YES 56.789 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/List.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



HASKELL
  ↳ BR

mainModule List
  ((nub :: [Int ->  [Int]) :: [Int ->  [Int])

module List where
  import qualified Maybe
import qualified Prelude

  nub :: Eq a => [a ->  [a]
nub l 
nub' l [] where 
nub' [] _ []
nub' (x : xsls 
 | x `elem` ls = 
nub' xs ls
 | otherwise = 
x : nub' xs (x : ls)


module Maybe where
  import qualified List
import qualified Prelude



Replaced joker patterns by fresh variables and removed binding patterns.

↳ HASKELL
  ↳ BR
HASKELL
      ↳ COR

mainModule List
  ((nub :: [Int ->  [Int]) :: [Int ->  [Int])

module List where
  import qualified Maybe
import qualified Prelude

  nub :: Eq a => [a ->  [a]
nub l 
nub' l [] where 
nub' [] vw []
nub' (x : xsls 
 | x `elem` ls = 
nub' xs ls
 | otherwise = 
x : nub' xs (x : ls)


module Maybe where
  import qualified List
import qualified Prelude



Cond Reductions:
The following Function with conditions
nub' [] vw = []
nub' (x : xsls
 | x `elem` ls
 = nub' xs ls
 | otherwise
 = x : nub' xs (x : ls)

is transformed to
nub' [] vw = nub'3 [] vw
nub' (x : xsls = nub'2 (x : xsls

nub'0 x xs ls True = x : nub' xs (x : ls)

nub'1 x xs ls True = nub' xs ls
nub'1 x xs ls False = nub'0 x xs ls otherwise

nub'2 (x : xsls = nub'1 x xs ls (x `elem` ls)

nub'3 [] vw = []
nub'3 wx wy = nub'2 wx wy

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



↳ HASKELL
  ↳ BR
    ↳ HASKELL
      ↳ COR
HASKELL
          ↳ LetRed

mainModule List
  ((nub :: [Int ->  [Int]) :: [Int ->  [Int])

module List where
  import qualified Maybe
import qualified Prelude

  nub :: Eq a => [a ->  [a]
nub l 
nub' l [] where 
nub' [] vw nub'3 [] vw
nub' (x : xsls nub'2 (x : xs) ls
nub'0 x xs ls True x : nub' xs (x : ls)
nub'1 x xs ls True nub' xs ls
nub'1 x xs ls False nub'0 x xs ls otherwise
nub'2 (x : xsls nub'1 x xs ls (x `elem` ls)
nub'3 [] vw []
nub'3 wx wy nub'2 wx wy


module Maybe where
  import qualified List
import qualified Prelude



Let/Where Reductions:
The bindings of the following Let/Where expression
nub' l []
where 
nub' [] vw = nub'3 [] vw
nub' (x : xsls = nub'2 (x : xsls
nub'0 x xs ls True = x : nub' xs (x : ls)
nub'1 x xs ls True = nub' xs ls
nub'1 x xs ls False = nub'0 x xs ls otherwise
nub'2 (x : xsls = nub'1 x xs ls (x `elem` ls)
nub'3 [] vw = []
nub'3 wx wy = nub'2 wx wy

are unpacked to the following functions on top level
nubNub'1 x xs ls True = nubNub' xs ls
nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise

nubNub'0 x xs ls True = x : nubNub' xs (x : ls)

nubNub'2 (x : xsls = nubNub'1 x xs ls (x `elem` ls)

nubNub'3 [] vw = []
nubNub'3 wx wy = nubNub'2 wx wy

nubNub' [] vw = nubNub'3 [] vw
nubNub' (x : xsls = nubNub'2 (x : xsls



↳ HASKELL
  ↳ BR
    ↳ HASKELL
      ↳ COR
        ↳ HASKELL
          ↳ LetRed
HASKELL
              ↳ Narrow

mainModule List
  (nub :: [Int ->  [Int])

module List where
  import qualified Maybe
import qualified Prelude

  nub :: Eq a => [a ->  [a]
nub l nubNub' l []

  
nubNub' [] vw nubNub'3 [] vw
nubNub' (x : xsls nubNub'2 (x : xs) ls

  
nubNub'0 x xs ls True x : nubNub' xs (x : ls)

  
nubNub'1 x xs ls True nubNub' xs ls
nubNub'1 x xs ls False nubNub'0 x xs ls otherwise

  
nubNub'2 (x : xsls nubNub'1 x xs ls (x `elem` ls)

  
nubNub'3 [] vw []
nubNub'3 wx wy nubNub'2 wx wy


module Maybe where
  import qualified List
import qualified Prelude



Haskell To QDPs


↳ HASKELL
  ↳ BR
    ↳ HASKELL
      ↳ COR
        ↳ HASKELL
          ↳ LetRed
            ↳ HASKELL
              ↳ Narrow
QDP
                  ↳ DependencyGraphProof

