx34, wx87600, wx70500, ba)

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

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



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

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

new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Succ(wx91000), ba) → new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, wx73500, wx91000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Succ(wx91000), ba) → new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, wx73500, wx91000, ba)

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

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

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

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



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

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

new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, Succ(wx73500), Succ(wx91000), ba) → new_lookupFM1429(wx30100, wx31, wx32, wx33, wx34, wx73500, wx91000, ba)

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

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



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

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

new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Succ(wx61600), ba) → new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, wx48800, wx61600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Succ(wx61600), ba) → new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, wx48800, wx61600, ba)

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

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

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

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



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

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

new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx48800), Succ(wx61600), ba) → new_lookupFM1379(wx30000, wx30100, wx31, wx32, wx33, wx34, wx48800, wx61600, ba)

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

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



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

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

new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, Succ(wx60200), Succ(wx48000), ba) → new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, wx60200, wx48000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, Succ(wx60200), Succ(wx48000), ba) → new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, wx60200, wx48000, ba)

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

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

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

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



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

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

new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, Succ(wx60200), Succ(wx48000), ba) → new_lookupFM1301(wx30000, wx31, wx32, wx33, wx34, wx60200, wx48000, ba)

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

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



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

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

new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Succ(wx61800), ba) → new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, wx48900, wx61800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Succ(wx61800), ba) → new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, wx48900, wx61800, ba)

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

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

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

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



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

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

new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, Succ(wx48900), Succ(wx61800), ba) → new_lookupFM1382(wx30000, wx31, wx32, wx33, wx34, wx48900, wx61800, ba)

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

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



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

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

new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60000), Succ(wx47900), ba) → new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60000, wx47900, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60000), Succ(wx47900), ba) → new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60000, wx47900, ba)

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

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

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

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



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

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

new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60000), Succ(wx47900), ba) → new_lookupFM1297(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60000, wx47900, ba)

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

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



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

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

new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77600), Succ(wx59900), ba) → new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77600, wx59900, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77600), Succ(wx59900), ba) → new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77600, wx59900, ba)

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

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

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

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



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

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

new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx77600), Succ(wx59900), ba) → new_lookupFM1293(wx30000, wx30100, wx31, wx32, wx33, wx34, wx77600, wx59900, ba)

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

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



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

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

new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, Succ(wx78000), Succ(wx61300), ba) → new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, wx78000, wx61300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, Succ(wx78000), Succ(wx61300), ba) → new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, wx78000, wx61300, ba)

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

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

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

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



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

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

new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, Succ(wx78000), Succ(wx61300), ba) → new_lookupFM1332(wx30100, wx31, wx32, wx33, wx34, wx78000, wx61300, ba)

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

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



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

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

new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88600), Succ(wx71000), ba) → new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88600, wx71000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88600), Succ(wx71000), ba) → new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88600, wx71000, ba)

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

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

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

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



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

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

new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88600), Succ(wx71000), ba) → new_lookupFM1337(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88600, wx71000, ba)

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

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



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

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

new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87400), Succ(wx70400), ba) → new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87400, wx70400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87400), Succ(wx70400), ba) → new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87400, wx70400, ba)

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

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

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

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



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

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

new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87400), Succ(wx70400), ba) → new_lookupFM1306(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87400, wx70400, ba)

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

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



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

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

new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Succ(wx90800), ba) → new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, wx73400, wx90800, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Succ(wx90800), ba) → new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, wx73400, wx90800, ba)

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

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

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

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



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

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

new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx73400), Succ(wx90800), ba) → new_lookupFM1425(wx30100, wx31, wx32, wx33, wx34, wx410000, wx73400, wx90800, ba)

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

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



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

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

new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88400), Succ(wx70900), ba) → new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88400, wx70900, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88400), Succ(wx70900), ba) → new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88400, wx70900, ba)

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

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

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

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



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

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

new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx88400), Succ(wx70900), ba) → new_lookupFM1328(wx30100, wx31, wx32, wx33, wx34, wx410000, wx88400, wx70900, ba)

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

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



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

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

new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Succ(wx90000), ba) → new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, wx72800, wx90000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Succ(wx90000), ba) → new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, wx72800, wx90000, ba)

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

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

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

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



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

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

new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72800), Succ(wx90000), ba) → new_lookupFM1409(wx30100, wx31, wx32, wx33, wx34, wx410000, wx72800, wx90000, ba)

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

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



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

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

new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87200), Succ(wx70300), ba) → new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87200, wx70300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87200), Succ(wx70300), ba) → new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87200, wx70300, ba)

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

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

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

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



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

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

new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx87200), Succ(wx70300), ba) → new_lookupFM1289(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx87200, wx70300, ba)

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

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



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

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

new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Succ(wx89400), ba) → new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx72500, wx89400, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Succ(wx89400), ba) → new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx72500, wx89400, ba)

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

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

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

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



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

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

new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, Succ(wx72500), Succ(wx89400), ba) → new_lookupFM1376(wx30000, wx30100, wx31, wx32, wx33, wx34, wx410000, wx72500, wx89400, ba)

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

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



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

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

new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60500), Succ(wx48200), ba) → new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60500, wx48200, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60500), Succ(wx48200), ba) → new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60500, wx48200, ba)

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

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

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

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



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

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

new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, Succ(wx60500), Succ(wx48200), ba) → new_lookupFM1319(wx30000, wx30100, wx31, wx32, wx33, wx34, wx60500, wx48200, ba)

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

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



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

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

new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, Succ(wx60700), Succ(wx48300), ba) → new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, wx60700, wx48300, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, Succ(wx60700), Succ(wx48300), ba) → new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, wx60700, wx48300, ba)

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

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

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

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



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

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

new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, Succ(wx60700), Succ(wx48300), ba) → new_lookupFM1323(wx30000, wx31, wx32, wx33, wx34, wx60700, wx48300, ba)

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

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



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

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

new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Succ(wx62600), ba) → new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, wx49600, wx62600, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero, wx30000) → Succ(wx30000)
new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat0(Zero, wx30000) → Zero
new_primPlusNat1(Succ(wx780), wx30000) → Succ(Succ(new_primPlusNat0(wx780, wx30000)))
new_primPlusNat0(Succ(wx7800), Zero) → Succ(wx7800)
new_primPlusNat0(Zero, Succ(wx300000)) → Succ(wx300000)
new_primPlusNat0(Succ(wx7800), Succ(wx300000)) → Succ(Succ(new_primPlusNat0(wx7800, wx300000)))
new_primMulNat0(Succ(wx40000), wx30000) → new_primPlusNat1(new_primMulNat0(wx40000, wx30000), wx30000)
new_primMulNat1Zero

The set Q consists of the following terms:

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

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

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

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

new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Succ(wx62600), ba) → new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, wx49600, wx62600, ba)

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

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

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

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



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

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

new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, Succ(wx49600), Succ(wx62600), ba) → new_lookupFM1405(wx30000, wx31, wx32, wx33, wx34, wx49600, wx62600, ba)

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

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