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

new_nubNub'113(wz1017, wz1018, wz1019, Neg(Succ(wz102000)), wz1021) → new_nubNub'129(wz1017, wz1018, wz1019, wz1021)
new_nubNub'124(wz1011, wz1012, wz1013, :(wz10150, wz10151)) → new_nubNub'10(wz1011, wz1012, wz1013, wz10150, wz10151)
new_nubNub'114(wz1097, wz1098, wz1099, Neg(Succ(wz110000)), wz1101) → new_nubNub'131(wz1097, wz1098, wz1099, wz1101)
new_nubNub'131(wz1097, wz1098, wz1099, :(wz11010, wz11011)) → new_nubNub'114(wz1097, wz1098, wz1099, wz11010, wz11011)
new_nubNub'115(Neg(Succ(wz3000)), :(Pos(Zero), wz311)) → new_nubNub'13(wz311, :(Neg(Succ(wz3000)), []))
new_nubNub'123(wz971, wz972, wz973, :(wz9750, wz9751)) → new_nubNub'19(wz971, wz972, wz973, wz9750, wz9751)
new_nubNub'119(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'120(Pos(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'118(Pos(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'118(Pos(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'115(Pos(Zero), :(Pos(Zero), wz311)) → new_nubNub'(wz311, Pos(Zero))
new_nubNub'2(Pos(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'121(Pos(Succ(wz82000)), wz821, Neg(wz8300), :(wz8310, wz8311)) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'110(wz31000, :(Pos(Succ(wz311000)), wz3111)) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'2(Pos(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'110(wz31000, :(Neg(Zero), wz3111)) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'0(:(Pos(Zero), wz821), :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'129(wz1017, wz1018, wz1019, []) → new_nubNub'13(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'116(wz820, wz821, []) → new_nubNub'115(wz820, wz821)
new_nubNub'120(Pos(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'10(wz1011, wz1012, wz1013, Neg(Zero), wz1015) → new_nubNub'125(wz1011, wz1012, wz1013, wz1015)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111)), Pos(Zero)) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'121(Neg(Zero), wz821, Neg(Succ(wz83000)), []) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'119(Neg(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'118(Neg(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'121(Pos(Zero), wz821, Neg(Zero), wz831) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'19(wz971, wz972, wz973, Pos(Zero), wz975) → new_nubNub'123(wz971, wz972, wz973, wz975)
new_nubNub'14(wz1111, wz1112, wz1113, Zero, Zero, wz1116) → new_nubNub'0(wz1112, wz1113)
new_nubNub'117(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'117(wz820, wz821, []) → new_nubNub'115(wz820, wz821)
new_nubNub'119(Neg(Succ(wz82000)), wz821, :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'17(wz1043, wz1044, wz1045) → new_nubNub'0(wz1043, :(Neg(Zero), :(Neg(Succ(wz1044)), wz1045)))
new_nubNub'115(Neg(Succ(wz3000)), :(Neg(Zero), wz311)) → new_nubNub'17(wz311, wz3000, [])
new_nubNub'116(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'120(Neg(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'(:(Neg(Zero), wz311), Pos(Zero)) → new_nubNub'16(wz311, :(Pos(Zero), []), [])
new_nubNub'121(Neg(Succ(wz82000)), wz821, Neg(Succ(wz83000)), wz831) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'121(Neg(Succ(wz82000)), wz821, Pos(wz8300), wz831) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'119(Pos(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'121(Pos(Succ(wz82000)), wz821, Neg(wz8300), []) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'0(:(Pos(Zero), wz821), :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'117(Neg(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'128(wz944, wz945, wz946, wz947, :(wz9490, wz9491)) → new_nubNub'111(wz944, wz945, wz946, wz947, wz9490, wz9491)
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, :(Pos(Succ(wz1136000)), wz11361)) → new_nubNub'1(wz1130, wz1131, wz1132, wz1133, wz1130, wz1136000, wz11361)
new_nubNub'119(Pos(Succ(wz82000)), wz821, :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'119(Neg(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111)), Neg(wz300)) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'3(:(Pos(Zero), wz3111), wz31000) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'118(Neg(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'112(wz31000, :(Pos(Zero), wz3111), wz300) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'0(:(wz820, wz821), []) → new_nubNub'115(wz820, wz821)
new_nubNub'116(Pos(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'119(Neg(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'0(:(Neg(Zero), wz821), :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'114(wz1097, wz1098, wz1099, Pos(Succ(wz110000)), []) → new_nubNub'17(wz1097, wz1098, wz1099)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Succ(wz11350), wz1136) → new_nubNub'1(wz1130, wz1131, wz1132, wz1133, wz11340, wz11350, wz1136)
new_nubNub'2(Neg(Succ(wz82000)), wz821, :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'120(Pos(Succ(wz82000)), wz821, :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Zero, Succ(wz11350), wz1136) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz1136)
new_nubNub'116(Neg(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'128(wz944, wz945, wz946, wz947, []) → new_nubNub'0(wz945, :(Pos(Succ(wz944)), :(Neg(wz946), wz947)))
new_nubNub'119(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'122(wz1123, wz1124, wz1125, Succ(wz11260), Succ(wz11270), wz1128) → new_nubNub'122(wz1123, wz1124, wz1125, wz11260, wz11270, wz1128)
new_nubNub'12(wz1037, wz1038, wz1039, Neg(Succ(wz104000)), wz1041) → new_nubNub'126(wz1037, wz1038, wz1039, wz1041)
new_nubNub'(:(Pos(Zero), wz311), Pos(Succ(wz3000))) → new_nubNub'13(wz311, :(Pos(Succ(wz3000)), []))
new_nubNub'121(Pos(Zero), wz821, Pos(Succ(wz83000)), []) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Pos(Zero), wz3111))) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'2(Pos(Succ(wz82000)), wz821, :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Zero), wz3111)), Neg(wz300)) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'118(Neg(Succ(wz82000)), wz821, :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'12(wz1037, wz1038, wz1039, Pos(Succ(wz104000)), :(wz10410, wz10411)) → new_nubNub'12(wz1037, wz1038, wz1039, wz10410, wz10411)
new_nubNub'2(wz820, wz821, []) → new_nubNub'115(wz820, wz821)
new_nubNub'119(Pos(Succ(wz82000)), wz821, :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'2(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'0(:(Neg(Zero), wz821), :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'120(Neg(Succ(wz82000)), wz821, :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'116(Pos(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'121(Pos(Zero), wz821, Neg(Succ(wz83000)), []) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'14(wz1111, wz1112, wz1113, Succ(wz11140), Succ(wz11150), wz1116) → new_nubNub'14(wz1111, wz1112, wz1113, wz11140, wz11150, wz1116)
new_nubNub'15(wz1023, wz1024, wz1025) → new_nubNub'0(wz1023, :(Neg(Zero), :(Pos(Succ(wz1024)), wz1025)))
new_nubNub'111(wz944, wz945, wz946, wz947, Pos(Succ(wz94800)), wz949) → new_nubNub'127(wz944, wz945, wz946, wz947, wz944, wz94800, wz949)
new_nubNub'115(Pos(Succ(wz3000)), :(Neg(Zero), wz311)) → new_nubNub'15(wz311, wz3000, [])
new_nubNub'112(wz31000, :(Pos(Succ(wz311000)), wz3111), wz300) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'(:(Neg(Succ(wz31000)), wz311), Neg(Succ(wz3000))) → new_nubNub'14(wz31000, wz311, :(Neg(Succ(wz3000)), []), wz31000, wz3000, [])
new_nubNub'119(Pos(Succ(wz82000)), wz821, :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'16(wz598, wz599, wz600) → new_nubNub'0(wz598, wz599)
new_nubNub'117(Pos(Succ(wz82000)), wz821, :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'115(Neg(Zero), :(Neg(Zero), wz311)) → new_nubNub'16(wz311, :(Neg(Zero), []), [])
new_nubNub'116(Neg(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'118(Neg(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'3(:(Neg(Succ(wz311000)), wz3111), wz31000) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, :(Pos(Zero), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'123(wz971, wz972, wz973, []) → new_nubNub'0(wz972, :(Pos(Succ(wz971)), :(Pos(Zero), wz973)))
new_nubNub'124(wz1011, wz1012, wz1013, []) → new_nubNub'13(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'116(Pos(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'118(Pos(Succ(wz82000)), wz821, :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'118(Pos(Succ(wz82000)), wz821, :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'11(wz1006, wz1007, wz1008, []) → new_nubNub'0(wz1007, :(Neg(Succ(wz1006)), wz1008))
new_nubNub'13(wz860, wz861) → new_nubNub'0(wz860, :(Pos(Zero), wz861))
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111))) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'3(:(Neg(Zero), wz3111), wz31000) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'111(wz944, wz945, wz946, wz947, Neg(wz9480), []) → new_nubNub'0(wz945, :(Pos(Succ(wz944)), :(Neg(wz946), wz947)))
new_nubNub'120(Neg(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'0(:(Neg(Zero), wz821), :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'116(Neg(Succ(wz82000)), wz821, :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'117(Pos(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'19(wz971, wz972, wz973, Pos(Succ(wz97400)), wz975) → new_nubNub'122(wz971, wz972, wz973, wz971, wz97400, wz975)
new_nubNub'2(Pos(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'0(:(Neg(Succ(wz82000)), wz821), :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'126(wz1037, wz1038, wz1039, []) → new_nubNub'15(wz1037, wz1038, wz1039)
new_nubNub'12(wz1037, wz1038, wz1039, Pos(Succ(wz104000)), []) → new_nubNub'15(wz1037, wz1038, wz1039)
new_nubNub'116(Neg(Succ(wz82000)), wz821, :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'2(Neg(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'120(Pos(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'119(Pos(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'0(:(Neg(Zero), wz821), :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'118(Pos(Succ(wz82000)), wz821, :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'2(Neg(Succ(wz82000)), wz821, :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'11(wz1006, wz1007, wz1008, :(Pos(wz100900), wz10091)) → new_nubNub'11(wz1006, wz1007, wz1008, wz10091)
new_nubNub'118(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'130(wz1017, wz1018, wz1019, wz1021) → new_nubNub'0(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'113(wz1017, wz1018, wz1019, Pos(Succ(wz102000)), []) → new_nubNub'13(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'0(:(Pos(Zero), wz821), :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'119(Neg(Succ(wz82000)), wz821, :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'117(Neg(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'120(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'0(:(Neg(Zero), wz821), :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'115(Neg(Zero), :(Neg(Succ(wz31000)), wz311)) → new_nubNub'11(wz31000, wz311, :(Neg(Zero), []), [])
new_nubNub'119(Neg(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'2(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'119(Neg(Succ(wz82000)), wz821, :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'119(Neg(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'122(wz1123, wz1124, wz1125, Zero, Zero, wz1128) → new_nubNub'0(wz1124, :(Pos(Zero), wz1125))
new_nubNub'117(Pos(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, []) → new_nubNub'0(wz1131, :(Pos(Succ(wz1130)), :(Pos(Succ(wz1132)), wz1133)))
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111))) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'120(Neg(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'0(:(Pos(Zero), wz821), :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'10(wz1011, wz1012, wz1013, Pos(Succ(wz101400)), []) → new_nubNub'13(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'121(Pos(Succ(wz82000)), wz821, Pos(Zero), :(wz8310, wz8311)) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'120(Pos(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'114(wz1097, wz1098, wz1099, Pos(Zero), wz1101) → new_nubNub'16(wz1097, :(Neg(Succ(wz1098)), wz1099), wz1101)
new_nubNub'112(wz31000, :(Neg(Zero), wz3111), wz300) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, :(Pos(Zero), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'3(:(Pos(Succ(wz311000)), wz3111), wz31000) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'2(Neg(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111)), Neg(wz300)) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'14(wz1111, wz1112, wz1113, Zero, Succ(wz11150), wz1116) → new_nubNub'11(wz1111, wz1112, wz1113, wz1116)
new_nubNub'14(wz1111, wz1112, wz1113, Succ(wz11140), Zero, wz1116) → new_nubNub'11(wz1111, wz1112, wz1113, wz1116)
new_nubNub'2(Neg(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'118(Neg(Succ(wz82000)), wz821, :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'2(Neg(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Zero), wz3111)), Pos(Zero)) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'(:(Pos(Zero), wz311), Pos(Zero)) → new_nubNub'(wz311, Pos(Zero))
new_nubNub'0(:(Pos(Zero), wz821), :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'10(wz1011, wz1012, wz1013, Neg(Succ(wz101400)), wz1015) → new_nubNub'124(wz1011, wz1012, wz1013, wz1015)
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'19(wz971, wz972, wz973, Neg(wz9740), :(wz9750, wz9751)) → new_nubNub'19(wz971, wz972, wz973, wz9750, wz9751)
new_nubNub'131(wz1097, wz1098, wz1099, []) → new_nubNub'17(wz1097, wz1098, wz1099)
new_nubNub'(:(Neg(Zero), wz311), Pos(Succ(wz3000))) → new_nubNub'15(wz311, wz3000, [])
new_nubNub'120(Neg(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'112(wz31000, :(Neg(Succ(wz311000)), wz3111), wz300) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'119(Pos(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'(:(Neg(Succ(wz31000)), wz311), Pos(wz300)) → new_nubNub'11(wz31000, wz311, :(Pos(wz300), []), [])
new_nubNub'111(wz944, wz945, wz946, wz947, Pos(Zero), wz949) → new_nubNub'128(wz944, wz945, wz946, wz947, wz949)
new_nubNub'121(Neg(Zero), wz821, Neg(Zero), wz831) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'117(Pos(Succ(wz82000)), wz821, :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'121(Pos(Succ(wz82000)), wz821, Pos(Zero), []) → new_nubNub'110(wz82000, wz821)
new_nubNub'111(wz944, wz945, wz946, wz947, Neg(wz9480), :(wz9490, wz9491)) → new_nubNub'111(wz944, wz945, wz946, wz947, wz9490, wz9491)
new_nubNub'118(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'120(Pos(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'120(Neg(Succ(wz82000)), wz821, :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'(:(Pos(Succ(wz31000)), wz311), Pos(Succ(wz3000))) → new_nubNub'1(wz31000, wz311, wz3000, [], wz31000, wz3000, [])
new_nubNub'2(Neg(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'2(Pos(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'116(Neg(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'117(Neg(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'12(wz1037, wz1038, wz1039, Neg(Zero), wz1041) → new_nubNub'16(wz1037, :(Pos(Succ(wz1038)), wz1039), wz1041)
new_nubNub'110(wz31000, :(Neg(Succ(wz311000)), wz3111)) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'4(:(Pos(Succ(wz311000)), wz3111), wz31000, wz300) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'116(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'118(Neg(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'0(:(Pos(Zero), wz821), :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'4(:(Neg(Succ(wz311000)), wz3111), wz31000, wz300) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'115(Pos(Zero), :(Neg(Zero), wz311)) → new_nubNub'16(wz311, :(Pos(Zero), []), [])
new_nubNub'121(Neg(Zero), wz821, Neg(Succ(wz83000)), :(wz8310, wz8311)) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'0(:(Neg(Zero), wz821), :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'2(Pos(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'116(Pos(Succ(wz82000)), wz821, :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'117(Pos(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'0(:(Neg(Succ(wz82000)), wz821), :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'116(Pos(Succ(wz82000)), wz821, :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'121(Neg(Zero), wz821, Pos(Succ(wz83000)), :(wz8310, wz8311)) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'116(Neg(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'118(Pos(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'120(Neg(Succ(wz82000)), wz821, :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'(:(Neg(Zero), wz311), Neg(Succ(wz3000))) → new_nubNub'17(wz311, wz3000, [])
new_nubNub'113(wz1017, wz1018, wz1019, Pos(Zero), wz1021) → new_nubNub'0(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'119(Pos(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'115(Pos(Succ(wz3000)), :(Pos(Zero), wz311)) → new_nubNub'13(wz311, :(Pos(Succ(wz3000)), []))
new_nubNub'118(Pos(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'120(Neg(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'118(Neg(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Zero, Zero, wz1136) → new_nubNub'0(wz1131, :(Pos(Succ(wz1132)), wz1133))
new_nubNub'117(Pos(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'120(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, []) → new_nubNub'0(wz1131, :(Pos(Succ(wz1130)), :(Pos(Succ(wz1132)), wz1133)))
new_nubNub'4(:(Pos(Zero), wz3111), wz31000, wz300) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'(:(Pos(Zero), wz311), Neg(Zero)) → new_nubNub'(wz311, Neg(Zero))
new_nubNub'110(wz31000, :(Pos(Zero), wz3111)) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'118(Neg(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Neg(Zero), wz3111))) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111))) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'121(Pos(Zero), wz821, Pos(Zero), wz831) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'117(Neg(Succ(wz82000)), wz821, :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'4(:(Neg(Zero), wz3111), wz31000, wz300) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'117(Neg(Succ(wz82000)), wz821, :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111))) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Succ(wz11070), Zero, wz1109) → new_nubNub'128(wz1103, wz1104, wz1105, wz1106, wz1109)
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Zero, Succ(wz11080), wz1109) → new_nubNub'128(wz1103, wz1104, wz1105, wz1106, wz1109)
new_nubNub'117(Pos(Succ(wz82000)), wz821, :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'116(Neg(Succ(wz82000)), wz821, :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'115(Neg(Zero), :(Pos(Zero), wz311)) → new_nubNub'(wz311, Neg(Zero))
new_nubNub'125(wz1011, wz1012, wz1013, wz1015) → new_nubNub'0(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'120(wz820, wz821, []) → new_nubNub'115(wz820, wz821)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, :(Pos(Succ(wz1136000)), wz11361)) → new_nubNub'1(wz1130, wz1131, wz1132, wz1133, wz1130, wz1136000, wz11361)
new_nubNub'118(Neg(Succ(wz82000)), wz821, :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'116(Neg(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'117(Pos(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'116(Pos(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'122(wz1123, wz1124, wz1125, Succ(wz11260), Zero, wz1128) → new_nubNub'123(wz1123, wz1124, wz1125, wz1128)
new_nubNub'122(wz1123, wz1124, wz1125, Zero, Succ(wz11270), wz1128) → new_nubNub'123(wz1123, wz1124, wz1125, wz1128)
new_nubNub'119(Pos(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'2(Pos(Succ(wz82000)), wz821, :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'114(wz1097, wz1098, wz1099, Pos(Succ(wz110000)), :(wz11010, wz11011)) → new_nubNub'114(wz1097, wz1098, wz1099, wz11010, wz11011)
new_nubNub'119(Pos(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'12(wz1037, wz1038, wz1039, Pos(Zero), wz1041) → new_nubNub'16(wz1037, :(Pos(Succ(wz1038)), wz1039), wz1041)
new_nubNub'(:(Pos(Zero), wz311), Neg(Succ(wz3000))) → new_nubNub'13(wz311, :(Neg(Succ(wz3000)), []))
new_nubNub'(:(Neg(Succ(wz31000)), wz311), Neg(Zero)) → new_nubNub'11(wz31000, wz311, :(Neg(Zero), []), [])
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Pos(Zero), wz3111))) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'2(Pos(Succ(wz82000)), wz821, :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'(:(Neg(Zero), wz311), Neg(Zero)) → new_nubNub'16(wz311, :(Neg(Zero), []), [])
new_nubNub'2(Neg(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'19(wz971, wz972, wz973, Neg(wz9740), []) → new_nubNub'0(wz972, :(Pos(Succ(wz971)), :(Pos(Zero), wz973)))
new_nubNub'119(Neg(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'11(wz1006, wz1007, wz1008, :(Neg(Zero), wz10091)) → new_nubNub'11(wz1006, wz1007, wz1008, wz10091)
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Neg(Zero), wz3111))) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'129(wz1017, wz1018, wz1019, :(wz10210, wz10211)) → new_nubNub'113(wz1017, wz1018, wz1019, wz10210, wz10211)
new_nubNub'121(Neg(Zero), wz821, Pos(Succ(wz83000)), []) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'121(Neg(Succ(wz82000)), wz821, Neg(Zero), wz831) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'121(Pos(Succ(wz82000)), wz821, Pos(Succ(wz83000)), wz831) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'116(Pos(Zero), wz821, :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'120(Pos(Succ(wz82000)), wz821, :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'118(Pos(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'117(Neg(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'116(Pos(Succ(wz82000)), wz821, :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'117(Pos(Zero), wz821, :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, :(Neg(wz113600), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'0(:(Neg(Succ(wz82000)), wz821), :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'117(Pos(Succ(wz82000)), wz821, :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'118(wz820, wz821, []) → new_nubNub'115(wz820, wz821)
new_nubNub'10(wz1011, wz1012, wz1013, Pos(Zero), wz1015) → new_nubNub'0(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'113(wz1017, wz1018, wz1019, Pos(Succ(wz102000)), :(wz10210, wz10211)) → new_nubNub'113(wz1017, wz1018, wz1019, wz10210, wz10211)
new_nubNub'2(Pos(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'117(Neg(Zero), wz821, :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'117(Neg(Succ(wz82000)), wz821, :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Zero), wz3111)), Neg(wz300)) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'11(wz1006, wz1007, wz1008, :(Neg(Succ(wz1009000)), wz10091)) → new_nubNub'14(wz1006, wz1007, wz1008, wz1006, wz1009000, wz10091)
new_nubNub'2(Neg(Succ(wz82000)), wz821, :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'120(Neg(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, :(Neg(wz113600), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'120(Pos(Succ(wz82000)), wz821, :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'115(Pos(wz300), :(Neg(Succ(wz31000)), wz311)) → new_nubNub'11(wz31000, wz311, :(Pos(wz300), []), [])
new_nubNub'120(Pos(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Zero, Zero, wz1109) → new_nubNub'0(wz1104, :(Neg(wz1105), wz1106))
new_nubNub'126(wz1037, wz1038, wz1039, :(wz10410, wz10411)) → new_nubNub'12(wz1037, wz1038, wz1039, wz10410, wz10411)
new_nubNub'114(wz1097, wz1098, wz1099, Neg(Zero), wz1101) → new_nubNub'16(wz1097, :(Neg(Succ(wz1098)), wz1099), wz1101)
new_nubNub'119(wz820, wz821, []) → new_nubNub'115(wz820, wz821)
new_nubNub'116(Neg(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'117(Neg(Zero), wz821, :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'121(Pos(Zero), wz821, Pos(Succ(wz83000)), :(wz8310, wz8311)) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'116(Pos(Zero), wz821, :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'10(wz1011, wz1012, wz1013, Pos(Succ(wz101400)), :(wz10150, wz10151)) → new_nubNub'10(wz1011, wz1012, wz1013, wz10150, wz10151)
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Succ(wz11070), Succ(wz11080), wz1109) → new_nubNub'127(wz1103, wz1104, wz1105, wz1106, wz11070, wz11080, wz1109)
new_nubNub'113(wz1017, wz1018, wz1019, Neg(Zero), wz1021) → new_nubNub'130(wz1017, wz1018, wz1019, wz1021)
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111)), Pos(Zero)) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'115(Pos(Succ(wz3000)), :(Pos(Succ(wz31000)), wz311)) → new_nubNub'1(wz31000, wz311, wz3000, [], wz31000, wz3000, [])
new_nubNub'121(Neg(Zero), wz821, Pos(Zero), wz831) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'121(Pos(Zero), wz821, Neg(Succ(wz83000)), :(wz8310, wz8311)) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Zero), wz3111)), Pos(Zero)) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'115(Neg(Succ(wz3000)), :(Neg(Succ(wz31000)), wz311)) → new_nubNub'14(wz31000, wz311, :(Neg(Succ(wz3000)), []), wz31000, wz3000, [])
new_nubNub'118(Pos(Zero), wz821, :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 160 less nodes.

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

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

new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111))) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'113(wz1017, wz1018, wz1019, Neg(Succ(wz102000)), wz1021) → new_nubNub'129(wz1017, wz1018, wz1019, wz1021)
new_nubNub'0(:(Pos(Zero), wz821), :(Pos(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Pos(Succ(wz83000)), []))
new_nubNub'10(wz1011, wz1012, wz1013, Pos(Succ(wz101400)), []) → new_nubNub'13(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'124(wz1011, wz1012, wz1013, :(wz10150, wz10151)) → new_nubNub'10(wz1011, wz1012, wz1013, wz10150, wz10151)
new_nubNub'114(wz1097, wz1098, wz1099, Neg(Succ(wz110000)), wz1101) → new_nubNub'131(wz1097, wz1098, wz1099, wz1101)
new_nubNub'114(wz1097, wz1098, wz1099, Pos(Zero), wz1101) → new_nubNub'16(wz1097, :(Neg(Succ(wz1098)), wz1099), wz1101)
new_nubNub'131(wz1097, wz1098, wz1099, :(wz11010, wz11011)) → new_nubNub'114(wz1097, wz1098, wz1099, wz11010, wz11011)
new_nubNub'112(wz31000, :(Neg(Zero), wz3111), wz300) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'123(wz971, wz972, wz973, :(wz9750, wz9751)) → new_nubNub'19(wz971, wz972, wz973, wz9750, wz9751)
new_nubNub'115(Neg(Succ(wz3000)), :(Pos(Zero), wz311)) → new_nubNub'13(wz311, :(Neg(Succ(wz3000)), []))
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Pos(Zero), :(wz8310, wz8311))) → new_nubNub'19(wz82000, wz821, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, :(Pos(Zero), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111)), Neg(wz300)) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'14(wz1111, wz1112, wz1113, Zero, Succ(wz11150), wz1116) → new_nubNub'11(wz1111, wz1112, wz1113, wz1116)
new_nubNub'14(wz1111, wz1112, wz1113, Succ(wz11140), Zero, wz1116) → new_nubNub'11(wz1111, wz1112, wz1113, wz1116)
new_nubNub'0(:(Pos(Zero), wz821), :(Pos(Zero), wz831)) → new_nubNub'0(wz821, :(Pos(Zero), wz831))
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Zero), wz3111)), Pos(Zero)) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'(:(Pos(Zero), wz311), Pos(Zero)) → new_nubNub'(wz311, Pos(Zero))
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Pos(Succ(wz83000)), wz831)) → new_nubNub'1(wz82000, wz821, wz83000, wz831, wz82000, wz83000, wz831)
new_nubNub'10(wz1011, wz1012, wz1013, Neg(Succ(wz101400)), wz1015) → new_nubNub'124(wz1011, wz1012, wz1013, wz1015)
new_nubNub'115(Pos(Zero), :(Pos(Zero), wz311)) → new_nubNub'(wz311, Pos(Zero))
new_nubNub'19(wz971, wz972, wz973, Neg(wz9740), :(wz9750, wz9751)) → new_nubNub'19(wz971, wz972, wz973, wz9750, wz9751)
new_nubNub'131(wz1097, wz1098, wz1099, []) → new_nubNub'17(wz1097, wz1098, wz1099)
new_nubNub'110(wz31000, :(Pos(Succ(wz311000)), wz3111)) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'110(wz31000, :(Neg(Zero), wz3111)) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'0(:(Pos(Zero), wz821), :(Neg(Zero), wz831)) → new_nubNub'0(wz821, :(Neg(Zero), wz831))
new_nubNub'129(wz1017, wz1018, wz1019, []) → new_nubNub'13(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'112(wz31000, :(Neg(Succ(wz311000)), wz3111), wz300) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'10(wz1011, wz1012, wz1013, Neg(Zero), wz1015) → new_nubNub'125(wz1011, wz1012, wz1013, wz1015)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111)), Pos(Zero)) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'(:(Neg(Succ(wz31000)), wz311), Pos(wz300)) → new_nubNub'11(wz31000, wz311, :(Pos(wz300), []), [])
new_nubNub'111(wz944, wz945, wz946, wz947, Pos(Zero), wz949) → new_nubNub'128(wz944, wz945, wz946, wz947, wz949)
new_nubNub'111(wz944, wz945, wz946, wz947, Neg(wz9480), :(wz9490, wz9491)) → new_nubNub'111(wz944, wz945, wz946, wz947, wz9490, wz9491)
new_nubNub'19(wz971, wz972, wz973, Pos(Zero), wz975) → new_nubNub'123(wz971, wz972, wz973, wz975)
new_nubNub'14(wz1111, wz1112, wz1113, Zero, Zero, wz1116) → new_nubNub'0(wz1112, wz1113)
new_nubNub'12(wz1037, wz1038, wz1039, Neg(Zero), wz1041) → new_nubNub'16(wz1037, :(Pos(Succ(wz1038)), wz1039), wz1041)
new_nubNub'110(wz31000, :(Neg(Succ(wz311000)), wz3111)) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'17(wz1043, wz1044, wz1045) → new_nubNub'0(wz1043, :(Neg(Zero), :(Neg(Succ(wz1044)), wz1045)))
new_nubNub'115(Neg(Succ(wz3000)), :(Neg(Zero), wz311)) → new_nubNub'17(wz311, wz3000, [])
new_nubNub'0(:(Pos(Zero), wz821), :(Neg(Succ(wz83000)), [])) → new_nubNub'13(wz821, :(Neg(Succ(wz83000)), []))
new_nubNub'0(:(Neg(Zero), wz821), :(Neg(Zero), wz831)) → new_nubNub'16(wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'115(Pos(Zero), :(Neg(Zero), wz311)) → new_nubNub'16(wz311, :(Pos(Zero), []), [])
new_nubNub'(:(Neg(Zero), wz311), Pos(Zero)) → new_nubNub'16(wz311, :(Pos(Zero), []), [])
new_nubNub'0(:(Neg(Succ(wz82000)), wz821), :(Pos(wz8300), wz831)) → new_nubNub'11(wz82000, wz821, :(Pos(wz8300), wz831), wz831)
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Pos(Zero), [])) → new_nubNub'110(wz82000, wz821)
new_nubNub'0(:(Pos(Zero), wz821), :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'113(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'128(wz944, wz945, wz946, wz947, :(wz9490, wz9491)) → new_nubNub'111(wz944, wz945, wz946, wz947, wz9490, wz9491)
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, :(Pos(Succ(wz1136000)), wz11361)) → new_nubNub'1(wz1130, wz1131, wz1132, wz1133, wz1130, wz1136000, wz11361)
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111)), Neg(wz300)) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Neg(wz300), [])), :(Neg(wz300), []))
new_nubNub'112(wz31000, :(Pos(Zero), wz3111), wz300) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'113(wz1017, wz1018, wz1019, Pos(Zero), wz1021) → new_nubNub'0(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'0(:(wz820, wz821), []) → new_nubNub'115(wz820, wz821)
new_nubNub'115(Pos(Succ(wz3000)), :(Pos(Zero), wz311)) → new_nubNub'13(wz311, :(Pos(Succ(wz3000)), []))
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Zero, Zero, wz1136) → new_nubNub'0(wz1131, :(Pos(Succ(wz1132)), wz1133))
new_nubNub'0(:(Neg(Zero), wz821), :(Neg(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'114(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'114(wz1097, wz1098, wz1099, Pos(Succ(wz110000)), []) → new_nubNub'17(wz1097, wz1098, wz1099)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Succ(wz11350), wz1136) → new_nubNub'1(wz1130, wz1131, wz1132, wz1133, wz11340, wz11350, wz1136)
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, []) → new_nubNub'0(wz1131, :(Pos(Succ(wz1130)), :(Pos(Succ(wz1132)), wz1133)))
new_nubNub'(:(Pos(Zero), wz311), Neg(Zero)) → new_nubNub'(wz311, Neg(Zero))
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Zero, Succ(wz11350), wz1136) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz1136)
new_nubNub'110(wz31000, :(Pos(Zero), wz3111)) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Neg(Zero), wz3111))) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'128(wz944, wz945, wz946, wz947, []) → new_nubNub'0(wz945, :(Pos(Succ(wz944)), :(Neg(wz946), wz947)))
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111))) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'122(wz1123, wz1124, wz1125, Succ(wz11260), Succ(wz11270), wz1128) → new_nubNub'122(wz1123, wz1124, wz1125, wz11260, wz11270, wz1128)
new_nubNub'12(wz1037, wz1038, wz1039, Neg(Succ(wz104000)), wz1041) → new_nubNub'126(wz1037, wz1038, wz1039, wz1041)
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111))) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Succ(wz11070), Zero, wz1109) → new_nubNub'128(wz1103, wz1104, wz1105, wz1106, wz1109)
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Zero, Succ(wz11080), wz1109) → new_nubNub'128(wz1103, wz1104, wz1105, wz1106, wz1109)
new_nubNub'115(Neg(Zero), :(Pos(Zero), wz311)) → new_nubNub'(wz311, Neg(Zero))
new_nubNub'125(wz1011, wz1012, wz1013, wz1015) → new_nubNub'0(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, :(Pos(Succ(wz1136000)), wz11361)) → new_nubNub'1(wz1130, wz1131, wz1132, wz1133, wz1130, wz1136000, wz11361)
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Pos(Zero), wz3111))) → new_nubNub'10(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Zero), wz3111)), Neg(wz300)) → new_nubNub'12(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Neg(wz8300), :(wz8310, wz8311))) → new_nubNub'111(wz82000, wz821, wz8300, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'122(wz1123, wz1124, wz1125, Succ(wz11260), Zero, wz1128) → new_nubNub'123(wz1123, wz1124, wz1125, wz1128)
new_nubNub'122(wz1123, wz1124, wz1125, Zero, Succ(wz11270), wz1128) → new_nubNub'123(wz1123, wz1124, wz1125, wz1128)
new_nubNub'114(wz1097, wz1098, wz1099, Pos(Succ(wz110000)), :(wz11010, wz11011)) → new_nubNub'114(wz1097, wz1098, wz1099, wz11010, wz11011)
new_nubNub'12(wz1037, wz1038, wz1039, Pos(Zero), wz1041) → new_nubNub'16(wz1037, :(Pos(Succ(wz1038)), wz1039), wz1041)
new_nubNub'12(wz1037, wz1038, wz1039, Pos(Succ(wz104000)), :(wz10410, wz10411)) → new_nubNub'12(wz1037, wz1038, wz1039, wz10410, wz10411)
new_nubNub'(:(Neg(Succ(wz31000)), wz311), Neg(Zero)) → new_nubNub'11(wz31000, wz311, :(Neg(Zero), []), [])
new_nubNub'115(Neg(wz300), :(Pos(Succ(wz31000)), :(Pos(Zero), wz3111))) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'0(:(Neg(Zero), wz821), :(Neg(Succ(wz83000)), [])) → new_nubNub'17(wz821, wz83000, [])
new_nubNub'(:(Neg(Zero), wz311), Neg(Zero)) → new_nubNub'16(wz311, :(Neg(Zero), []), [])
new_nubNub'19(wz971, wz972, wz973, Neg(wz9740), []) → new_nubNub'0(wz972, :(Pos(Succ(wz971)), :(Pos(Zero), wz973)))
new_nubNub'11(wz1006, wz1007, wz1008, :(Neg(Zero), wz10091)) → new_nubNub'11(wz1006, wz1007, wz1008, wz10091)
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Neg(Zero), wz3111))) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'129(wz1017, wz1018, wz1019, :(wz10210, wz10211)) → new_nubNub'113(wz1017, wz1018, wz1019, wz10210, wz10211)
new_nubNub'15(wz1023, wz1024, wz1025) → new_nubNub'0(wz1023, :(Neg(Zero), :(Pos(Succ(wz1024)), wz1025)))
new_nubNub'14(wz1111, wz1112, wz1113, Succ(wz11140), Succ(wz11150), wz1116) → new_nubNub'14(wz1111, wz1112, wz1113, wz11140, wz11150, wz1116)
new_nubNub'111(wz944, wz945, wz946, wz947, Pos(Succ(wz94800)), wz949) → new_nubNub'127(wz944, wz945, wz946, wz947, wz944, wz94800, wz949)
new_nubNub'115(Pos(Succ(wz3000)), :(Neg(Zero), wz311)) → new_nubNub'15(wz311, wz3000, [])
new_nubNub'112(wz31000, :(Pos(Succ(wz311000)), wz3111), wz300) → new_nubNub'1(wz311000, wz3111, wz31000, :(Neg(wz300), []), wz311000, wz31000, :(Neg(wz300), []))
new_nubNub'1(wz1130, wz1131, wz1132, wz1133, Succ(wz11340), Zero, :(Neg(wz113600), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'0(:(Neg(Succ(wz82000)), wz821), :(Neg(Zero), wz831)) → new_nubNub'11(wz82000, wz821, :(Neg(Zero), wz831), wz831)
new_nubNub'16(wz598, wz599, wz600) → new_nubNub'0(wz598, wz599)
new_nubNub'0(:(Pos(Succ(wz82000)), wz821), :(Neg(wz8300), [])) → new_nubNub'112(wz82000, wz821, wz8300)
new_nubNub'10(wz1011, wz1012, wz1013, Pos(Zero), wz1015) → new_nubNub'0(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'113(wz1017, wz1018, wz1019, Pos(Succ(wz102000)), :(wz10210, wz10211)) → new_nubNub'113(wz1017, wz1018, wz1019, wz10210, wz10211)
new_nubNub'115(Neg(Zero), :(Neg(Zero), wz311)) → new_nubNub'16(wz311, :(Neg(Zero), []), [])
new_nubNub'11(wz1006, wz1007, wz1008, :(Neg(Succ(wz1009000)), wz10091)) → new_nubNub'14(wz1006, wz1007, wz1008, wz1006, wz1009000, wz10091)
new_nubNub'(:(Pos(Succ(wz31000)), :(Pos(Zero), wz3111)), Neg(wz300)) → new_nubNub'10(wz3111, wz31000, :(Neg(wz300), []), Neg(wz300), [])
new_nubNub'123(wz971, wz972, wz973, []) → new_nubNub'0(wz972, :(Pos(Succ(wz971)), :(Pos(Zero), wz973)))
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, :(Pos(Zero), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, :(Neg(wz113600), wz11361)) → new_nubNub'18(wz1130, wz1131, wz1132, wz1133, wz11361)
new_nubNub'124(wz1011, wz1012, wz1013, []) → new_nubNub'13(wz1011, :(Pos(Succ(wz1012)), wz1013))
new_nubNub'115(Pos(wz300), :(Neg(Succ(wz31000)), wz311)) → new_nubNub'11(wz31000, wz311, :(Pos(wz300), []), [])
new_nubNub'11(wz1006, wz1007, wz1008, []) → new_nubNub'0(wz1007, :(Neg(Succ(wz1006)), wz1008))
new_nubNub'13(wz860, wz861) → new_nubNub'0(wz860, :(Pos(Zero), wz861))
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Zero, Zero, wz1109) → new_nubNub'0(wz1104, :(Neg(wz1105), wz1106))
new_nubNub'115(Pos(Zero), :(Pos(Succ(wz31000)), :(Pos(Succ(wz311000)), wz3111))) → new_nubNub'1(wz311000, wz3111, wz31000, :(Pos(Zero), []), wz311000, wz31000, :(Pos(Zero), []))
new_nubNub'114(wz1097, wz1098, wz1099, Neg(Zero), wz1101) → new_nubNub'16(wz1097, :(Neg(Succ(wz1098)), wz1099), wz1101)
new_nubNub'111(wz944, wz945, wz946, wz947, Neg(wz9480), []) → new_nubNub'0(wz945, :(Pos(Succ(wz944)), :(Neg(wz946), wz947)))
new_nubNub'126(wz1037, wz1038, wz1039, :(wz10410, wz10411)) → new_nubNub'12(wz1037, wz1038, wz1039, wz10410, wz10411)
new_nubNub'0(:(Neg(Zero), wz821), :(Pos(Succ(wz83000)), [])) → new_nubNub'15(wz821, wz83000, [])
new_nubNub'19(wz971, wz972, wz973, Pos(Succ(wz97400)), wz975) → new_nubNub'122(wz971, wz972, wz973, wz971, wz97400, wz975)
new_nubNub'0(:(Neg(Succ(wz82000)), wz821), :(Neg(Succ(wz83000)), wz831)) → new_nubNub'14(wz82000, wz821, :(Neg(Succ(wz83000)), wz831), wz82000, wz83000, wz831)
new_nubNub'126(wz1037, wz1038, wz1039, []) → new_nubNub'15(wz1037, wz1038, wz1039)
new_nubNub'12(wz1037, wz1038, wz1039, Pos(Succ(wz104000)), []) → new_nubNub'15(wz1037, wz1038, wz1039)
new_nubNub'10(wz1011, wz1012, wz1013, Pos(Succ(wz101400)), :(wz10150, wz10151)) → new_nubNub'10(wz1011, wz1012, wz1013, wz10150, wz10151)
new_nubNub'127(wz1103, wz1104, wz1105, wz1106, Succ(wz11070), Succ(wz11080), wz1109) → new_nubNub'127(wz1103, wz1104, wz1105, wz1106, wz11070, wz11080, wz1109)
new_nubNub'113(wz1017, wz1018, wz1019, Neg(Zero), wz1021) → new_nubNub'130(wz1017, wz1018, wz1019, wz1021)
new_nubNub'0(:(Neg(Zero), wz821), :(Pos(Zero), wz831)) → new_nubNub'16(wz821, :(Pos(Zero), wz831), wz831)
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Succ(wz311000)), wz3111)), Pos(Zero)) → new_nubNub'11(wz311000, wz3111, :(Pos(Succ(wz31000)), :(Pos(Zero), [])), :(Pos(Zero), []))
new_nubNub'11(wz1006, wz1007, wz1008, :(Pos(wz100900), wz10091)) → new_nubNub'11(wz1006, wz1007, wz1008, wz10091)
new_nubNub'130(wz1017, wz1018, wz1019, wz1021) → new_nubNub'0(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'113(wz1017, wz1018, wz1019, Pos(Succ(wz102000)), []) → new_nubNub'13(wz1017, :(Neg(Succ(wz1018)), wz1019))
new_nubNub'0(:(Pos(Zero), wz821), :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'10(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'115(Pos(Succ(wz3000)), :(Pos(Succ(wz31000)), wz311)) → new_nubNub'1(wz31000, wz311, wz3000, [], wz31000, wz3000, [])
new_nubNub'0(:(Neg(Zero), wz821), :(Pos(Succ(wz83000)), :(wz8310, wz8311))) → new_nubNub'12(wz821, wz83000, :(wz8310, wz8311), wz8310, wz8311)
new_nubNub'115(Neg(Zero), :(Neg(Succ(wz31000)), wz311)) → new_nubNub'11(wz31000, wz311, :(Neg(Zero), []), [])
new_nubNub'(:(Pos(Succ(wz31000)), :(Neg(Zero), wz3111)), Pos(Zero)) → new_nubNub'12(wz3111, wz31000, :(Pos(Zero), []), Pos(Zero), [])
new_nubNub'115(Neg(Succ(wz3000)), :(Neg(Succ(wz31000)), wz311)) → new_nubNub'14(wz31000, wz311, :(Neg(Succ(wz3000)), []), wz31000, wz3000, [])
new_nubNub'122(wz1123, wz1124, wz1125, Zero, Zero, wz1128) → new_nubNub'0(wz1124, :(Pos(Zero), wz1125))
new_nubNub'18(wz1130, wz1131, wz1132, wz1133, []) → new_nubNub'0(wz1131, :(Pos(Succ(wz1130)), :(Pos(Succ(wz1132)), wz1133)))

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: