H-Termination proof of /home/matraf/haskell/eval_FullyBlown

MAYBE 86.92 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/empty.hs
H-Termination of the given Haskell-Program with start terms could not be shown:

↳ HASKELL

  ↳ LR

mainModule Main

((enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int]) :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

Lambda Reductions:
The following Lambda expression

\(m,_)→m

is transformed to

m0 (m,_) = m

The following Lambda expression

\(_,r)→r

is transformed to

r0 (_,r) = r

The following Lambda expression

\(q,_)→q

is transformed to

q1 (q,_) = q

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

mainModule Main

((enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int]) :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

If Reductions:
The following If expression

if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero

is transformed to

primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y))

primDivNatS0 x y False = Zero

The following If expression

if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x

is transformed to

primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y)

primModNatS0 x y False = Succ x

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

mainModule Main

((enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int]) :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

Replaced joker patterns by fresh variables and removed binding patterns.
Binding Reductions:
The bind variable of the following binding Pattern

frac@(Double vy vz)

is replaced by the following term

Double vy vz

The bind variable of the following binding Pattern

frac@(Float ww wx)

is replaced by the following term

Float ww wx

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

mainModule Main

((enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int]) :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

Cond Reductions:
The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

The following Function with conditions

takeWhile p [] = []

takeWhile p (x : xs)

| p x

= x : takeWhile p xs

| otherwise

= []

is transformed to

takeWhile p [] = takeWhile3 p []

takeWhile p (x : xs) = takeWhile2 p (x : xs)

takeWhile1 p x xs True = x : takeWhile p xs

takeWhile1 p x xs False = takeWhile0 p x xs otherwise

takeWhile0 p x xs True = []

takeWhile2 p (x : xs) = takeWhile1 p x xs (p x)

takeWhile3 p [] = []

takeWhile3 xy xz = takeWhile2 xy xz

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

mainModule Main

((enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int]) :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

Let/Where Reductions:
The bindings of the following Let/Where expression

m

where

m = m0 vu6

m0 (m,vv) = m

vu6 = properFraction x

are unpacked to the following functions on top level

truncateM0 yu (m,vv) = m

truncateM yu = truncateM0 yu (truncateVu6 yu)

truncateVu6 yu = properFraction yu

The bindings of the following Let/Where expression

(fromIntegral q,r :% y)

where

q = q1 vu30

q1 (q,wz) = q

r = r0 vu30

r0 (xu,r) = r

vu30 = quotRem x y

are unpacked to the following functions on top level

properFractionQ yv yw = properFractionQ1 yv yw (properFractionVu30 yv yw)

properFractionR yv yw = properFractionR0 yv yw (properFractionVu30 yv yw)

properFractionQ1 yv yw (q,wz) = q

properFractionVu30 yv yw = quotRem yv yw

properFractionR0 yv yw (xu,r) = r

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

mainModule Main

((enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int]) :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                          ↳ Narrow

mainModule Main

(enumFromTo :: Ratio Int -> Ratio Int -> [Ratio Int])

module Main where

import qualified Prelude

Haskell To QDPs

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44[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (primQuotInt (Neg yx300) (Neg Zero)) (numericEnumFrom $! primQuotInt (Neg yx300) (Neg Zero) + fromInt (Pos (Succ Zero))) (not (primCmpInt (primQuotInt (Neg yx300) (Neg Zero)) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3];
45 -> 3763[label="",style="dashed", color="red", weight=0];
45[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Pos (primDivNatS yx300 (Succ yx3100))) (numericEnumFrom $! Pos (primDivNatS yx300 (Succ yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primDivNatS yx300 (Succ yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];45 -> 3764[label="",style="dashed", color="magenta", weight=3];
45 -> 3765[label="",style="dashed", color="magenta", weight=3];
45 -> 3766[label="",style="dashed", color="magenta", weight=3];
45 -> 3767[label="",style="dashed", color="magenta", weight=3];
45 -> 3768[label="",style="dashed", color="magenta", weight=3];
46[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (error []) (numericEnumFrom $! error [] + fromInt (Pos (Succ Zero))) (not (primCmpInt (error []) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="triangle"];46 -> 55[label="",style="solid", color="black", weight=3];
47[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS yx300 (Succ yx3100))) (numericEnumFrom $! Neg (primDivNatS yx300 (Succ yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS yx300 (Succ yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="burlywood",shape="triangle"];4582[label="yx300/Succ yx3000",fontsize=10,color="white",style="solid",shape="box"];47 -> 4582[label="",style="solid", color="burlywood", weight=9];
4582 -> 56[label="",style="solid", color="burlywood", weight=3];
4583[label="yx300/Zero",fontsize=10,color="white",style="solid",shape="box"];47 -> 4583[label="",style="solid", color="burlywood", weight=9];
4583 -> 57[label="",style="solid", color="burlywood", weight=3];
48 -> 46[label="",style="dashed", color="red", weight=0];
48[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (error []) (numericEnumFrom $! error [] + fromInt (Pos (Succ Zero))) (not (primCmpInt (error []) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];49 -> 47[label="",style="dashed", color="red", weight=0];
49[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS yx300 (Succ yx3100))) (numericEnumFrom $! Neg (primDivNatS yx300 (Succ yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS yx300 (Succ yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];49 -> 58[label="",style="dashed", color="magenta", weight=3];
49 -> 59[label="",style="dashed", color="magenta", weight=3];
50 -> 46[label="",style="dashed", color="red", weight=0];
50[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (error []) (numericEnumFrom $! error [] + fromInt (Pos (Succ Zero))) (not (primCmpInt (error []) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];51 -> 3763[label="",style="dashed", color="red", weight=0];
51[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Pos (primDivNatS yx300 (Succ yx3100))) (numericEnumFrom $! Pos (primDivNatS yx300 (Succ yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Pos (primDivNatS yx300 (Succ yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];51 -> 3769[label="",style="dashed", color="magenta", weight=3];
51 -> 3770[label="",style="dashed", color="magenta", weight=3];
51 -> 3771[label="",style="dashed", color="magenta", weight=3];
51 -> 3772[label="",style="dashed", color="magenta", weight=3];
51 -> 3773[label="",style="dashed", color="magenta", weight=3];
52 -> 46[label="",style="dashed", color="red", weight=0];
52[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (error []) (numericEnumFrom $! error [] + fromInt (Pos (Succ Zero))) (not (primCmpInt (error []) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];3764 -> 1688[label="",style="dashed", color="red", weight=0];
3764[label="primDivNatS yx300 (Succ yx3100)",fontsize=16,color="magenta"];3764 -> 3999[label="",style="dashed", color="magenta", weight=3];
3764 -> 4000[label="",style="dashed", color="magenta", weight=3];
3765 -> 576[label="",style="dashed", color="red", weight=0];
3765[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3765 -> 4001[label="",style="dashed", color="magenta", weight=3];
3766 -> 460[label="",style="dashed", color="red", weight=0];
3766[label="fromEnum yx4",fontsize=16,color="magenta"];3766 -> 4002[label="",style="dashed", color="magenta", weight=3];
3767 -> 1688[label="",style="dashed", color="red", weight=0];
3767[label="primDivNatS yx300 (Succ yx3100)",fontsize=16,color="magenta"];3767 -> 4003[label="",style="dashed", color="magenta", weight=3];
3767 -> 4004[label="",style="dashed", color="magenta", weight=3];
3768 -> 1688[label="",style="dashed", color="red", weight=0];
3768[label="primDivNatS yx300 (Succ yx3100)",fontsize=16,color="magenta"];3768 -> 4005[label="",style="dashed", color="magenta", weight=3];
3768 -> 4006[label="",style="dashed", color="magenta", weight=3];
3763[label="map toEnum (takeWhile1 (flip (<=) yx199) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos yx251) yx199 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4594[label="yx251/Succ yx2510",fontsize=10,color="white",style="solid",shape="box"];3763 -> 4594[label="",style="solid", color="burlywood", weight=9];
4594 -> 4007[label="",style="solid", color="burlywood", weight=3];
4595[label="yx251/Zero",fontsize=10,color="white",style="solid",shape="box"];3763 -> 4595[label="",style="solid", color="burlywood", weight=9];
4595 -> 4008[label="",style="solid", color="burlywood", weight=3];
55[label="error []",fontsize=16,color="red",shape="box"];56[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS (Succ yx3000) (Succ yx3100))) (numericEnumFrom $! Neg (primDivNatS (Succ yx3000) (Succ yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS (Succ yx3000) (Succ yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];56 -> 64[label="",style="solid", color="black", weight=3];
57[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS Zero (Succ yx3100))) (numericEnumFrom $! Neg (primDivNatS Zero (Succ yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS Zero (Succ yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];57 -> 65[label="",style="solid", color="black", weight=3];
58[label="yx3100",fontsize=16,color="green",shape="box"];59[label="yx300",fontsize=16,color="green",shape="box"];3769 -> 1688[label="",style="dashed", color="red", weight=0];
3769[label="primDivNatS yx300 (Succ yx3100)",fontsize=16,color="magenta"];3769 -> 4009[label="",style="dashed", color="magenta", weight=3];
3769 -> 4010[label="",style="dashed", color="magenta", weight=3];
3770 -> 576[label="",style="dashed", color="red", weight=0];
3770[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3770 -> 4011[label="",style="dashed", color="magenta", weight=3];
3771 -> 460[label="",style="dashed", color="red", weight=0];
3771[label="fromEnum yx4",fontsize=16,color="magenta"];3771 -> 4012[label="",style="dashed", color="magenta", weight=3];
3772 -> 1688[label="",style="dashed", color="red", weight=0];
3772[label="primDivNatS yx300 (Succ yx3100)",fontsize=16,color="magenta"];3772 -> 4013[label="",style="dashed", color="magenta", weight=3];
3772 -> 4014[label="",style="dashed", color="magenta", weight=3];
3773 -> 1688[label="",style="dashed", color="red", weight=0];
3773[label="primDivNatS yx300 (Succ yx3100)",fontsize=16,color="magenta"];3773 -> 4015[label="",style="dashed", color="magenta", weight=3];
3773 -> 4016[label="",style="dashed", color="magenta", weight=3];
3999[label="yx300",fontsize=16,color="green",shape="box"];4000[label="yx3100",fontsize=16,color="green",shape="box"];1688[label="primDivNatS yx400 (Succ yx4100)",fontsize=16,color="burlywood",shape="triangle"];4601[label="yx400/Succ yx4000",fontsize=10,color="white",style="solid",shape="box"];1688 -> 4601[label="",style="solid", color="burlywood", weight=9];
4601 -> 1725[label="",style="solid", color="burlywood", weight=3];
4602[label="yx400/Zero",fontsize=10,color="white",style="solid",shape="box"];1688 -> 4602[label="",style="solid", color="burlywood", weight=9];
4602 -> 1726[label="",style="solid", color="burlywood", weight=3];
4001[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];576[label="fromInt yx8",fontsize=16,color="black",shape="triangle"];576 -> 650[label="",style="solid", color="black", weight=3];
4002[label="yx4",fontsize=16,color="green",shape="box"];460[label="fromEnum yx7\n  Integral a",fontsize=16,color="black",shape="triangle"];460 -> 519[label="",style="solid", color="black", weight=3];
4003[label="yx300",fontsize=16,color="green",shape="box"];4004[label="yx3100",fontsize=16,color="green",shape="box"];4005[label="yx300",fontsize=16,color="green",shape="box"];4006[label="yx3100",fontsize=16,color="green",shape="box"];4007[label="map toEnum (takeWhile1 (flip (<=) yx199) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos (Succ yx2510)) yx199 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4603[label="yx199/Pos yx1990",fontsize=10,color="white",style="solid",shape="box"];4007 -> 4603[label="",style="solid", color="burlywood", weight=9];
4603 -> 4027[label="",style="solid", color="burlywood", weight=3];
4604[label="yx199/Neg yx1990",fontsize=10,color="white",style="solid",shape="box"];4007 -> 4604[label="",style="solid", color="burlywood", weight=9];
4604 -> 4028[label="",style="solid", color="burlywood", weight=3];
4008[label="map toEnum (takeWhile1 (flip (<=) yx199) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) yx199 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4605[label="yx199/Pos yx1990",fontsize=10,color="white",style="solid",shape="box"];4008 -> 4605[label="",style="solid", color="burlywood", weight=9];
4605 -> 4029[label="",style="solid", color="burlywood", weight=3];
4606[label="yx199/Neg yx1990",fontsize=10,color="white",style="solid",shape="box"];4008 -> 4606[label="",style="solid", color="burlywood", weight=9];
4606 -> 4030[label="",style="solid", color="burlywood", weight=3];
64[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 yx3000 yx3100 (primGEqNatS yx3000 yx3100))) (numericEnumFrom $! Neg (primDivNatS0 yx3000 yx3100 (primGEqNatS yx3000 yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 yx3000 yx3100 (primGEqNatS yx3000 yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="burlywood",shape="box"];4607[label="yx3000/Succ yx30000",fontsize=10,color="white",style="solid",shape="box"];64 -> 4607[label="",style="solid", color="burlywood", weight=9];
4607 -> 69[label="",style="solid", color="burlywood", weight=3];
4608[label="yx3000/Zero",fontsize=10,color="white",style="solid",shape="box"];64 -> 4608[label="",style="solid", color="burlywood", weight=9];
4608 -> 70[label="",style="solid", color="burlywood", weight=3];
65[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="triangle"];65 -> 71[label="",style="solid", color="black", weight=3];
4009[label="yx300",fontsize=16,color="green",shape="box"];4010[label="yx3100",fontsize=16,color="green",shape="box"];4011[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];4012[label="yx4",fontsize=16,color="green",shape="box"];4013[label="yx300",fontsize=16,color="green",shape="box"];4014[label="yx3100",fontsize=16,color="green",shape="box"];4015[label="yx300",fontsize=16,color="green",shape="box"];4016[label="yx3100",fontsize=16,color="green",shape="box"];1725[label="primDivNatS (Succ yx4000) (Succ yx4100)",fontsize=16,color="black",shape="box"];1725 -> 1747[label="",style="solid", color="black", weight=3];
1726[label="primDivNatS Zero (Succ yx4100)",fontsize=16,color="black",shape="box"];1726 -> 1748[label="",style="solid", color="black", weight=3];
650[label="yx8",fontsize=16,color="green",shape="box"];519[label="truncate yx7\n  Integral a",fontsize=16,color="black",shape="box"];519 -> 578[label="",style="solid", color="black", weight=3];
4027[label="map toEnum (takeWhile1 (flip (<=) (Pos yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos (Succ yx2510)) (Pos yx1990) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4027 -> 4046[label="",style="solid", color="black", weight=3];
4028[label="map toEnum (takeWhile1 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos (Succ yx2510)) (Neg yx1990) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4028 -> 4047[label="",style="solid", color="black", weight=3];
4029[label="map toEnum (takeWhile1 (flip (<=) (Pos yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) (Pos yx1990) == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4609[label="yx1990/Succ yx19900",fontsize=10,color="white",style="solid",shape="box"];4029 -> 4609[label="",style="solid", color="burlywood", weight=9];
4609 -> 4048[label="",style="solid", color="burlywood", weight=3];
4610[label="yx1990/Zero",fontsize=10,color="white",style="solid",shape="box"];4029 -> 4610[label="",style="solid", color="burlywood", weight=9];
4610 -> 4049[label="",style="solid", color="burlywood", weight=3];
4030[label="map toEnum (takeWhile1 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) (Neg yx1990) == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4611[label="yx1990/Succ yx19900",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4611[label="",style="solid", color="burlywood", weight=9];
4611 -> 4050[label="",style="solid", color="burlywood", weight=3];
4612[label="yx1990/Zero",fontsize=10,color="white",style="solid",shape="box"];4030 -> 4612[label="",style="solid", color="burlywood", weight=9];
4612 -> 4051[label="",style="solid", color="burlywood", weight=3];
69[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 (Succ yx30000) yx3100 (primGEqNatS (Succ yx30000) yx3100))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx30000) yx3100 (primGEqNatS (Succ yx30000) yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 (Succ yx30000) yx3100 (primGEqNatS (Succ yx30000) yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="burlywood",shape="box"];4613[label="yx3100/Succ yx31000",fontsize=10,color="white",style="solid",shape="box"];69 -> 4613[label="",style="solid", color="burlywood", weight=9];
4613 -> 77[label="",style="solid", color="burlywood", weight=3];
4614[label="yx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];69 -> 4614[label="",style="solid", color="burlywood", weight=9];
4614 -> 78[label="",style="solid", color="burlywood", weight=3];
70[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 Zero yx3100 (primGEqNatS Zero yx3100))) (numericEnumFrom $! Neg (primDivNatS0 Zero yx3100 (primGEqNatS Zero yx3100)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 Zero yx3100 (primGEqNatS Zero yx3100))) (fromEnum yx4) == GT)))",fontsize=16,color="burlywood",shape="box"];4615[label="yx3100/Succ yx31000",fontsize=10,color="white",style="solid",shape="box"];70 -> 4615[label="",style="solid", color="burlywood", weight=9];
4615 -> 79[label="",style="solid", color="burlywood", weight=3];
4616[label="yx3100/Zero",fontsize=10,color="white",style="solid",shape="box"];70 -> 4616[label="",style="solid", color="burlywood", weight=9];
4616 -> 80[label="",style="solid", color="burlywood", weight=3];
71[label="map toEnum (takeWhile1 (flip (<=) (truncate yx4)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (truncate yx4) == GT)))",fontsize=16,color="black",shape="box"];71 -> 81[label="",style="solid", color="black", weight=3];
1747 -> 1151[label="",style="dashed", color="red", weight=0];
1747[label="primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)",fontsize=16,color="magenta"];1748[label="Zero",fontsize=16,color="green",shape="box"];578[label="truncateM yx7\n  Integral a",fontsize=16,color="black",shape="box"];578 -> 652[label="",style="solid", color="black", weight=3];
4046[label="map toEnum (takeWhile1 (flip (<=) (Pos yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpNat (Succ yx2510) yx1990 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4618[label="yx1990/Succ yx19900",fontsize=10,color="white",style="solid",shape="box"];4046 -> 4618[label="",style="solid", color="burlywood", weight=9];
4618 -> 4054[label="",style="solid", color="burlywood", weight=3];
4619[label="yx1990/Zero",fontsize=10,color="white",style="solid",shape="box"];4046 -> 4619[label="",style="solid", color="burlywood", weight=9];
4619 -> 4055[label="",style="solid", color="burlywood", weight=3];
4047[label="map toEnum (takeWhile1 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (GT == GT)))\n  Enum a",fontsize=16,color="black",shape="triangle"];4047 -> 4056[label="",style="solid", color="black", weight=3];
4048[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx19900))) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) (Pos (Succ yx19900)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4048 -> 4057[label="",style="solid", color="black", weight=3];
4049[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) (Pos Zero) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4049 -> 4058[label="",style="solid", color="black", weight=3];
4050[label="map toEnum (takeWhile1 (flip (<=) (Neg (Succ yx19900))) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) (Neg (Succ yx19900)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4050 -> 4059[label="",style="solid", color="black", weight=3];
4051[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpInt (Pos Zero) (Neg Zero) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4051 -> 4060[label="",style="solid", color="black", weight=3];
77[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 (Succ yx30000) (Succ yx31000) (primGEqNatS (Succ yx30000) (Succ yx31000)))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx30000) (Succ yx31000) (primGEqNatS (Succ yx30000) (Succ yx31000))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 (Succ yx30000) (Succ yx31000) (primGEqNatS (Succ yx30000) (Succ yx31000)))) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];77 -> 87[label="",style="solid", color="black", weight=3];
78[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 (Succ yx30000) Zero (primGEqNatS (Succ yx30000) Zero))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx30000) Zero (primGEqNatS (Succ yx30000) Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 (Succ yx30000) Zero (primGEqNatS (Succ yx30000) Zero))) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];78 -> 88[label="",style="solid", color="black", weight=3];
79[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 Zero (Succ yx31000) (primGEqNatS Zero (Succ yx31000)))) (numericEnumFrom $! Neg (primDivNatS0 Zero (Succ yx31000) (primGEqNatS Zero (Succ yx31000))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 Zero (Succ yx31000) (primGEqNatS Zero (Succ yx31000)))) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];79 -> 89[label="",style="solid", color="black", weight=3];
80[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))) (numericEnumFrom $! Neg (primDivNatS0 Zero Zero (primGEqNatS Zero Zero)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 Zero Zero (primGEqNatS Zero Zero))) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];80 -> 90[label="",style="solid", color="black", weight=3];
81[label="map toEnum (takeWhile1 (flip (<=) (truncateM yx4)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (truncateM yx4) == GT)))",fontsize=16,color="black",shape="box"];81 -> 91[label="",style="solid", color="black", weight=3];
1151[label="primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)",fontsize=16,color="burlywood",shape="triangle"];4620[label="yx4000/Succ yx40000",fontsize=10,color="white",style="solid",shape="box"];1151 -> 4620[label="",style="solid", color="burlywood", weight=9];
4620 -> 1276[label="",style="solid", color="burlywood", weight=3];
4621[label="yx4000/Zero",fontsize=10,color="white",style="solid",shape="box"];1151 -> 4621[label="",style="solid", color="burlywood", weight=9];
4621 -> 1277[label="",style="solid", color="burlywood", weight=3];
652[label="truncateM0 yx7 (truncateVu6 yx7)\n  Integral a",fontsize=16,color="black",shape="box"];652 -> 821[label="",style="solid", color="black", weight=3];
4054[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx19900))) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpNat (Succ yx2510) (Succ yx19900) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4054 -> 4065[label="",style="solid", color="black", weight=3];
4055[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpNat (Succ yx2510) Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4055 -> 4066[label="",style="solid", color="black", weight=3];
4056[label="map toEnum (takeWhile1 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not True))\n  Enum a",fontsize=16,color="black",shape="box"];4056 -> 4067[label="",style="solid", color="black", weight=3];
4057 -> 4430[label="",style="dashed", color="red", weight=0];
4057[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx19900))) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpNat Zero (Succ yx19900) == GT)))\n  Enum a",fontsize=16,color="magenta"];4057 -> 4431[label="",style="dashed", color="magenta", weight=3];
4057 -> 4432[label="",style="dashed", color="magenta", weight=3];
4057 -> 4433[label="",style="dashed", color="magenta", weight=3];
4057 -> 4434[label="",style="dashed", color="magenta", weight=3];
4057 -> 4435[label="",style="dashed", color="magenta", weight=3];
4057 -> 4436[label="",style="dashed", color="magenta", weight=3];
4058[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (EQ == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4058 -> 4069[label="",style="solid", color="black", weight=3];
4059 -> 4047[label="",style="dashed", color="red", weight=0];
4059[label="map toEnum (takeWhile1 (flip (<=) (Neg (Succ yx19900))) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (GT == GT)))\n  Enum a",fontsize=16,color="magenta"];4059 -> 4070[label="",style="dashed", color="magenta", weight=3];
4060[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (EQ == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4060 -> 4071[label="",style="solid", color="black", weight=3];
87 -> 2236[label="",style="dashed", color="red", weight=0];
87[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 (Succ yx30000) (Succ yx31000) (primGEqNatS yx30000 yx31000))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx30000) (Succ yx31000) (primGEqNatS yx30000 yx31000)) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 (Succ yx30000) (Succ yx31000) (primGEqNatS yx30000 yx31000))) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];87 -> 2237[label="",style="dashed", color="magenta", weight=3];
87 -> 2238[label="",style="dashed", color="magenta", weight=3];
87 -> 2239[label="",style="dashed", color="magenta", weight=3];
87 -> 2240[label="",style="dashed", color="magenta", weight=3];
87 -> 2241[label="",style="dashed", color="magenta", weight=3];
87 -> 2242[label="",style="dashed", color="magenta", weight=3];
87 -> 2243[label="",style="dashed", color="magenta", weight=3];
88[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 (Succ yx30000) Zero True)) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx30000) Zero True) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 (Succ yx30000) Zero True)) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];88 -> 100[label="",style="solid", color="black", weight=3];
89[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 Zero (Succ yx31000) False)) (numericEnumFrom $! Neg (primDivNatS0 Zero (Succ yx31000) False) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 Zero (Succ yx31000) False)) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];89 -> 101[label="",style="solid", color="black", weight=3];
90[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (primDivNatS0 Zero Zero True)) (numericEnumFrom $! Neg (primDivNatS0 Zero Zero True) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (primDivNatS0 Zero Zero True)) (fromEnum yx4) == GT)))",fontsize=16,color="black",shape="box"];90 -> 102[label="",style="solid", color="black", weight=3];
91[label="map toEnum (takeWhile1 (flip (<=) (truncateM0 yx4 (truncateVu6 yx4))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (truncateM0 yx4 (truncateVu6 yx4)) == GT)))",fontsize=16,color="black",shape="box"];91 -> 103[label="",style="solid", color="black", weight=3];
1276[label="primDivNatS0 (Succ yx40000) yx4100 (primGEqNatS (Succ yx40000) yx4100)",fontsize=16,color="burlywood",shape="box"];4625[label="yx4100/Succ yx41000",fontsize=10,color="white",style="solid",shape="box"];1276 -> 4625[label="",style="solid", color="burlywood", weight=9];
4625 -> 1405[label="",style="solid", color="burlywood", weight=3];
4626[label="yx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];1276 -> 4626[label="",style="solid", color="burlywood", weight=9];
4626 -> 1406[label="",style="solid", color="burlywood", weight=3];
1277[label="primDivNatS0 Zero yx4100 (primGEqNatS Zero yx4100)",fontsize=16,color="burlywood",shape="box"];4627[label="yx4100/Succ yx41000",fontsize=10,color="white",style="solid",shape="box"];1277 -> 4627[label="",style="solid", color="burlywood", weight=9];
4627 -> 1407[label="",style="solid", color="burlywood", weight=3];
4628[label="yx4100/Zero",fontsize=10,color="white",style="solid",shape="box"];1277 -> 4628[label="",style="solid", color="burlywood", weight=9];
4628 -> 1408[label="",style="solid", color="burlywood", weight=3];
821[label="truncateM0 yx7 (properFraction yx7)\n  Integral a",fontsize=16,color="burlywood",shape="box"];4629[label="yx7/yx70 :% yx71",fontsize=10,color="white",style="solid",shape="box"];821 -> 4629[label="",style="solid", color="burlywood", weight=9];
4629 -> 1033[label="",style="solid", color="burlywood", weight=3];
4065 -> 4430[label="",style="dashed", color="red", weight=0];
4065[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx19900))) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (primCmpNat yx2510 yx19900 == GT)))\n  Enum a",fontsize=16,color="magenta"];4065 -> 4437[label="",style="dashed", color="magenta", weight=3];
4065 -> 4438[label="",style="dashed", color="magenta", weight=3];
4065 -> 4439[label="",style="dashed", color="magenta", weight=3];
4065 -> 4440[label="",style="dashed", color="magenta", weight=3];
4065 -> 4441[label="",style="dashed", color="magenta", weight=3];
4065 -> 4442[label="",style="dashed", color="magenta", weight=3];
4066[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not (GT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4066 -> 4076[label="",style="solid", color="black", weight=3];
4067[label="map toEnum (takeWhile1 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) False)\n  Enum a",fontsize=16,color="black",shape="box"];4067 -> 4077[label="",style="solid", color="black", weight=3];
4431[label="yx237",fontsize=16,color="green",shape="box"];4432[label="yx250",fontsize=16,color="green",shape="box"];4433[label="yx19900",fontsize=16,color="green",shape="box"];4434[label="Succ yx19900",fontsize=16,color="green",shape="box"];4435[label="Zero",fontsize=16,color="green",shape="box"];4436[label="yx249",fontsize=16,color="green",shape="box"];4430[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat yx276 yx277 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4631[label="yx276/Succ yx2760",fontsize=10,color="white",style="solid",shape="box"];4430 -> 4631[label="",style="solid", color="burlywood", weight=9];
4631 -> 4491[label="",style="solid", color="burlywood", weight=3];
4632[label="yx276/Zero",fontsize=10,color="white",style="solid",shape="box"];4430 -> 4632[label="",style="solid", color="burlywood", weight=9];
4632 -> 4492[label="",style="solid", color="burlywood", weight=3];
4069[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not False))\n  Enum a",fontsize=16,color="black",shape="box"];4069 -> 4079[label="",style="solid", color="black", weight=3];
4070[label="Succ yx19900",fontsize=16,color="green",shape="box"];4071[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not False))\n  Enum a",fontsize=16,color="black",shape="box"];4071 -> 4080[label="",style="solid", color="black", weight=3];
2237[label="yx31000",fontsize=16,color="green",shape="box"];2238[label="yx30000",fontsize=16,color="green",shape="box"];2239 -> 460[label="",style="dashed", color="red", weight=0];
2239[label="fromEnum yx4",fontsize=16,color="magenta"];2239 -> 2314[label="",style="dashed", color="magenta", weight=3];
2240 -> 576[label="",style="dashed", color="red", weight=0];
2240[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];2240 -> 2315[label="",style="dashed", color="magenta", weight=3];
2241[label="yx30000",fontsize=16,color="green",shape="box"];2242 -> 460[label="",style="dashed", color="red", weight=0];
2242[label="fromEnum yx4",fontsize=16,color="magenta"];2242 -> 2316[label="",style="dashed", color="magenta", weight=3];
2243[label="yx31000",fontsize=16,color="green",shape="box"];2236[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS yx210 yx211))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS yx210 yx211)) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS yx210 yx211))) yx213 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4636[label="yx210/Succ yx2100",fontsize=10,color="white",style="solid",shape="box"];2236 -> 4636[label="",style="solid", color="burlywood", weight=9];
4636 -> 2317[label="",style="solid", color="burlywood", weight=3];
4637[label="yx210/Zero",fontsize=10,color="white",style="solid",shape="box"];2236 -> 4637[label="",style="solid", color="burlywood", weight=9];
4637 -> 2318[label="",style="solid", color="burlywood", weight=3];
100 -> 2774[label="",style="dashed", color="red", weight=0];
100[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (Succ (primDivNatS (primMinusNatS (Succ yx30000) Zero) (Succ Zero)))) (numericEnumFrom $! Neg (Succ (primDivNatS (primMinusNatS (Succ yx30000) Zero) (Succ Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (Succ (primDivNatS (primMinusNatS (Succ yx30000) Zero) (Succ Zero)))) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];100 -> 2775[label="",style="dashed", color="magenta", weight=3];
100 -> 2776[label="",style="dashed", color="magenta", weight=3];
100 -> 2777[label="",style="dashed", color="magenta", weight=3];
100 -> 2778[label="",style="dashed", color="magenta", weight=3];
100 -> 2779[label="",style="dashed", color="magenta", weight=3];
100 -> 2780[label="",style="dashed", color="magenta", weight=3];
101 -> 65[label="",style="dashed", color="red", weight=0];
101[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];102 -> 2774[label="",style="dashed", color="red", weight=0];
102[label="map toEnum (takeWhile1 (flip (<=) (fromEnum yx4)) (Neg (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))) (numericEnumFrom $! Neg (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))) + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg (Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero)))) (fromEnum yx4) == GT)))",fontsize=16,color="magenta"];102 -> 2781[label="",style="dashed", color="magenta", weight=3];
102 -> 2782[label="",style="dashed", color="magenta", weight=3];
102 -> 2783[label="",style="dashed", color="magenta", weight=3];
102 -> 2784[label="",style="dashed", color="magenta", weight=3];
102 -> 2785[label="",style="dashed", color="magenta", weight=3];
102 -> 2786[label="",style="dashed", color="magenta", weight=3];
103[label="map toEnum (takeWhile1 (flip (<=) (truncateM0 yx4 (properFraction yx4))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (truncateM0 yx4 (properFraction yx4)) == GT)))",fontsize=16,color="burlywood",shape="box"];4641[label="yx4/yx40 :% yx41",fontsize=10,color="white",style="solid",shape="box"];103 -> 4641[label="",style="solid", color="burlywood", weight=9];
4641 -> 117[label="",style="solid", color="burlywood", weight=3];
1405[label="primDivNatS0 (Succ yx40000) (Succ yx41000) (primGEqNatS (Succ yx40000) (Succ yx41000))",fontsize=16,color="black",shape="box"];1405 -> 1541[label="",style="solid", color="black", weight=3];
1406[label="primDivNatS0 (Succ yx40000) Zero (primGEqNatS (Succ yx40000) Zero)",fontsize=16,color="black",shape="box"];1406 -> 1542[label="",style="solid", color="black", weight=3];
1407[label="primDivNatS0 Zero (Succ yx41000) (primGEqNatS Zero (Succ yx41000))",fontsize=16,color="black",shape="box"];1407 -> 1543[label="",style="solid", color="black", weight=3];
1408[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1408 -> 1544[label="",style="solid", color="black", weight=3];
1033[label="truncateM0 (yx70 :% yx71) (properFraction (yx70 :% yx71))\n  Integral a",fontsize=16,color="black",shape="box"];1033 -> 1174[label="",style="solid", color="black", weight=3];
4437[label="yx237",fontsize=16,color="green",shape="box"];4438[label="yx250",fontsize=16,color="green",shape="box"];4439[label="yx19900",fontsize=16,color="green",shape="box"];4440[label="yx19900",fontsize=16,color="green",shape="box"];4441[label="yx2510",fontsize=16,color="green",shape="box"];4442[label="yx249",fontsize=16,color="green",shape="box"];4076[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) (not True))\n  Enum a",fontsize=16,color="black",shape="box"];4076 -> 4085[label="",style="solid", color="black", weight=3];
4077[label="map toEnum (takeWhile0 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) otherwise)\n  Enum a",fontsize=16,color="black",shape="box"];4077 -> 4086[label="",style="solid", color="black", weight=3];
4491[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat (Succ yx2760) yx277 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4642[label="yx277/Succ yx2770",fontsize=10,color="white",style="solid",shape="box"];4491 -> 4642[label="",style="solid", color="burlywood", weight=9];
4642 -> 4493[label="",style="solid", color="burlywood", weight=3];
4643[label="yx277/Zero",fontsize=10,color="white",style="solid",shape="box"];4491 -> 4643[label="",style="solid", color="burlywood", weight=9];
4643 -> 4494[label="",style="solid", color="burlywood", weight=3];
4492[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat Zero yx277 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4644[label="yx277/Succ yx2770",fontsize=10,color="white",style="solid",shape="box"];4492 -> 4644[label="",style="solid", color="burlywood", weight=9];
4644 -> 4495[label="",style="solid", color="burlywood", weight=3];
4645[label="yx277/Zero",fontsize=10,color="white",style="solid",shape="box"];4492 -> 4645[label="",style="solid", color="burlywood", weight=9];
4645 -> 4496[label="",style="solid", color="burlywood", weight=3];
4079[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) True)\n  Enum a",fontsize=16,color="black",shape="box"];4079 -> 4088[label="",style="solid", color="black", weight=3];
4080[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) True)\n  Enum a",fontsize=16,color="black",shape="box"];4080 -> 4089[label="",style="solid", color="black", weight=3];
2314[label="yx4",fontsize=16,color="green",shape="box"];2315[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];2316[label="yx4",fontsize=16,color="green",shape="box"];2317[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) yx211))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) yx211)) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) yx211))) yx213 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4646[label="yx211/Succ yx2110",fontsize=10,color="white",style="solid",shape="box"];2317 -> 4646[label="",style="solid", color="burlywood", weight=9];
4646 -> 2347[label="",style="solid", color="burlywood", weight=3];
4647[label="yx211/Zero",fontsize=10,color="white",style="solid",shape="box"];2317 -> 4647[label="",style="solid", color="burlywood", weight=9];
4647 -> 2348[label="",style="solid", color="burlywood", weight=3];
2318[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero yx211))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero yx211)) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero yx211))) yx213 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4648[label="yx211/Succ yx2110",fontsize=10,color="white",style="solid",shape="box"];2318 -> 4648[label="",style="solid", color="burlywood", weight=9];
4648 -> 2349[label="",style="solid", color="burlywood", weight=3];
4649[label="yx211/Zero",fontsize=10,color="white",style="solid",shape="box"];2318 -> 4649[label="",style="solid", color="burlywood", weight=9];
4649 -> 2350[label="",style="solid", color="burlywood", weight=3];
2775 -> 1688[label="",style="dashed", color="red", weight=0];
2775[label="primDivNatS (primMinusNatS (Succ yx30000) Zero) (Succ Zero)",fontsize=16,color="magenta"];2775 -> 2994[label="",style="dashed", color="magenta", weight=3];
2775 -> 2995[label="",style="dashed", color="magenta", weight=3];
2776 -> 1688[label="",style="dashed", color="red", weight=0];
2776[label="primDivNatS (primMinusNatS (Succ yx30000) Zero) (Succ Zero)",fontsize=16,color="magenta"];2776 -> 2996[label="",style="dashed", color="magenta", weight=3];
2776 -> 2997[label="",style="dashed", color="magenta", weight=3];
2777 -> 460[label="",style="dashed", color="red", weight=0];
2777[label="fromEnum yx4",fontsize=16,color="magenta"];2777 -> 2998[label="",style="dashed", color="magenta", weight=3];
2778 -> 576[label="",style="dashed", color="red", weight=0];
2778[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];2778 -> 2999[label="",style="dashed", color="magenta", weight=3];
2779 -> 1688[label="",style="dashed", color="red", weight=0];
2779[label="primDivNatS (primMinusNatS (Succ yx30000) Zero) (Succ Zero)",fontsize=16,color="magenta"];2779 -> 3000[label="",style="dashed", color="magenta", weight=3];
2779 -> 3001[label="",style="dashed", color="magenta", weight=3];
2780 -> 460[label="",style="dashed", color="red", weight=0];
2780[label="fromEnum yx4",fontsize=16,color="magenta"];2780 -> 3002[label="",style="dashed", color="magenta", weight=3];
2774[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpInt (Neg (Succ yx219)) yx213 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4656[label="yx213/Pos yx2130",fontsize=10,color="white",style="solid",shape="box"];2774 -> 4656[label="",style="solid", color="burlywood", weight=9];
4656 -> 3003[label="",style="solid", color="burlywood", weight=3];
4657[label="yx213/Neg yx2130",fontsize=10,color="white",style="solid",shape="box"];2774 -> 4657[label="",style="solid", color="burlywood", weight=9];
4657 -> 3004[label="",style="solid", color="burlywood", weight=3];
2781 -> 1688[label="",style="dashed", color="red", weight=0];
2781[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2781 -> 3005[label="",style="dashed", color="magenta", weight=3];
2781 -> 3006[label="",style="dashed", color="magenta", weight=3];
2782 -> 1688[label="",style="dashed", color="red", weight=0];
2782[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2782 -> 3007[label="",style="dashed", color="magenta", weight=3];
2782 -> 3008[label="",style="dashed", color="magenta", weight=3];
2783 -> 460[label="",style="dashed", color="red", weight=0];
2783[label="fromEnum yx4",fontsize=16,color="magenta"];2783 -> 3009[label="",style="dashed", color="magenta", weight=3];
2784 -> 576[label="",style="dashed", color="red", weight=0];
2784[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];2784 -> 3010[label="",style="dashed", color="magenta", weight=3];
2785 -> 1688[label="",style="dashed", color="red", weight=0];
2785[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2785 -> 3011[label="",style="dashed", color="magenta", weight=3];
2785 -> 3012[label="",style="dashed", color="magenta", weight=3];
2786 -> 460[label="",style="dashed", color="red", weight=0];
2786[label="fromEnum yx4",fontsize=16,color="magenta"];2786 -> 3013[label="",style="dashed", color="magenta", weight=3];
117[label="map toEnum (takeWhile1 (flip (<=) (truncateM0 (yx40 :% yx41) (properFraction (yx40 :% yx41)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (truncateM0 (yx40 :% yx41) (properFraction (yx40 :% yx41))) == GT)))",fontsize=16,color="black",shape="box"];117 -> 131[label="",style="solid", color="black", weight=3];
1541 -> 3702[label="",style="dashed", color="red", weight=0];
1541[label="primDivNatS0 (Succ yx40000) (Succ yx41000) (primGEqNatS yx40000 yx41000)",fontsize=16,color="magenta"];1541 -> 3703[label="",style="dashed", color="magenta", weight=3];
1541 -> 3704[label="",style="dashed", color="magenta", weight=3];
1541 -> 3705[label="",style="dashed", color="magenta", weight=3];
1541 -> 3706[label="",style="dashed", color="magenta", weight=3];
1542[label="primDivNatS0 (Succ yx40000) Zero True",fontsize=16,color="black",shape="box"];1542 -> 1755[label="",style="solid", color="black", weight=3];
1543[label="primDivNatS0 Zero (Succ yx41000) False",fontsize=16,color="black",shape="box"];1543 -> 1756[label="",style="solid", color="black", weight=3];
1544[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1544 -> 1757[label="",style="solid", color="black", weight=3];
1174[label="truncateM0 (yx70 :% yx71) (fromIntegral (properFractionQ yx70 yx71),properFractionR yx70 yx71 :% yx71)\n  Integral a",fontsize=16,color="black",shape="box"];1174 -> 1302[label="",style="solid", color="black", weight=3];
4085[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) False)\n  Enum a",fontsize=16,color="black",shape="box"];4085 -> 4094[label="",style="solid", color="black", weight=3];
4086[label="map toEnum (takeWhile0 (flip (<=) (Neg yx1990)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) True)\n  Enum a",fontsize=16,color="black",shape="box"];4086 -> 4095[label="",style="solid", color="black", weight=3];
4493[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat (Succ yx2760) (Succ yx2770) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4493 -> 4497[label="",style="solid", color="black", weight=3];
4494[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat (Succ yx2760) Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4494 -> 4498[label="",style="solid", color="black", weight=3];
4495[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat Zero (Succ yx2770) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4495 -> 4499[label="",style="solid", color="black", weight=3];
4496[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat Zero Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4496 -> 4500[label="",style="solid", color="black", weight=3];
4088[label="map toEnum (Pos yx249 : takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos yx250 + yx237))\n  Enum a",fontsize=16,color="black",shape="box"];4088 -> 4097[label="",style="solid", color="black", weight=3];
4089[label="map toEnum (Pos yx249 : takeWhile (flip (<=) (Neg Zero)) (numericEnumFrom $! Pos yx250 + yx237))\n  Enum a",fontsize=16,color="black",shape="box"];4089 -> 4098[label="",style="solid", color="black", weight=3];
2347[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) (Succ yx2110)))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) (Succ yx2110))) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) (Succ yx2110)))) yx213 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];2347 -> 2384[label="",style="solid", color="black", weight=3];
2348[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) Zero))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) Zero)) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS (Succ yx2100) Zero))) yx213 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];2348 -> 2385[label="",style="solid", color="black", weight=3];
2349[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero (Succ yx2110)))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero (Succ yx2110))) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero (Succ yx2110)))) yx213 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];2349 -> 2386[label="",style="solid", color="black", weight=3];
2350[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero Zero))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero Zero)) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS Zero Zero))) yx213 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];2350 -> 2387[label="",style="solid", color="black", weight=3];
2994 -> 1727[label="",style="dashed", color="red", weight=0];
2994[label="primMinusNatS (Succ yx30000) Zero",fontsize=16,color="magenta"];2995[label="Zero",fontsize=16,color="green",shape="box"];2996 -> 1727[label="",style="dashed", color="red", weight=0];
2996[label="primMinusNatS (Succ yx30000) Zero",fontsize=16,color="magenta"];2997[label="Zero",fontsize=16,color="green",shape="box"];2998[label="yx4",fontsize=16,color="green",shape="box"];2999[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3000 -> 1727[label="",style="dashed", color="red", weight=0];
3000[label="primMinusNatS (Succ yx30000) Zero",fontsize=16,color="magenta"];3001[label="Zero",fontsize=16,color="green",shape="box"];3002[label="yx4",fontsize=16,color="green",shape="box"];3003[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpInt (Neg (Succ yx219)) (Pos yx2130) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3003 -> 3048[label="",style="solid", color="black", weight=3];
3004[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpInt (Neg (Succ yx219)) (Neg yx2130) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3004 -> 3049[label="",style="solid", color="black", weight=3];
3005 -> 1731[label="",style="dashed", color="red", weight=0];
3005[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];3006[label="Zero",fontsize=16,color="green",shape="box"];3007 -> 1731[label="",style="dashed", color="red", weight=0];
3007[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];3008[label="Zero",fontsize=16,color="green",shape="box"];3009[label="yx4",fontsize=16,color="green",shape="box"];3010[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3011 -> 1731[label="",style="dashed", color="red", weight=0];
3011[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];3012[label="Zero",fontsize=16,color="green",shape="box"];3013[label="yx4",fontsize=16,color="green",shape="box"];131[label="map toEnum (takeWhile1 (flip (<=) (truncateM0 (yx40 :% yx41) (fromIntegral (properFractionQ yx40 yx41),properFractionR yx40 yx41 :% yx41))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (truncateM0 (yx40 :% yx41) (fromIntegral (properFractionQ yx40 yx41),properFractionR yx40 yx41 :% yx41)) == GT)))",fontsize=16,color="black",shape="box"];131 -> 147[label="",style="solid", color="black", weight=3];
3703[label="yx41000",fontsize=16,color="green",shape="box"];3704[label="yx40000",fontsize=16,color="green",shape="box"];3705[label="yx41000",fontsize=16,color="green",shape="box"];3706[label="yx40000",fontsize=16,color="green",shape="box"];3702[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS yx247 yx248)",fontsize=16,color="burlywood",shape="triangle"];4671[label="yx247/Succ yx2470",fontsize=10,color="white",style="solid",shape="box"];3702 -> 4671[label="",style="solid", color="burlywood", weight=9];
4671 -> 3743[label="",style="solid", color="burlywood", weight=3];
4672[label="yx247/Zero",fontsize=10,color="white",style="solid",shape="box"];3702 -> 4672[label="",style="solid", color="burlywood", weight=9];
4672 -> 3744[label="",style="solid", color="burlywood", weight=3];
1755[label="Succ (primDivNatS (primMinusNatS (Succ yx40000) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1755 -> 2071[label="",style="dashed", color="green", weight=3];
1756[label="Zero",fontsize=16,color="green",shape="box"];1757[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1757 -> 2072[label="",style="dashed", color="green", weight=3];
1302[label="fromIntegral (properFractionQ yx70 yx71)\n  Integral a",fontsize=16,color="black",shape="box"];1302 -> 1447[label="",style="solid", color="black", weight=3];
4094[label="map toEnum (takeWhile0 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) otherwise)\n  Enum a",fontsize=16,color="black",shape="box"];4094 -> 4104[label="",style="solid", color="black", weight=3];
4095 -> 3178[label="",style="dashed", color="red", weight=0];
4095[label="map toEnum []\n  Enum a",fontsize=16,color="magenta"];4497 -> 4430[label="",style="dashed", color="red", weight=0];
4497[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (primCmpNat yx2760 yx2770 == GT)))\n  Enum a",fontsize=16,color="magenta"];4497 -> 4501[label="",style="dashed", color="magenta", weight=3];
4497 -> 4502[label="",style="dashed", color="magenta", weight=3];
4498[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (GT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4498 -> 4503[label="",style="solid", color="black", weight=3];
4499[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (LT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4499 -> 4504[label="",style="solid", color="black", weight=3];
4500[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not (EQ == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4500 -> 4505[label="",style="solid", color="black", weight=3];
4097[label="toEnum (Pos yx249) : map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos yx250 + yx237))\n  Enum a",fontsize=16,color="green",shape="box"];4097 -> 4106[label="",style="dashed", color="green", weight=3];
4097 -> 4107[label="",style="dashed", color="green", weight=3];
4098[label="toEnum (Pos yx249) : map toEnum (takeWhile (flip (<=) (Neg Zero)) (numericEnumFrom $! Pos yx250 + yx237))\n  Enum a",fontsize=16,color="green",shape="box"];4098 -> 4108[label="",style="dashed", color="green", weight=3];
4098 -> 4109[label="",style="dashed", color="green", weight=3];
2384 -> 2236[label="",style="dashed", color="red", weight=0];
2384[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS yx2100 yx2110))) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS yx2100 yx2110)) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) (primGEqNatS yx2100 yx2110))) yx213 == GT)))\n  Enum a",fontsize=16,color="magenta"];2384 -> 2420[label="",style="dashed", color="magenta", weight=3];
2384 -> 2421[label="",style="dashed", color="magenta", weight=3];
2385[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) True)) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) True) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) True)) yx213 == GT)))\n  Enum a",fontsize=16,color="black",shape="triangle"];2385 -> 2422[label="",style="solid", color="black", weight=3];
2386[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) False)) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) False) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) False)) yx213 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];2386 -> 2423[label="",style="solid", color="black", weight=3];
2387 -> 2385[label="",style="dashed", color="red", weight=0];
2387[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primDivNatS0 (Succ yx208) (Succ yx209) True)) (numericEnumFrom $! Neg (primDivNatS0 (Succ yx208) (Succ yx209) True) + yx212) (not (primCmpInt (Neg (primDivNatS0 (Succ yx208) (Succ yx209) True)) yx213 == GT)))\n  Enum a",fontsize=16,color="magenta"];1727[label="primMinusNatS (Succ yx30000) Zero",fontsize=16,color="black",shape="triangle"];1727 -> 1749[label="",style="solid", color="black", weight=3];
3048[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (LT == GT)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3048 -> 3083[label="",style="solid", color="black", weight=3];
3049[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat yx2130 (Succ yx219) == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4677[label="yx2130/Succ yx21300",fontsize=10,color="white",style="solid",shape="box"];3049 -> 4677[label="",style="solid", color="burlywood", weight=9];
4677 -> 3084[label="",style="solid", color="burlywood", weight=3];
4678[label="yx2130/Zero",fontsize=10,color="white",style="solid",shape="box"];3049 -> 4678[label="",style="solid", color="burlywood", weight=9];
4678 -> 3085[label="",style="solid", color="burlywood", weight=3];
1731[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];1731 -> 1752[label="",style="solid", color="black", weight=3];
147[label="map toEnum (takeWhile1 (flip (<=) (fromIntegral (properFractionQ yx40 yx41))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (fromIntegral (properFractionQ yx40 yx41)) == GT)))",fontsize=16,color="black",shape="box"];147 -> 165[label="",style="solid", color="black", weight=3];
3743[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS (Succ yx2470) yx248)",fontsize=16,color="burlywood",shape="box"];4679[label="yx248/Succ yx2480",fontsize=10,color="white",style="solid",shape="box"];3743 -> 4679[label="",style="solid", color="burlywood", weight=9];
4679 -> 3755[label="",style="solid", color="burlywood", weight=3];
4680[label="yx248/Zero",fontsize=10,color="white",style="solid",shape="box"];3743 -> 4680[label="",style="solid", color="burlywood", weight=9];
4680 -> 3756[label="",style="solid", color="burlywood", weight=3];
3744[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS Zero yx248)",fontsize=16,color="burlywood",shape="box"];4681[label="yx248/Succ yx2480",fontsize=10,color="white",style="solid",shape="box"];3744 -> 4681[label="",style="solid", color="burlywood", weight=9];
4681 -> 3757[label="",style="solid", color="burlywood", weight=3];
4682[label="yx248/Zero",fontsize=10,color="white",style="solid",shape="box"];3744 -> 4682[label="",style="solid", color="burlywood", weight=9];
4682 -> 3758[label="",style="solid", color="burlywood", weight=3];
2071 -> 1688[label="",style="dashed", color="red", weight=0];
2071[label="primDivNatS (primMinusNatS (Succ yx40000) Zero) (Succ Zero)",fontsize=16,color="magenta"];2071 -> 2099[label="",style="dashed", color="magenta", weight=3];
2071 -> 2100[label="",style="dashed", color="magenta", weight=3];
2072 -> 1688[label="",style="dashed", color="red", weight=0];
2072[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2072 -> 2101[label="",style="dashed", color="magenta", weight=3];
2072 -> 2102[label="",style="dashed", color="magenta", weight=3];
1447[label="fromInteger . toInteger\n  Integral a",fontsize=16,color="black",shape="box"];1447 -> 1584[label="",style="solid", color="black", weight=3];
4104[label="map toEnum (takeWhile0 (flip (<=) (Pos Zero)) (Pos yx249) (numericEnumFrom $! Pos yx250 + yx237) True)\n  Enum a",fontsize=16,color="black",shape="box"];4104 -> 4116[label="",style="solid", color="black", weight=3];
3178[label="map toEnum []\n  Enum a",fontsize=16,color="black",shape="triangle"];3178 -> 3214[label="",style="solid", color="black", weight=3];
4501[label="yx2770",fontsize=16,color="green",shape="box"];4502[label="yx2760",fontsize=16,color="green",shape="box"];4503[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not True))\n  Enum a",fontsize=16,color="black",shape="box"];4503 -> 4506[label="",style="solid", color="black", weight=3];
4504[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not False))\n  Enum a",fontsize=16,color="black",shape="triangle"];4504 -> 4507[label="",style="solid", color="black", weight=3];
4505 -> 4504[label="",style="dashed", color="red", weight=0];
4505[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) (not False))\n  Enum a",fontsize=16,color="magenta"];4106[label="toEnum (Pos yx249)\n  Enum a",fontsize=16,color="blue",shape="box"];4686[label="toEnum :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4686[label="",style="solid", color="blue", weight=9];
4686 -> 4119[label="",style="solid", color="blue", weight=3];
4687[label="toEnum :: Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4687[label="",style="solid", color="blue", weight=9];
4687 -> 4120[label="",style="solid", color="blue", weight=3];
4688[label="toEnum :: Int -> ()",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4688[label="",style="solid", color="blue", weight=9];
4688 -> 4121[label="",style="solid", color="blue", weight=3];
4689[label="toEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4689[label="",style="solid", color="blue", weight=9];
4689 -> 4122[label="",style="solid", color="blue", weight=3];
4690[label="toEnum :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4690[label="",style="solid", color="blue", weight=9];
4690 -> 4123[label="",style="solid", color="blue", weight=3];
4691[label="toEnum :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4691[label="",style="solid", color="blue", weight=9];
4691 -> 4124[label="",style="solid", color="blue", weight=3];
4692[label="toEnum :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4692[label="",style="solid", color="blue", weight=9];
4692 -> 4125[label="",style="solid", color="blue", weight=3];
4693[label="toEnum :: Int -> Char",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4693[label="",style="solid", color="blue", weight=9];
4693 -> 4126[label="",style="solid", color="blue", weight=3];
4694[label="toEnum :: Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];4106 -> 4694[label="",style="solid", color="blue", weight=9];
4694 -> 4127[label="",style="solid", color="blue", weight=3];
4107[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom $! Pos yx250 + yx237))\n  Enum a",fontsize=16,color="black",shape="box"];4107 -> 4128[label="",style="solid", color="black", weight=3];
4108[label="toEnum (Pos yx249)\n  Enum a",fontsize=16,color="blue",shape="box"];4695[label="toEnum :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4695[label="",style="solid", color="blue", weight=9];
4695 -> 4129[label="",style="solid", color="blue", weight=3];
4696[label="toEnum :: Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4696[label="",style="solid", color="blue", weight=9];
4696 -> 4130[label="",style="solid", color="blue", weight=3];
4697[label="toEnum :: Int -> ()",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4697[label="",style="solid", color="blue", weight=9];
4697 -> 4131[label="",style="solid", color="blue", weight=3];
4698[label="toEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4698[label="",style="solid", color="blue", weight=9];
4698 -> 4132[label="",style="solid", color="blue", weight=3];
4699[label="toEnum :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4699[label="",style="solid", color="blue", weight=9];
4699 -> 4133[label="",style="solid", color="blue", weight=3];
4700[label="toEnum :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4700[label="",style="solid", color="blue", weight=9];
4700 -> 4134[label="",style="solid", color="blue", weight=3];
4701[label="toEnum :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4701[label="",style="solid", color="blue", weight=9];
4701 -> 4135[label="",style="solid", color="blue", weight=3];
4702[label="toEnum :: Int -> Char",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4702[label="",style="solid", color="blue", weight=9];
4702 -> 4136[label="",style="solid", color="blue", weight=3];
4703[label="toEnum :: Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];4108 -> 4703[label="",style="solid", color="blue", weight=9];
4703 -> 4137[label="",style="solid", color="blue", weight=3];
4109[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (numericEnumFrom $! Pos yx250 + yx237))\n  Enum a",fontsize=16,color="black",shape="box"];4109 -> 4138[label="",style="solid", color="black", weight=3];
2420[label="yx2100",fontsize=16,color="green",shape="box"];2421[label="yx2110",fontsize=16,color="green",shape="box"];2422 -> 2774[label="",style="dashed", color="red", weight=0];
2422[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ (primDivNatS (primMinusNatS (Succ yx208) (Succ yx209)) (Succ (Succ yx209))))) (numericEnumFrom $! Neg (Succ (primDivNatS (primMinusNatS (Succ yx208) (Succ yx209)) (Succ (Succ yx209)))) + yx212) (not (primCmpInt (Neg (Succ (primDivNatS (primMinusNatS (Succ yx208) (Succ yx209)) (Succ (Succ yx209))))) yx213 == GT)))\n  Enum a",fontsize=16,color="magenta"];2422 -> 2823[label="",style="dashed", color="magenta", weight=3];
2422 -> 2824[label="",style="dashed", color="magenta", weight=3];
2422 -> 2825[label="",style="dashed", color="magenta", weight=3];
2423[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) yx213 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4705[label="yx213/Pos yx2130",fontsize=10,color="white",style="solid",shape="box"];2423 -> 4705[label="",style="solid", color="burlywood", weight=9];
4705 -> 3016[label="",style="solid", color="burlywood", weight=3];
4706[label="yx213/Neg yx2130",fontsize=10,color="white",style="solid",shape="box"];2423 -> 4706[label="",style="solid", color="burlywood", weight=9];
4706 -> 3017[label="",style="solid", color="burlywood", weight=3];
1749[label="Succ yx30000",fontsize=16,color="green",shape="box"];3083[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not False))\n  Enum a",fontsize=16,color="black",shape="triangle"];3083 -> 3114[label="",style="solid", color="black", weight=3];
3084[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat (Succ yx21300) (Succ yx219) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3084 -> 3115[label="",style="solid", color="black", weight=3];
3085[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat Zero (Succ yx219) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3085 -> 3116[label="",style="solid", color="black", weight=3];
1752[label="Zero",fontsize=16,color="green",shape="box"];165[label="map toEnum (takeWhile1 (flip (<=) (fromInteger . toInteger)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (fromInteger . toInteger) == GT)))",fontsize=16,color="black",shape="box"];165 -> 183[label="",style="solid", color="black", weight=3];
3755[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS (Succ yx2470) (Succ yx2480))",fontsize=16,color="black",shape="box"];3755 -> 4017[label="",style="solid", color="black", weight=3];
3756[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS (Succ yx2470) Zero)",fontsize=16,color="black",shape="box"];3756 -> 4018[label="",style="solid", color="black", weight=3];
3757[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS Zero (Succ yx2480))",fontsize=16,color="black",shape="box"];3757 -> 4019[label="",style="solid", color="black", weight=3];
3758[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];3758 -> 4020[label="",style="solid", color="black", weight=3];
2099 -> 1727[label="",style="dashed", color="red", weight=0];
2099[label="primMinusNatS (Succ yx40000) Zero",fontsize=16,color="magenta"];2099 -> 2122[label="",style="dashed", color="magenta", weight=3];
2100[label="Zero",fontsize=16,color="green",shape="box"];2101 -> 1731[label="",style="dashed", color="red", weight=0];
2101[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];2102[label="Zero",fontsize=16,color="green",shape="box"];1584[label="fromInteger (toInteger (properFractionQ yx70 yx71))\n  Integral a",fontsize=16,color="blue",shape="box"];4709[label="toInteger :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];1584 -> 4709[label="",style="solid", color="blue", weight=9];
4709 -> 2037[label="",style="solid", color="blue", weight=3];
4710[label="toInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];1584 -> 4710[label="",style="solid", color="blue", weight=9];
4710 -> 2038[label="",style="solid", color="blue", weight=3];
4116 -> 3178[label="",style="dashed", color="red", weight=0];
4116[label="map toEnum []\n  Enum a",fontsize=16,color="magenta"];3214[label="[]\n  Enum a",fontsize=16,color="green",shape="box"];4506[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) False)\n  Enum a",fontsize=16,color="black",shape="box"];4506 -> 4508[label="",style="solid", color="black", weight=3];
4507[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) True)\n  Enum a",fontsize=16,color="black",shape="box"];4507 -> 4509[label="",style="solid", color="black", weight=3];
4119[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4119 -> 4154[label="",style="solid", color="black", weight=3];
4120[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4120 -> 4155[label="",style="solid", color="black", weight=3];
4121[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4121 -> 4156[label="",style="solid", color="black", weight=3];
4122[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4122 -> 4157[label="",style="solid", color="black", weight=3];
4123[label="toEnum (Pos yx249)\n  Integral a",fontsize=16,color="black",shape="triangle"];4123 -> 4158[label="",style="solid", color="black", weight=3];
4124[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4124 -> 4159[label="",style="solid", color="black", weight=3];
4125[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4125 -> 4160[label="",style="solid", color="black", weight=3];
4126[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4126 -> 4161[label="",style="solid", color="black", weight=3];
4127[label="toEnum (Pos yx249)",fontsize=16,color="black",shape="triangle"];4127 -> 4162[label="",style="solid", color="black", weight=3];
4128[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (Pos yx250 + yx237 `seq` numericEnumFrom (Pos yx250 + yx237)))\n  Enum a",fontsize=16,color="black",shape="box"];4128 -> 4163[label="",style="solid", color="black", weight=3];
4129 -> 4119[label="",style="dashed", color="red", weight=0];
4129[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4130 -> 4120[label="",style="dashed", color="red", weight=0];
4130[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4131 -> 4121[label="",style="dashed", color="red", weight=0];
4131[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4132 -> 4122[label="",style="dashed", color="red", weight=0];
4132[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4133 -> 4123[label="",style="dashed", color="red", weight=0];
4133[label="toEnum (Pos yx249)\n  Integral a",fontsize=16,color="magenta"];4134 -> 4124[label="",style="dashed", color="red", weight=0];
4134[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4135 -> 4125[label="",style="dashed", color="red", weight=0];
4135[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4136 -> 4126[label="",style="dashed", color="red", weight=0];
4136[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4137 -> 4127[label="",style="dashed", color="red", weight=0];
4137[label="toEnum (Pos yx249)",fontsize=16,color="magenta"];4138[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (Pos yx250 + yx237 `seq` numericEnumFrom (Pos yx250 + yx237)))\n  Enum a",fontsize=16,color="black",shape="box"];4138 -> 4164[label="",style="solid", color="black", weight=3];
2823 -> 1688[label="",style="dashed", color="red", weight=0];
2823[label="primDivNatS (primMinusNatS (Succ yx208) (Succ yx209)) (Succ (Succ yx209))",fontsize=16,color="magenta"];2823 -> 3028[label="",style="dashed", color="magenta", weight=3];
2823 -> 3029[label="",style="dashed", color="magenta", weight=3];
2824 -> 1688[label="",style="dashed", color="red", weight=0];
2824[label="primDivNatS (primMinusNatS (Succ yx208) (Succ yx209)) (Succ (Succ yx209))",fontsize=16,color="magenta"];2824 -> 3030[label="",style="dashed", color="magenta", weight=3];
2824 -> 3031[label="",style="dashed", color="magenta", weight=3];
2825 -> 1688[label="",style="dashed", color="red", weight=0];
2825[label="primDivNatS (primMinusNatS (Succ yx208) (Succ yx209)) (Succ (Succ yx209))",fontsize=16,color="magenta"];2825 -> 3032[label="",style="dashed", color="magenta", weight=3];
2825 -> 3033[label="",style="dashed", color="magenta", weight=3];
3016[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) (Pos yx2130) == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4724[label="yx2130/Succ yx21300",fontsize=10,color="white",style="solid",shape="box"];3016 -> 4724[label="",style="solid", color="burlywood", weight=9];
4724 -> 3053[label="",style="solid", color="burlywood", weight=3];
4725[label="yx2130/Zero",fontsize=10,color="white",style="solid",shape="box"];3016 -> 4725[label="",style="solid", color="burlywood", weight=9];
4725 -> 3054[label="",style="solid", color="burlywood", weight=3];
3017[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) (Neg yx2130) == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4726[label="yx2130/Succ yx21300",fontsize=10,color="white",style="solid",shape="box"];3017 -> 4726[label="",style="solid", color="burlywood", weight=9];
4726 -> 3055[label="",style="solid", color="burlywood", weight=3];
4727[label="yx2130/Zero",fontsize=10,color="white",style="solid",shape="box"];3017 -> 4727[label="",style="solid", color="burlywood", weight=9];
4727 -> 3056[label="",style="solid", color="burlywood", weight=3];
3114[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) True)\n  Enum a",fontsize=16,color="black",shape="box"];3114 -> 3148[label="",style="solid", color="black", weight=3];
3115[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat yx21300 yx219 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4728[label="yx21300/Succ yx213000",fontsize=10,color="white",style="solid",shape="box"];3115 -> 4728[label="",style="solid", color="burlywood", weight=9];
4728 -> 3149[label="",style="solid", color="burlywood", weight=3];
4729[label="yx21300/Zero",fontsize=10,color="white",style="solid",shape="box"];3115 -> 4729[label="",style="solid", color="burlywood", weight=9];
4729 -> 3150[label="",style="solid", color="burlywood", weight=3];
3116 -> 3048[label="",style="dashed", color="red", weight=0];
3116[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (LT == GT)))\n  Enum a",fontsize=16,color="magenta"];183[label="map toEnum (takeWhile1 (flip (<=) (fromInteger (toInteger (properFractionQ yx40 yx41)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (fromInteger (toInteger (properFractionQ yx40 yx41))) == GT)))",fontsize=16,color="black",shape="box"];183 -> 203[label="",style="solid", color="black", weight=3];
4017 -> 3702[label="",style="dashed", color="red", weight=0];
4017[label="primDivNatS0 (Succ yx245) (Succ yx246) (primGEqNatS yx2470 yx2480)",fontsize=16,color="magenta"];4017 -> 4031[label="",style="dashed", color="magenta", weight=3];
4017 -> 4032[label="",style="dashed", color="magenta", weight=3];
4018[label="primDivNatS0 (Succ yx245) (Succ yx246) True",fontsize=16,color="black",shape="triangle"];4018 -> 4033[label="",style="solid", color="black", weight=3];
4019[label="primDivNatS0 (Succ yx245) (Succ yx246) False",fontsize=16,color="black",shape="box"];4019 -> 4034[label="",style="solid", color="black", weight=3];
4020 -> 4018[label="",style="dashed", color="red", weight=0];
4020[label="primDivNatS0 (Succ yx245) (Succ yx246) True",fontsize=16,color="magenta"];2122[label="yx40000",fontsize=16,color="green",shape="box"];2037[label="fromInteger (toInteger (properFractionQ yx70 yx71))",fontsize=16,color="black",shape="box"];2037 -> 2323[label="",style="solid", color="black", weight=3];
2038[label="fromInteger (toInteger (properFractionQ yx70 yx71))",fontsize=16,color="black",shape="box"];2038 -> 2324[label="",style="solid", color="black", weight=3];
4508[label="map toEnum (takeWhile0 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) otherwise)\n  Enum a",fontsize=16,color="black",shape="box"];4508 -> 4510[label="",style="solid", color="black", weight=3];
4509[label="map toEnum (Pos yx273 : takeWhile (flip (<=) (Pos (Succ yx272))) (numericEnumFrom $! Pos yx274 + yx275))\n  Enum a",fontsize=16,color="black",shape="box"];4509 -> 4511[label="",style="solid", color="black", weight=3];
4154[label="error []",fontsize=16,color="red",shape="box"];4155[label="error []",fontsize=16,color="red",shape="box"];4156[label="error []",fontsize=16,color="red",shape="box"];4157[label="error []",fontsize=16,color="red",shape="box"];4158[label="fromInt (Pos yx249)\n  Integral a",fontsize=16,color="black",shape="box"];4158 -> 4172[label="",style="solid", color="black", weight=3];
4159[label="error []",fontsize=16,color="red",shape="box"];4160[label="error []",fontsize=16,color="red",shape="box"];4161[label="error []",fontsize=16,color="red",shape="box"];4162[label="error []",fontsize=16,color="red",shape="box"];4163[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (Pos yx250 + yx237)) (numericEnumFrom (Pos yx250 + yx237))))\n  Enum a",fontsize=16,color="black",shape="box"];4163 -> 4173[label="",style="solid", color="black", weight=3];
4164[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (Pos yx250 + yx237)) (numericEnumFrom (Pos yx250 + yx237))))\n  Enum a",fontsize=16,color="black",shape="box"];4164 -> 4174[label="",style="solid", color="black", weight=3];
3028 -> 3018[label="",style="dashed", color="red", weight=0];
3028[label="primMinusNatS (Succ yx208) (Succ yx209)",fontsize=16,color="magenta"];3028 -> 3062[label="",style="dashed", color="magenta", weight=3];
3028 -> 3063[label="",style="dashed", color="magenta", weight=3];
3029[label="Succ yx209",fontsize=16,color="green",shape="box"];3030 -> 3018[label="",style="dashed", color="red", weight=0];
3030[label="primMinusNatS (Succ yx208) (Succ yx209)",fontsize=16,color="magenta"];3030 -> 3064[label="",style="dashed", color="magenta", weight=3];
3030 -> 3065[label="",style="dashed", color="magenta", weight=3];
3031[label="Succ yx209",fontsize=16,color="green",shape="box"];3032 -> 3018[label="",style="dashed", color="red", weight=0];
3032[label="primMinusNatS (Succ yx208) (Succ yx209)",fontsize=16,color="magenta"];3032 -> 3066[label="",style="dashed", color="magenta", weight=3];
3032 -> 3067[label="",style="dashed", color="magenta", weight=3];
3033[label="Succ yx209",fontsize=16,color="green",shape="box"];3053[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) (Pos (Succ yx21300)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3053 -> 3089[label="",style="solid", color="black", weight=3];
3054[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3054 -> 3090[label="",style="solid", color="black", weight=3];
3055[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) (Neg (Succ yx21300)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3055 -> 3091[label="",style="solid", color="black", weight=3];
3056[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpInt (Neg Zero) (Neg Zero) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3056 -> 3092[label="",style="solid", color="black", weight=3];
3148[label="map toEnum (Neg (Succ yx217) : takeWhile (flip (<=) yx207) (numericEnumFrom $! Neg (Succ yx218) + yx212))\n  Enum a",fontsize=16,color="black",shape="box"];3148 -> 3169[label="",style="solid", color="black", weight=3];
3149[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat (Succ yx213000) yx219 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4736[label="yx219/Succ yx2190",fontsize=10,color="white",style="solid",shape="box"];3149 -> 4736[label="",style="solid", color="burlywood", weight=9];
4736 -> 3170[label="",style="solid", color="burlywood", weight=3];
4737[label="yx219/Zero",fontsize=10,color="white",style="solid",shape="box"];3149 -> 4737[label="",style="solid", color="burlywood", weight=9];
4737 -> 3171[label="",style="solid", color="burlywood", weight=3];
3150[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat Zero yx219 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4738[label="yx219/Succ yx2190",fontsize=10,color="white",style="solid",shape="box"];3150 -> 4738[label="",style="solid", color="burlywood", weight=9];
4738 -> 3172[label="",style="solid", color="burlywood", weight=3];
4739[label="yx219/Zero",fontsize=10,color="white",style="solid",shape="box"];3150 -> 4739[label="",style="solid", color="burlywood", weight=9];
4739 -> 3173[label="",style="solid", color="burlywood", weight=3];
203[label="map toEnum (takeWhile1 (flip (<=) (fromInteger (Integer (properFractionQ yx40 yx41)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (fromInteger (Integer (properFractionQ yx40 yx41))) == GT)))",fontsize=16,color="black",shape="box"];203 -> 225[label="",style="solid", color="black", weight=3];
4031[label="yx2480",fontsize=16,color="green",shape="box"];4032[label="yx2470",fontsize=16,color="green",shape="box"];4033[label="Succ (primDivNatS (primMinusNatS (Succ yx245) (Succ yx246)) (Succ (Succ yx246)))",fontsize=16,color="green",shape="box"];4033 -> 4052[label="",style="dashed", color="green", weight=3];
4034[label="Zero",fontsize=16,color="green",shape="box"];2323 -> 3166[label="",style="dashed", color="red", weight=0];
2323[label="fromInteger (Integer (properFractionQ yx70 yx71))",fontsize=16,color="magenta"];2323 -> 3167[label="",style="dashed", color="magenta", weight=3];
2324[label="fromInteger (properFractionQ yx70 yx71)",fontsize=16,color="black",shape="box"];2324 -> 2356[label="",style="solid", color="black", weight=3];
4510[label="map toEnum (takeWhile0 (flip (<=) (Pos (Succ yx272))) (Pos yx273) (numericEnumFrom $! Pos yx274 + yx275) True)\n  Enum a",fontsize=16,color="black",shape="box"];4510 -> 4512[label="",style="solid", color="black", weight=3];
4511[label="toEnum (Pos yx273) : map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (numericEnumFrom $! Pos yx274 + yx275))\n  Enum a",fontsize=16,color="green",shape="box"];4511 -> 4513[label="",style="dashed", color="green", weight=3];
4511 -> 4514[label="",style="dashed", color="green", weight=3];
4172[label="intToRatio (Pos yx249)\n  Integral a",fontsize=16,color="black",shape="box"];4172 -> 4183[label="",style="solid", color="black", weight=3];
4173[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (primPlusInt (Pos yx250) yx237)) (numericEnumFrom (primPlusInt (Pos yx250) yx237))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4741[label="yx237/Pos yx2370",fontsize=10,color="white",style="solid",shape="box"];4173 -> 4741[label="",style="solid", color="burlywood", weight=9];
4741 -> 4184[label="",style="solid", color="burlywood", weight=3];
4742[label="yx237/Neg yx2370",fontsize=10,color="white",style="solid",shape="box"];4173 -> 4742[label="",style="solid", color="burlywood", weight=9];
4742 -> 4185[label="",style="solid", color="burlywood", weight=3];
4174[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (primPlusInt (Pos yx250) yx237)) (numericEnumFrom (primPlusInt (Pos yx250) yx237))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4743[label="yx237/Pos yx2370",fontsize=10,color="white",style="solid",shape="box"];4174 -> 4743[label="",style="solid", color="burlywood", weight=9];
4743 -> 4186[label="",style="solid", color="burlywood", weight=3];
4744[label="yx237/Neg yx2370",fontsize=10,color="white",style="solid",shape="box"];4174 -> 4744[label="",style="solid", color="burlywood", weight=9];
4744 -> 4187[label="",style="solid", color="burlywood", weight=3];
3062[label="yx209",fontsize=16,color="green",shape="box"];3063[label="yx208",fontsize=16,color="green",shape="box"];3018[label="primMinusNatS (Succ yx200) (Succ yx201)",fontsize=16,color="black",shape="triangle"];3018 -> 3057[label="",style="solid", color="black", weight=3];
3064[label="yx209",fontsize=16,color="green",shape="box"];3065[label="yx208",fontsize=16,color="green",shape="box"];3066[label="yx209",fontsize=16,color="green",shape="box"];3067[label="yx208",fontsize=16,color="green",shape="box"];3089[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (LT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3089 -> 3120[label="",style="solid", color="black", weight=3];
3090[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (EQ == GT)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3090 -> 3121[label="",style="solid", color="black", weight=3];
3091[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (primCmpNat (Succ yx21300) Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3091 -> 3122[label="",style="solid", color="black", weight=3];
3092 -> 3090[label="",style="dashed", color="red", weight=0];
3092[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (EQ == GT)))\n  Enum a",fontsize=16,color="magenta"];3169[label="toEnum (Neg (Succ yx217)) : map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom $! Neg (Succ yx218) + yx212))\n  Enum a",fontsize=16,color="green",shape="box"];3169 -> 3204[label="",style="dashed", color="green", weight=3];
3169 -> 3205[label="",style="dashed", color="green", weight=3];
3170[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat (Succ yx213000) (Succ yx2190) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3170 -> 3206[label="",style="solid", color="black", weight=3];
3171[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat (Succ yx213000) Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3171 -> 3207[label="",style="solid", color="black", weight=3];
3172[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat Zero (Succ yx2190) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3172 -> 3208[label="",style="solid", color="black", weight=3];
3173[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat Zero Zero == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3173 -> 3209[label="",style="solid", color="black", weight=3];
225[label="map toEnum (takeWhile1 (flip (<=) (properFractionQ yx40 yx41)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (properFractionQ yx40 yx41) == GT)))",fontsize=16,color="black",shape="box"];225 -> 247[label="",style="solid", color="black", weight=3];
4052 -> 1688[label="",style="dashed", color="red", weight=0];
4052[label="primDivNatS (primMinusNatS (Succ yx245) (Succ yx246)) (Succ (Succ yx246))",fontsize=16,color="magenta"];4052 -> 4061[label="",style="dashed", color="magenta", weight=3];
4052 -> 4062[label="",style="dashed", color="magenta", weight=3];
3167[label="properFractionQ yx70 yx71",fontsize=16,color="black",shape="box"];3167 -> 3185[label="",style="solid", color="black", weight=3];
3166[label="fromInteger (Integer yx220)",fontsize=16,color="black",shape="triangle"];3166 -> 3186[label="",style="solid", color="black", weight=3];
2356[label="fromInteger (properFractionQ1 yx70 yx71 (properFractionVu30 yx70 yx71))",fontsize=16,color="black",shape="box"];2356 -> 2393[label="",style="solid", color="black", weight=3];
4512 -> 3178[label="",style="dashed", color="red", weight=0];
4512[label="map toEnum []\n  Enum a",fontsize=16,color="magenta"];4513[label="toEnum (Pos yx273)\n  Enum a",fontsize=16,color="blue",shape="box"];4748[label="toEnum :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4748[label="",style="solid", color="blue", weight=9];
4748 -> 4515[label="",style="solid", color="blue", weight=3];
4749[label="toEnum :: Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4749[label="",style="solid", color="blue", weight=9];
4749 -> 4516[label="",style="solid", color="blue", weight=3];
4750[label="toEnum :: Int -> ()",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4750[label="",style="solid", color="blue", weight=9];
4750 -> 4517[label="",style="solid", color="blue", weight=3];
4751[label="toEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4751[label="",style="solid", color="blue", weight=9];
4751 -> 4518[label="",style="solid", color="blue", weight=3];
4752[label="toEnum :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4752[label="",style="solid", color="blue", weight=9];
4752 -> 4519[label="",style="solid", color="blue", weight=3];
4753[label="toEnum :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4753[label="",style="solid", color="blue", weight=9];
4753 -> 4520[label="",style="solid", color="blue", weight=3];
4754[label="toEnum :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4754[label="",style="solid", color="blue", weight=9];
4754 -> 4521[label="",style="solid", color="blue", weight=3];
4755[label="toEnum :: Int -> Char",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4755[label="",style="solid", color="blue", weight=9];
4755 -> 4522[label="",style="solid", color="blue", weight=3];
4756[label="toEnum :: Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];4513 -> 4756[label="",style="solid", color="blue", weight=9];
4756 -> 4523[label="",style="solid", color="blue", weight=3];
4514[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (numericEnumFrom $! Pos yx274 + yx275))\n  Enum a",fontsize=16,color="black",shape="box"];4514 -> 4524[label="",style="solid", color="black", weight=3];
4183[label="fromInt (Pos yx249) :% fromInt (Pos (Succ Zero))\n  Integral a",fontsize=16,color="green",shape="box"];4183 -> 4195[label="",style="dashed", color="green", weight=3];
4183 -> 4196[label="",style="dashed", color="green", weight=3];
4184[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (primPlusInt (Pos yx250) (Pos yx2370))) (numericEnumFrom (primPlusInt (Pos yx250) (Pos yx2370)))))\n  Enum a",fontsize=16,color="black",shape="box"];4184 -> 4197[label="",style="solid", color="black", weight=3];
4185[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (primPlusInt (Pos yx250) (Neg yx2370))) (numericEnumFrom (primPlusInt (Pos yx250) (Neg yx2370)))))\n  Enum a",fontsize=16,color="black",shape="box"];4185 -> 4198[label="",style="solid", color="black", weight=3];
4186[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (primPlusInt (Pos yx250) (Pos yx2370))) (numericEnumFrom (primPlusInt (Pos yx250) (Pos yx2370)))))\n  Enum a",fontsize=16,color="black",shape="box"];4186 -> 4199[label="",style="solid", color="black", weight=3];
4187[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (primPlusInt (Pos yx250) (Neg yx2370))) (numericEnumFrom (primPlusInt (Pos yx250) (Neg yx2370)))))\n  Enum a",fontsize=16,color="black",shape="box"];4187 -> 4200[label="",style="solid", color="black", weight=3];
3057[label="primMinusNatS yx200 yx201",fontsize=16,color="burlywood",shape="triangle"];4757[label="yx200/Succ yx2000",fontsize=10,color="white",style="solid",shape="box"];3057 -> 4757[label="",style="solid", color="burlywood", weight=9];
4757 -> 3093[label="",style="solid", color="burlywood", weight=3];
4758[label="yx200/Zero",fontsize=10,color="white",style="solid",shape="box"];3057 -> 4758[label="",style="solid", color="burlywood", weight=9];
4758 -> 3094[label="",style="solid", color="burlywood", weight=3];
3120[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not False))\n  Enum a",fontsize=16,color="black",shape="triangle"];3120 -> 3156[label="",style="solid", color="black", weight=3];
3121 -> 3120[label="",style="dashed", color="red", weight=0];
3121[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not False))\n  Enum a",fontsize=16,color="magenta"];3122[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not (GT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3122 -> 3157[label="",style="solid", color="black", weight=3];
3204[label="toEnum (Neg (Succ yx217))\n  Enum a",fontsize=16,color="blue",shape="box"];4760[label="toEnum :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4760[label="",style="solid", color="blue", weight=9];
4760 -> 3237[label="",style="solid", color="blue", weight=3];
4761[label="toEnum :: Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4761[label="",style="solid", color="blue", weight=9];
4761 -> 3238[label="",style="solid", color="blue", weight=3];
4762[label="toEnum :: Int -> ()",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4762[label="",style="solid", color="blue", weight=9];
4762 -> 3239[label="",style="solid", color="blue", weight=3];
4763[label="toEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4763[label="",style="solid", color="blue", weight=9];
4763 -> 3240[label="",style="solid", color="blue", weight=3];
4764[label="toEnum :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4764[label="",style="solid", color="blue", weight=9];
4764 -> 3241[label="",style="solid", color="blue", weight=3];
4765[label="toEnum :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4765[label="",style="solid", color="blue", weight=9];
4765 -> 3242[label="",style="solid", color="blue", weight=3];
4766[label="toEnum :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4766[label="",style="solid", color="blue", weight=9];
4766 -> 3243[label="",style="solid", color="blue", weight=3];
4767[label="toEnum :: Int -> Char",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4767[label="",style="solid", color="blue", weight=9];
4767 -> 3244[label="",style="solid", color="blue", weight=3];
4768[label="toEnum :: Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];3204 -> 4768[label="",style="solid", color="blue", weight=9];
4768 -> 3245[label="",style="solid", color="blue", weight=3];
3205[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom $! Neg (Succ yx218) + yx212))\n  Enum a",fontsize=16,color="black",shape="box"];3205 -> 3246[label="",style="solid", color="black", weight=3];
3206 -> 3115[label="",style="dashed", color="red", weight=0];
3206[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (primCmpNat yx213000 yx2190 == GT)))\n  Enum a",fontsize=16,color="magenta"];3206 -> 3247[label="",style="dashed", color="magenta", weight=3];
3206 -> 3248[label="",style="dashed", color="magenta", weight=3];
3207[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (GT == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3207 -> 3249[label="",style="solid", color="black", weight=3];
3208 -> 3048[label="",style="dashed", color="red", weight=0];
3208[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (LT == GT)))\n  Enum a",fontsize=16,color="magenta"];3209[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not (EQ == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3209 -> 3250[label="",style="solid", color="black", weight=3];
247[label="map toEnum (takeWhile1 (flip (<=) (properFractionQ1 yx40 yx41 (properFractionVu30 yx40 yx41))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (properFractionQ1 yx40 yx41 (properFractionVu30 yx40 yx41)) == GT)))",fontsize=16,color="black",shape="box"];247 -> 271[label="",style="solid", color="black", weight=3];
4061 -> 3057[label="",style="dashed", color="red", weight=0];
4061[label="primMinusNatS (Succ yx245) (Succ yx246)",fontsize=16,color="magenta"];4061 -> 4072[label="",style="dashed", color="magenta", weight=3];
4061 -> 4073[label="",style="dashed", color="magenta", weight=3];
4062[label="Succ yx246",fontsize=16,color="green",shape="box"];3185[label="properFractionQ1 yx70 yx71 (properFractionVu30 yx70 yx71)",fontsize=16,color="black",shape="box"];3185 -> 3220[label="",style="solid", color="black", weight=3];
3186[label="yx220",fontsize=16,color="green",shape="box"];2393[label="fromInteger (properFractionQ1 yx70 yx71 (quotRem yx70 yx71))",fontsize=16,color="burlywood",shape="box"];4772[label="yx70/Integer yx700",fontsize=10,color="white",style="solid",shape="box"];2393 -> 4772[label="",style="solid", color="burlywood", weight=9];
4772 -> 3035[label="",style="solid", color="burlywood", weight=3];
4515 -> 4119[label="",style="dashed", color="red", weight=0];
4515[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4515 -> 4525[label="",style="dashed", color="magenta", weight=3];
4516 -> 4120[label="",style="dashed", color="red", weight=0];
4516[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4516 -> 4526[label="",style="dashed", color="magenta", weight=3];
4517 -> 4121[label="",style="dashed", color="red", weight=0];
4517[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4517 -> 4527[label="",style="dashed", color="magenta", weight=3];
4518 -> 4122[label="",style="dashed", color="red", weight=0];
4518[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4518 -> 4528[label="",style="dashed", color="magenta", weight=3];
4519 -> 4123[label="",style="dashed", color="red", weight=0];
4519[label="toEnum (Pos yx273)\n  Integral a",fontsize=16,color="magenta"];4519 -> 4529[label="",style="dashed", color="magenta", weight=3];
4520 -> 4124[label="",style="dashed", color="red", weight=0];
4520[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4520 -> 4530[label="",style="dashed", color="magenta", weight=3];
4521 -> 4125[label="",style="dashed", color="red", weight=0];
4521[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4521 -> 4531[label="",style="dashed", color="magenta", weight=3];
4522 -> 4126[label="",style="dashed", color="red", weight=0];
4522[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4522 -> 4532[label="",style="dashed", color="magenta", weight=3];
4523 -> 4127[label="",style="dashed", color="red", weight=0];
4523[label="toEnum (Pos yx273)",fontsize=16,color="magenta"];4523 -> 4533[label="",style="dashed", color="magenta", weight=3];
4524[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (Pos yx274 + yx275 `seq` numericEnumFrom (Pos yx274 + yx275)))\n  Enum a",fontsize=16,color="black",shape="box"];4524 -> 4534[label="",style="solid", color="black", weight=3];
4195[label="fromInt (Pos yx249)\n  Integral a",fontsize=16,color="blue",shape="box"];4782[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];4195 -> 4782[label="",style="solid", color="blue", weight=9];
4782 -> 4209[label="",style="solid", color="blue", weight=3];
4783[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];4195 -> 4783[label="",style="solid", color="blue", weight=9];
4783 -> 4210[label="",style="solid", color="blue", weight=3];
4196[label="fromInt (Pos (Succ Zero))\n  Integral a",fontsize=16,color="blue",shape="box"];4784[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];4196 -> 4784[label="",style="solid", color="blue", weight=9];
4784 -> 4211[label="",style="solid", color="blue", weight=3];
4785[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];4196 -> 4785[label="",style="solid", color="blue", weight=9];
4785 -> 4212[label="",style="solid", color="blue", weight=3];
4197 -> 4213[label="",style="dashed", color="red", weight=0];
4197[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (Pos (primPlusNat yx250 yx2370))) (numericEnumFrom (Pos (primPlusNat yx250 yx2370)))))\n  Enum a",fontsize=16,color="magenta"];4197 -> 4214[label="",style="dashed", color="magenta", weight=3];
4197 -> 4215[label="",style="dashed", color="magenta", weight=3];
4198 -> 3483[label="",style="dashed", color="red", weight=0];
4198[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (primMinusNat yx250 yx2370)) (numericEnumFrom (primMinusNat yx250 yx2370))))\n  Enum a",fontsize=16,color="magenta"];4198 -> 4216[label="",style="dashed", color="magenta", weight=3];
4198 -> 4217[label="",style="dashed", color="magenta", weight=3];
4198 -> 4218[label="",style="dashed", color="magenta", weight=3];
4199 -> 4219[label="",style="dashed", color="red", weight=0];
4199[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (Pos (primPlusNat yx250 yx2370))) (numericEnumFrom (Pos (primPlusNat yx250 yx2370)))))\n  Enum a",fontsize=16,color="magenta"];4199 -> 4220[label="",style="dashed", color="magenta", weight=3];
4199 -> 4221[label="",style="dashed", color="magenta", weight=3];
4200 -> 3483[label="",style="dashed", color="red", weight=0];
4200[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (primMinusNat yx250 yx2370)) (numericEnumFrom (primMinusNat yx250 yx2370))))\n  Enum a",fontsize=16,color="magenta"];4200 -> 4222[label="",style="dashed", color="magenta", weight=3];
4200 -> 4223[label="",style="dashed", color="magenta", weight=3];
4200 -> 4224[label="",style="dashed", color="magenta", weight=3];
3093[label="primMinusNatS (Succ yx2000) yx201",fontsize=16,color="burlywood",shape="box"];4790[label="yx201/Succ yx2010",fontsize=10,color="white",style="solid",shape="box"];3093 -> 4790[label="",style="solid", color="burlywood", weight=9];
4790 -> 3123[label="",style="solid", color="burlywood", weight=3];
4791[label="yx201/Zero",fontsize=10,color="white",style="solid",shape="box"];3093 -> 4791[label="",style="solid", color="burlywood", weight=9];
4791 -> 3124[label="",style="solid", color="burlywood", weight=3];
3094[label="primMinusNatS Zero yx201",fontsize=16,color="burlywood",shape="box"];4792[label="yx201/Succ yx2010",fontsize=10,color="white",style="solid",shape="box"];3094 -> 4792[label="",style="solid", color="burlywood", weight=9];
4792 -> 3125[label="",style="solid", color="burlywood", weight=3];
4793[label="yx201/Zero",fontsize=10,color="white",style="solid",shape="box"];3094 -> 4793[label="",style="solid", color="burlywood", weight=9];
4793 -> 3126[label="",style="solid", color="burlywood", weight=3];
3156[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) True)\n  Enum a",fontsize=16,color="black",shape="box"];3156 -> 3179[label="",style="solid", color="black", weight=3];
3157[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) (not True))\n  Enum a",fontsize=16,color="black",shape="box"];3157 -> 3180[label="",style="solid", color="black", weight=3];
3237[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3237 -> 3284[label="",style="solid", color="black", weight=3];
3238[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3238 -> 3285[label="",style="solid", color="black", weight=3];
3239[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3239 -> 3286[label="",style="solid", color="black", weight=3];
3240[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3240 -> 3287[label="",style="solid", color="black", weight=3];
3241[label="toEnum (Neg (Succ yx217))\n  Integral a",fontsize=16,color="black",shape="box"];3241 -> 3288[label="",style="solid", color="black", weight=3];
3242[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3242 -> 3289[label="",style="solid", color="black", weight=3];
3243[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3243 -> 3290[label="",style="solid", color="black", weight=3];
3244[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3244 -> 3291[label="",style="solid", color="black", weight=3];
3245[label="toEnum (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3245 -> 3292[label="",style="solid", color="black", weight=3];
3246[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (Succ yx218) + yx212 `seq` numericEnumFrom (Neg (Succ yx218) + yx212)))\n  Enum a",fontsize=16,color="black",shape="box"];3246 -> 3293[label="",style="solid", color="black", weight=3];
3247[label="yx2190",fontsize=16,color="green",shape="box"];3248[label="yx213000",fontsize=16,color="green",shape="box"];3249[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not True))\n  Enum a",fontsize=16,color="black",shape="box"];3249 -> 3294[label="",style="solid", color="black", weight=3];
3250 -> 3083[label="",style="dashed", color="red", weight=0];
3250[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) (not False))\n  Enum a",fontsize=16,color="magenta"];271[label="map toEnum (takeWhile1 (flip (<=) (properFractionQ1 yx40 yx41 (quotRem yx40 yx41))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (properFractionQ1 yx40 yx41 (quotRem yx40 yx41)) == GT)))",fontsize=16,color="black",shape="box"];271 -> 297[label="",style="solid", color="black", weight=3];
4072[label="Succ yx246",fontsize=16,color="green",shape="box"];4073[label="Succ yx245",fontsize=16,color="green",shape="box"];3220[label="properFractionQ1 yx70 yx71 (quotRem yx70 yx71)",fontsize=16,color="black",shape="box"];3220 -> 3265[label="",style="solid", color="black", weight=3];
3035[label="fromInteger (properFractionQ1 (Integer yx700) yx71 (quotRem (Integer yx700) yx71))",fontsize=16,color="burlywood",shape="box"];4795[label="yx71/Integer yx710",fontsize=10,color="white",style="solid",shape="box"];3035 -> 4795[label="",style="solid", color="burlywood", weight=9];
4795 -> 3069[label="",style="solid", color="burlywood", weight=3];
4525[label="yx273",fontsize=16,color="green",shape="box"];4526[label="yx273",fontsize=16,color="green",shape="box"];4527[label="yx273",fontsize=16,color="green",shape="box"];4528[label="yx273",fontsize=16,color="green",shape="box"];4529[label="yx273",fontsize=16,color="green",shape="box"];4530[label="yx273",fontsize=16,color="green",shape="box"];4531[label="yx273",fontsize=16,color="green",shape="box"];4532[label="yx273",fontsize=16,color="green",shape="box"];4533[label="yx273",fontsize=16,color="green",shape="box"];4534[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (Pos yx274 + yx275)) (numericEnumFrom (Pos yx274 + yx275))))\n  Enum a",fontsize=16,color="black",shape="box"];4534 -> 4535[label="",style="solid", color="black", weight=3];
4209 -> 576[label="",style="dashed", color="red", weight=0];
4209[label="fromInt (Pos yx249)",fontsize=16,color="magenta"];4209 -> 4238[label="",style="dashed", color="magenta", weight=3];
4210[label="fromInt (Pos yx249)",fontsize=16,color="black",shape="triangle"];4210 -> 4239[label="",style="solid", color="black", weight=3];
4211 -> 576[label="",style="dashed", color="red", weight=0];
4211[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4211 -> 4240[label="",style="dashed", color="magenta", weight=3];
4212 -> 4210[label="",style="dashed", color="red", weight=0];
4212[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4212 -> 4241[label="",style="dashed", color="magenta", weight=3];
4214 -> 3745[label="",style="dashed", color="red", weight=0];
4214[label="primPlusNat yx250 yx2370",fontsize=16,color="magenta"];4214 -> 4242[label="",style="dashed", color="magenta", weight=3];
4214 -> 4243[label="",style="dashed", color="magenta", weight=3];
4215 -> 3745[label="",style="dashed", color="red", weight=0];
4215[label="primPlusNat yx250 yx2370",fontsize=16,color="magenta"];4215 -> 4244[label="",style="dashed", color="magenta", weight=3];
4215 -> 4245[label="",style="dashed", color="magenta", weight=3];
4213[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (enforceWHNF (WHNF (Pos yx253)) (numericEnumFrom (Pos yx252))))\n  Enum a",fontsize=16,color="black",shape="triangle"];4213 -> 4246[label="",style="solid", color="black", weight=3];
4216[label="yx250",fontsize=16,color="green",shape="box"];4217[label="Pos Zero",fontsize=16,color="green",shape="box"];4218[label="yx2370",fontsize=16,color="green",shape="box"];3483[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat yx21200 yx218)) (numericEnumFrom (primMinusNat yx21200 yx218))))\n  Enum a",fontsize=16,color="burlywood",shape="triangle"];4801[label="yx21200/Succ yx212000",fontsize=10,color="white",style="solid",shape="box"];3483 -> 4801[label="",style="solid", color="burlywood", weight=9];
4801 -> 3517[label="",style="solid", color="burlywood", weight=3];
4802[label="yx21200/Zero",fontsize=10,color="white",style="solid",shape="box"];3483 -> 4802[label="",style="solid", color="burlywood", weight=9];
4802 -> 3518[label="",style="solid", color="burlywood", weight=3];
4220 -> 3745[label="",style="dashed", color="red", weight=0];
4220[label="primPlusNat yx250 yx2370",fontsize=16,color="magenta"];4220 -> 4247[label="",style="dashed", color="magenta", weight=3];
4220 -> 4248[label="",style="dashed", color="magenta", weight=3];
4221 -> 3745[label="",style="dashed", color="red", weight=0];
4221[label="primPlusNat yx250 yx2370",fontsize=16,color="magenta"];4221 -> 4249[label="",style="dashed", color="magenta", weight=3];
4221 -> 4250[label="",style="dashed", color="magenta", weight=3];
4219[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (enforceWHNF (WHNF (Pos yx255)) (numericEnumFrom (Pos yx254))))\n  Enum a",fontsize=16,color="black",shape="triangle"];4219 -> 4251[label="",style="solid", color="black", weight=3];
4222[label="yx250",fontsize=16,color="green",shape="box"];4223[label="Neg Zero",fontsize=16,color="green",shape="box"];4224[label="yx2370",fontsize=16,color="green",shape="box"];3123[label="primMinusNatS (Succ yx2000) (Succ yx2010)",fontsize=16,color="black",shape="box"];3123 -> 3158[label="",style="solid", color="black", weight=3];
3124[label="primMinusNatS (Succ yx2000) Zero",fontsize=16,color="black",shape="box"];3124 -> 3159[label="",style="solid", color="black", weight=3];
3125[label="primMinusNatS Zero (Succ yx2010)",fontsize=16,color="black",shape="box"];3125 -> 3160[label="",style="solid", color="black", weight=3];
3126[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];3126 -> 3161[label="",style="solid", color="black", weight=3];
3179[label="map toEnum (Neg Zero : takeWhile (flip (<=) yx207) (numericEnumFrom $! Neg Zero + yx212))\n  Enum a",fontsize=16,color="black",shape="box"];3179 -> 3215[label="",style="solid", color="black", weight=3];
3180[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) False)\n  Enum a",fontsize=16,color="black",shape="box"];3180 -> 3216[label="",style="solid", color="black", weight=3];
3284[label="error []",fontsize=16,color="red",shape="box"];3285[label="error []",fontsize=16,color="red",shape="box"];3286[label="error []",fontsize=16,color="red",shape="box"];3287[label="error []",fontsize=16,color="red",shape="box"];3288[label="fromInt (Neg (Succ yx217))\n  Integral a",fontsize=16,color="black",shape="box"];3288 -> 3331[label="",style="solid", color="black", weight=3];
3289[label="error []",fontsize=16,color="red",shape="box"];3290[label="error []",fontsize=16,color="red",shape="box"];3291[label="error []",fontsize=16,color="red",shape="box"];3292[label="error []",fontsize=16,color="red",shape="box"];3293[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Neg (Succ yx218) + yx212)) (numericEnumFrom (Neg (Succ yx218) + yx212))))\n  Enum a",fontsize=16,color="black",shape="box"];3293 -> 3332[label="",style="solid", color="black", weight=3];
3294[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) False)\n  Enum a",fontsize=16,color="black",shape="box"];3294 -> 3333[label="",style="solid", color="black", weight=3];
297[label="map toEnum (takeWhile1 (flip (<=) (properFractionQ1 yx40 yx41 (primQrmInt yx40 yx41))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (properFractionQ1 yx40 yx41 (primQrmInt yx40 yx41)) == GT)))",fontsize=16,color="black",shape="box"];297 -> 323[label="",style="solid", color="black", weight=3];
3265[label="properFractionQ1 yx70 yx71 (primQrmInt yx70 yx71)",fontsize=16,color="black",shape="box"];3265 -> 3317[label="",style="solid", color="black", weight=3];
3069[label="fromInteger (properFractionQ1 (Integer yx700) (Integer yx710) (quotRem (Integer yx700) (Integer yx710)))",fontsize=16,color="black",shape="box"];3069 -> 3099[label="",style="solid", color="black", weight=3];
4535[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (primPlusInt (Pos yx274) yx275)) (numericEnumFrom (primPlusInt (Pos yx274) yx275))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4805[label="yx275/Pos yx2750",fontsize=10,color="white",style="solid",shape="box"];4535 -> 4805[label="",style="solid", color="burlywood", weight=9];
4805 -> 4536[label="",style="solid", color="burlywood", weight=3];
4806[label="yx275/Neg yx2750",fontsize=10,color="white",style="solid",shape="box"];4535 -> 4806[label="",style="solid", color="burlywood", weight=9];
4806 -> 4537[label="",style="solid", color="burlywood", weight=3];
4238[label="Pos yx249",fontsize=16,color="green",shape="box"];4239[label="Integer (Pos yx249)",fontsize=16,color="green",shape="box"];4240[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];4241[label="Succ Zero",fontsize=16,color="green",shape="box"];4242[label="yx2370",fontsize=16,color="green",shape="box"];4243[label="yx250",fontsize=16,color="green",shape="box"];3745[label="primPlusNat yx218 yx21200",fontsize=16,color="burlywood",shape="triangle"];4807[label="yx218/Succ yx2180",fontsize=10,color="white",style="solid",shape="box"];3745 -> 4807[label="",style="solid", color="burlywood", weight=9];
4807 -> 3759[label="",style="solid", color="burlywood", weight=3];
4808[label="yx218/Zero",fontsize=10,color="white",style="solid",shape="box"];3745 -> 4808[label="",style="solid", color="burlywood", weight=9];
4808 -> 3760[label="",style="solid", color="burlywood", weight=3];
4244[label="yx2370",fontsize=16,color="green",shape="box"];4245[label="yx250",fontsize=16,color="green",shape="box"];4246[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (numericEnumFrom (Pos yx252)))\n  Enum a",fontsize=16,color="black",shape="box"];4246 -> 4262[label="",style="solid", color="black", weight=3];
3517[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat (Succ yx212000) yx218)) (numericEnumFrom (primMinusNat (Succ yx212000) yx218))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4809[label="yx218/Succ yx2180",fontsize=10,color="white",style="solid",shape="box"];3517 -> 4809[label="",style="solid", color="burlywood", weight=9];
4809 -> 3525[label="",style="solid", color="burlywood", weight=3];
4810[label="yx218/Zero",fontsize=10,color="white",style="solid",shape="box"];3517 -> 4810[label="",style="solid", color="burlywood", weight=9];
4810 -> 3526[label="",style="solid", color="burlywood", weight=3];
3518[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat Zero yx218)) (numericEnumFrom (primMinusNat Zero yx218))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4811[label="yx218/Succ yx2180",fontsize=10,color="white",style="solid",shape="box"];3518 -> 4811[label="",style="solid", color="burlywood", weight=9];
4811 -> 3527[label="",style="solid", color="burlywood", weight=3];
4812[label="yx218/Zero",fontsize=10,color="white",style="solid",shape="box"];3518 -> 4812[label="",style="solid", color="burlywood", weight=9];
4812 -> 3528[label="",style="solid", color="burlywood", weight=3];
4247[label="yx2370",fontsize=16,color="green",shape="box"];4248[label="yx250",fontsize=16,color="green",shape="box"];4249[label="yx2370",fontsize=16,color="green",shape="box"];4250[label="yx250",fontsize=16,color="green",shape="box"];4251[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (numericEnumFrom (Pos yx254)))\n  Enum a",fontsize=16,color="black",shape="box"];4251 -> 4263[label="",style="solid", color="black", weight=3];
3158 -> 3057[label="",style="dashed", color="red", weight=0];
3158[label="primMinusNatS yx2000 yx2010",fontsize=16,color="magenta"];3158 -> 3181[label="",style="dashed", color="magenta", weight=3];
3158 -> 3182[label="",style="dashed", color="magenta", weight=3];
3159[label="Succ yx2000",fontsize=16,color="green",shape="box"];3160[label="Zero",fontsize=16,color="green",shape="box"];3161[label="Zero",fontsize=16,color="green",shape="box"];3215[label="toEnum (Neg Zero) : map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom $! Neg Zero + yx212))\n  Enum a",fontsize=16,color="green",shape="box"];3215 -> 3252[label="",style="dashed", color="green", weight=3];
3215 -> 3253[label="",style="dashed", color="green", weight=3];
3216[label="map toEnum (takeWhile0 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) otherwise)\n  Enum a",fontsize=16,color="black",shape="box"];3216 -> 3254[label="",style="solid", color="black", weight=3];
3331[label="intToRatio (Neg (Succ yx217))\n  Integral a",fontsize=16,color="black",shape="box"];3331 -> 3349[label="",style="solid", color="black", weight=3];
3332[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primPlusInt (Neg (Succ yx218)) yx212)) (numericEnumFrom (primPlusInt (Neg (Succ yx218)) yx212))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4814[label="yx212/Pos yx2120",fontsize=10,color="white",style="solid",shape="box"];3332 -> 4814[label="",style="solid", color="burlywood", weight=9];
4814 -> 3350[label="",style="solid", color="burlywood", weight=3];
4815[label="yx212/Neg yx2120",fontsize=10,color="white",style="solid",shape="box"];3332 -> 4815[label="",style="solid", color="burlywood", weight=9];
4815 -> 3351[label="",style="solid", color="burlywood", weight=3];
3333[label="map toEnum (takeWhile0 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) otherwise)\n  Enum a",fontsize=16,color="black",shape="box"];3333 -> 3352[label="",style="solid", color="black", weight=3];
323[label="map toEnum (takeWhile1 (flip (<=) (properFractionQ1 yx40 yx41 (primQuotInt yx40 yx41,primRemInt yx40 yx41))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (properFractionQ1 yx40 yx41 (primQuotInt yx40 yx41,primRemInt yx40 yx41)) == GT)))",fontsize=16,color="black",shape="box"];323 -> 353[label="",style="solid", color="black", weight=3];
3317 -> 3347[label="",style="dashed", color="red", weight=0];
3317[label="properFractionQ1 yx70 yx71 (primQuotInt yx70 yx71,primRemInt yx70 yx71)",fontsize=16,color="magenta"];3317 -> 3348[label="",style="dashed", color="magenta", weight=3];
3099[label="fromInteger (properFractionQ1 (Integer yx700) (Integer yx710) (Integer (primQuotInt yx700 yx710),Integer (primRemInt yx700 yx710)))",fontsize=16,color="black",shape="box"];3099 -> 3131[label="",style="solid", color="black", weight=3];
4536[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (primPlusInt (Pos yx274) (Pos yx2750))) (numericEnumFrom (primPlusInt (Pos yx274) (Pos yx2750)))))\n  Enum a",fontsize=16,color="black",shape="box"];4536 -> 4538[label="",style="solid", color="black", weight=3];
4537[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (primPlusInt (Pos yx274) (Neg yx2750))) (numericEnumFrom (primPlusInt (Pos yx274) (Neg yx2750)))))\n  Enum a",fontsize=16,color="black",shape="box"];4537 -> 4539[label="",style="solid", color="black", weight=3];
3759[label="primPlusNat (Succ yx2180) yx21200",fontsize=16,color="burlywood",shape="box"];4817[label="yx21200/Succ yx212000",fontsize=10,color="white",style="solid",shape="box"];3759 -> 4817[label="",style="solid", color="burlywood", weight=9];
4817 -> 4023[label="",style="solid", color="burlywood", weight=3];
4818[label="yx21200/Zero",fontsize=10,color="white",style="solid",shape="box"];3759 -> 4818[label="",style="solid", color="burlywood", weight=9];
4818 -> 4024[label="",style="solid", color="burlywood", weight=3];
3760[label="primPlusNat Zero yx21200",fontsize=16,color="burlywood",shape="box"];4819[label="yx21200/Succ yx212000",fontsize=10,color="white",style="solid",shape="box"];3760 -> 4819[label="",style="solid", color="burlywood", weight=9];
4819 -> 4025[label="",style="solid", color="burlywood", weight=3];
4820[label="yx21200/Zero",fontsize=10,color="white",style="solid",shape="box"];3760 -> 4820[label="",style="solid", color="burlywood", weight=9];
4820 -> 4026[label="",style="solid", color="burlywood", weight=3];
4262 -> 4271[label="",style="dashed", color="red", weight=0];
4262[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (Pos yx252 : (numericEnumFrom $! Pos yx252 + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];4262 -> 4272[label="",style="dashed", color="magenta", weight=3];
3525[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat (Succ yx212000) (Succ yx2180))) (numericEnumFrom (primMinusNat (Succ yx212000) (Succ yx2180)))))\n  Enum a",fontsize=16,color="black",shape="box"];3525 -> 3550[label="",style="solid", color="black", weight=3];
3526[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat (Succ yx212000) Zero)) (numericEnumFrom (primMinusNat (Succ yx212000) Zero))))\n  Enum a",fontsize=16,color="black",shape="box"];3526 -> 3551[label="",style="solid", color="black", weight=3];
3527[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat Zero (Succ yx2180))) (numericEnumFrom (primMinusNat Zero (Succ yx2180)))))\n  Enum a",fontsize=16,color="black",shape="box"];3527 -> 3552[label="",style="solid", color="black", weight=3];
3528[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat Zero Zero)) (numericEnumFrom (primMinusNat Zero Zero))))\n  Enum a",fontsize=16,color="black",shape="box"];3528 -> 3553[label="",style="solid", color="black", weight=3];
4263 -> 4273[label="",style="dashed", color="red", weight=0];
4263[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (Pos yx254 : (numericEnumFrom $! Pos yx254 + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];4263 -> 4274[label="",style="dashed", color="magenta", weight=3];
3181[label="yx2010",fontsize=16,color="green",shape="box"];3182[label="yx2000",fontsize=16,color="green",shape="box"];3252[label="toEnum (Neg Zero)\n  Enum a",fontsize=16,color="blue",shape="box"];4823[label="toEnum :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4823[label="",style="solid", color="blue", weight=9];
4823 -> 3296[label="",style="solid", color="blue", weight=3];
4824[label="toEnum :: Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4824[label="",style="solid", color="blue", weight=9];
4824 -> 3297[label="",style="solid", color="blue", weight=3];
4825[label="toEnum :: Int -> ()",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4825[label="",style="solid", color="blue", weight=9];
4825 -> 3298[label="",style="solid", color="blue", weight=3];
4826[label="toEnum :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4826[label="",style="solid", color="blue", weight=9];
4826 -> 3299[label="",style="solid", color="blue", weight=3];
4827[label="toEnum :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4827[label="",style="solid", color="blue", weight=9];
4827 -> 3300[label="",style="solid", color="blue", weight=3];
4828[label="toEnum :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4828[label="",style="solid", color="blue", weight=9];
4828 -> 3301[label="",style="solid", color="blue", weight=3];
4829[label="toEnum :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4829[label="",style="solid", color="blue", weight=9];
4829 -> 3302[label="",style="solid", color="blue", weight=3];
4830[label="toEnum :: Int -> Char",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4830[label="",style="solid", color="blue", weight=9];
4830 -> 3303[label="",style="solid", color="blue", weight=3];
4831[label="toEnum :: Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];3252 -> 4831[label="",style="solid", color="blue", weight=9];
4831 -> 3304[label="",style="solid", color="blue", weight=3];
3253[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom $! Neg Zero + yx212))\n  Enum a",fontsize=16,color="black",shape="box"];3253 -> 3305[label="",style="solid", color="black", weight=3];
3254[label="map toEnum (takeWhile0 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx212) True)\n  Enum a",fontsize=16,color="black",shape="box"];3254 -> 3306[label="",style="solid", color="black", weight=3];
3349[label="fromInt (Neg (Succ yx217)) :% fromInt (Pos (Succ Zero))\n  Integral a",fontsize=16,color="green",shape="box"];3349 -> 3401[label="",style="dashed", color="green", weight=3];
3349 -> 3402[label="",style="dashed", color="green", weight=3];
3350[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primPlusInt (Neg (Succ yx218)) (Pos yx2120))) (numericEnumFrom (primPlusInt (Neg (Succ yx218)) (Pos yx2120)))))\n  Enum a",fontsize=16,color="black",shape="box"];3350 -> 3403[label="",style="solid", color="black", weight=3];
3351[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primPlusInt (Neg (Succ yx218)) (Neg yx2120))) (numericEnumFrom (primPlusInt (Neg (Succ yx218)) (Neg yx2120)))))\n  Enum a",fontsize=16,color="black",shape="box"];3351 -> 3404[label="",style="solid", color="black", weight=3];
3352[label="map toEnum (takeWhile0 (flip (<=) yx207) (Neg (Succ yx217)) (numericEnumFrom $! Neg (Succ yx218) + yx212) True)\n  Enum a",fontsize=16,color="black",shape="box"];3352 -> 3405[label="",style="solid", color="black", weight=3];
353[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt yx40 yx41)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt yx40 yx41) == GT)))",fontsize=16,color="burlywood",shape="box"];4832[label="yx40/Pos yx400",fontsize=10,color="white",style="solid",shape="box"];353 -> 4832[label="",style="solid", color="burlywood", weight=9];
4832 -> 385[label="",style="solid", color="burlywood", weight=3];
4833[label="yx40/Neg yx400",fontsize=10,color="white",style="solid",shape="box"];353 -> 4833[label="",style="solid", color="burlywood", weight=9];
4833 -> 386[label="",style="solid", color="burlywood", weight=3];
3348 -> 3168[label="",style="dashed", color="red", weight=0];
3348[label="primQuotInt yx70 yx71",fontsize=16,color="magenta"];3348 -> 3360[label="",style="dashed", color="magenta", weight=3];
3348 -> 3361[label="",style="dashed", color="magenta", weight=3];
3347[label="properFractionQ1 yx70 yx71 (yx224,primRemInt yx70 yx71)",fontsize=16,color="black",shape="triangle"];3347 -> 3362[label="",style="solid", color="black", weight=3];
3131 -> 3166[label="",style="dashed", color="red", weight=0];
3131[label="fromInteger (Integer (primQuotInt yx700 yx710))",fontsize=16,color="magenta"];3131 -> 3168[label="",style="dashed", color="magenta", weight=3];
4538 -> 4540[label="",style="dashed", color="red", weight=0];
4538[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (Pos (primPlusNat yx274 yx2750))) (numericEnumFrom (Pos (primPlusNat yx274 yx2750)))))\n  Enum a",fontsize=16,color="magenta"];4538 -> 4541[label="",style="dashed", color="magenta", weight=3];
4538 -> 4542[label="",style="dashed", color="magenta", weight=3];
4539 -> 3483[label="",style="dashed", color="red", weight=0];
4539[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (primMinusNat yx274 yx2750)) (numericEnumFrom (primMinusNat yx274 yx2750))))\n  Enum a",fontsize=16,color="magenta"];4539 -> 4543[label="",style="dashed", color="magenta", weight=3];
4539 -> 4544[label="",style="dashed", color="magenta", weight=3];
4539 -> 4545[label="",style="dashed", color="magenta", weight=3];
4023[label="primPlusNat (Succ yx2180) (Succ yx212000)",fontsize=16,color="black",shape="box"];4023 -> 4042[label="",style="solid", color="black", weight=3];
4024[label="primPlusNat (Succ yx2180) Zero",fontsize=16,color="black",shape="box"];4024 -> 4043[label="",style="solid", color="black", weight=3];
4025[label="primPlusNat Zero (Succ yx212000)",fontsize=16,color="black",shape="box"];4025 -> 4044[label="",style="solid", color="black", weight=3];
4026[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];4026 -> 4045[label="",style="solid", color="black", weight=3];
4272 -> 576[label="",style="dashed", color="red", weight=0];
4272[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4272 -> 4284[label="",style="dashed", color="magenta", weight=3];
4271[label="map toEnum (takeWhile (flip (<=) (Pos Zero)) (Pos yx252 : (numericEnumFrom $! Pos yx252 + yx258)))\n  Enum a",fontsize=16,color="black",shape="triangle"];4271 -> 4285[label="",style="solid", color="black", weight=3];
3550 -> 3483[label="",style="dashed", color="red", weight=0];
3550[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat yx212000 yx2180)) (numericEnumFrom (primMinusNat yx212000 yx2180))))\n  Enum a",fontsize=16,color="magenta"];3550 -> 3568[label="",style="dashed", color="magenta", weight=3];
3550 -> 3569[label="",style="dashed", color="magenta", weight=3];
3551[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Pos (Succ yx212000))) (numericEnumFrom (Pos (Succ yx212000)))))\n  Enum a",fontsize=16,color="black",shape="triangle"];3551 -> 3570[label="",style="solid", color="black", weight=3];
3552 -> 3484[label="",style="dashed", color="red", weight=0];
3552[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Neg (Succ yx2180))) (numericEnumFrom (Neg (Succ yx2180)))))\n  Enum a",fontsize=16,color="magenta"];3552 -> 3571[label="",style="dashed", color="magenta", weight=3];
3553[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Pos Zero)) (numericEnumFrom (Pos Zero))))\n  Enum a",fontsize=16,color="black",shape="triangle"];3553 -> 3572[label="",style="solid", color="black", weight=3];
4274 -> 576[label="",style="dashed", color="red", weight=0];
4274[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4274 -> 4286[label="",style="dashed", color="magenta", weight=3];
4273[label="map toEnum (takeWhile (flip (<=) (Neg Zero)) (Pos yx254 : (numericEnumFrom $! Pos yx254 + yx259)))\n  Enum a",fontsize=16,color="black",shape="triangle"];4273 -> 4287[label="",style="solid", color="black", weight=3];
3296[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3296 -> 3335[label="",style="solid", color="black", weight=3];
3297[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3297 -> 3336[label="",style="solid", color="black", weight=3];
3298[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3298 -> 3337[label="",style="solid", color="black", weight=3];
3299[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3299 -> 3338[label="",style="solid", color="black", weight=3];
3300[label="toEnum (Neg Zero)\n  Integral a",fontsize=16,color="black",shape="box"];3300 -> 3339[label="",style="solid", color="black", weight=3];
3301[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3301 -> 3340[label="",style="solid", color="black", weight=3];
3302[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3302 -> 3341[label="",style="solid", color="black", weight=3];
3303[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3303 -> 3342[label="",style="solid", color="black", weight=3];
3304[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];3304 -> 3343[label="",style="solid", color="black", weight=3];
3305[label="map toEnum (takeWhile (flip (<=) yx207) (Neg Zero + yx212 `seq` numericEnumFrom (Neg Zero + yx212)))\n  Enum a",fontsize=16,color="black",shape="box"];3305 -> 3344[label="",style="solid", color="black", weight=3];
3306 -> 3178[label="",style="dashed", color="red", weight=0];
3306[label="map toEnum []\n  Enum a",fontsize=16,color="magenta"];3401[label="fromInt (Neg (Succ yx217))\n  Integral a",fontsize=16,color="blue",shape="box"];4843[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3401 -> 4843[label="",style="solid", color="blue", weight=9];
4843 -> 3442[label="",style="solid", color="blue", weight=3];
4844[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];3401 -> 4844[label="",style="solid", color="blue", weight=9];
4844 -> 3443[label="",style="solid", color="blue", weight=3];
3402[label="fromInt (Pos (Succ Zero))\n  Integral a",fontsize=16,color="blue",shape="box"];4845[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];3402 -> 4845[label="",style="solid", color="blue", weight=9];
4845 -> 3444[label="",style="solid", color="blue", weight=3];
4846[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];3402 -> 4846[label="",style="solid", color="blue", weight=9];
4846 -> 3445[label="",style="solid", color="blue", weight=3];
3403[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat yx2120 (Succ yx218))) (numericEnumFrom (primMinusNat yx2120 (Succ yx218)))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4847[label="yx2120/Succ yx21200",fontsize=10,color="white",style="solid",shape="box"];3403 -> 4847[label="",style="solid", color="burlywood", weight=9];
4847 -> 3446[label="",style="solid", color="burlywood", weight=3];
4848[label="yx2120/Zero",fontsize=10,color="white",style="solid",shape="box"];3403 -> 4848[label="",style="solid", color="burlywood", weight=9];
4848 -> 3447[label="",style="solid", color="burlywood", weight=3];
3404[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Neg (primPlusNat (Succ yx218) yx2120))) (numericEnumFrom (Neg (primPlusNat (Succ yx218) yx2120)))))\n  Enum a",fontsize=16,color="black",shape="box"];3404 -> 3448[label="",style="solid", color="black", weight=3];
3405 -> 3178[label="",style="dashed", color="red", weight=0];
3405[label="map toEnum []\n  Enum a",fontsize=16,color="magenta"];385[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) yx41)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) yx41) == GT)))",fontsize=16,color="burlywood",shape="box"];4850[label="yx41/Pos yx410",fontsize=10,color="white",style="solid",shape="box"];385 -> 4850[label="",style="solid", color="burlywood", weight=9];
4850 -> 422[label="",style="solid", color="burlywood", weight=3];
4851[label="yx41/Neg yx410",fontsize=10,color="white",style="solid",shape="box"];385 -> 4851[label="",style="solid", color="burlywood", weight=9];
4851 -> 423[label="",style="solid", color="burlywood", weight=3];
386[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) yx41)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) yx41) == GT)))",fontsize=16,color="burlywood",shape="box"];4852[label="yx41/Pos yx410",fontsize=10,color="white",style="solid",shape="box"];386 -> 4852[label="",style="solid", color="burlywood", weight=9];
4852 -> 424[label="",style="solid", color="burlywood", weight=3];
4853[label="yx41/Neg yx410",fontsize=10,color="white",style="solid",shape="box"];386 -> 4853[label="",style="solid", color="burlywood", weight=9];
4853 -> 425[label="",style="solid", color="burlywood", weight=3];
3360[label="yx71",fontsize=16,color="green",shape="box"];3361[label="yx70",fontsize=16,color="green",shape="box"];3168[label="primQuotInt yx700 yx710",fontsize=16,color="burlywood",shape="triangle"];4854[label="yx700/Pos yx7000",fontsize=10,color="white",style="solid",shape="box"];3168 -> 4854[label="",style="solid", color="burlywood", weight=9];
4854 -> 3187[label="",style="solid", color="burlywood", weight=3];
4855[label="yx700/Neg yx7000",fontsize=10,color="white",style="solid",shape="box"];3168 -> 4855[label="",style="solid", color="burlywood", weight=9];
4855 -> 3188[label="",style="solid", color="burlywood", weight=3];
3362[label="yx224",fontsize=16,color="green",shape="box"];4541 -> 3745[label="",style="dashed", color="red", weight=0];
4541[label="primPlusNat yx274 yx2750",fontsize=16,color="magenta"];4541 -> 4546[label="",style="dashed", color="magenta", weight=3];
4541 -> 4547[label="",style="dashed", color="magenta", weight=3];
4542 -> 3745[label="",style="dashed", color="red", weight=0];
4542[label="primPlusNat yx274 yx2750",fontsize=16,color="magenta"];4542 -> 4548[label="",style="dashed", color="magenta", weight=3];
4542 -> 4549[label="",style="dashed", color="magenta", weight=3];
4540[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (enforceWHNF (WHNF (Pos yx279)) (numericEnumFrom (Pos yx278))))\n  Enum a",fontsize=16,color="black",shape="triangle"];4540 -> 4550[label="",style="solid", color="black", weight=3];
4543[label="yx274",fontsize=16,color="green",shape="box"];4544[label="Pos (Succ yx272)",fontsize=16,color="green",shape="box"];4545[label="yx2750",fontsize=16,color="green",shape="box"];4042[label="Succ (Succ (primPlusNat yx2180 yx212000))",fontsize=16,color="green",shape="box"];4042 -> 4053[label="",style="dashed", color="green", weight=3];
4043[label="Succ yx2180",fontsize=16,color="green",shape="box"];4044[label="Succ yx212000",fontsize=16,color="green",shape="box"];4045[label="Zero",fontsize=16,color="green",shape="box"];4284[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];4285[label="map toEnum (takeWhile2 (flip (<=) (Pos Zero)) (Pos yx252 : (numericEnumFrom $! Pos yx252 + yx258)))\n  Enum a",fontsize=16,color="black",shape="box"];4285 -> 4295[label="",style="solid", color="black", weight=3];
3568[label="yx212000",fontsize=16,color="green",shape="box"];3569[label="yx2180",fontsize=16,color="green",shape="box"];3570[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom (Pos (Succ yx212000))))\n  Enum a",fontsize=16,color="black",shape="box"];3570 -> 3593[label="",style="solid", color="black", weight=3];
3571[label="yx2180",fontsize=16,color="green",shape="box"];3484[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Neg (Succ yx218))) (numericEnumFrom (Neg (Succ yx218)))))\n  Enum a",fontsize=16,color="black",shape="triangle"];3484 -> 3519[label="",style="solid", color="black", weight=3];
3572[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom (Pos Zero)))\n  Enum a",fontsize=16,color="black",shape="box"];3572 -> 3594[label="",style="solid", color="black", weight=3];
4286[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];4287[label="map toEnum (takeWhile2 (flip (<=) (Neg Zero)) (Pos yx254 : (numericEnumFrom $! Pos yx254 + yx259)))\n  Enum a",fontsize=16,color="black",shape="box"];4287 -> 4296[label="",style="solid", color="black", weight=3];
3335[label="error []",fontsize=16,color="red",shape="box"];3336[label="error []",fontsize=16,color="red",shape="box"];3337[label="error []",fontsize=16,color="red",shape="box"];3338[label="error []",fontsize=16,color="red",shape="box"];3339[label="fromInt (Neg Zero)\n  Integral a",fontsize=16,color="black",shape="box"];3339 -> 3355[label="",style="solid", color="black", weight=3];
3340[label="error []",fontsize=16,color="red",shape="box"];3341[label="error []",fontsize=16,color="red",shape="box"];3342[label="error []",fontsize=16,color="red",shape="box"];3343[label="error []",fontsize=16,color="red",shape="box"];3344[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Neg Zero + yx212)) (numericEnumFrom (Neg Zero + yx212))))\n  Enum a",fontsize=16,color="black",shape="box"];3344 -> 3356[label="",style="solid", color="black", weight=3];
3442 -> 576[label="",style="dashed", color="red", weight=0];
3442[label="fromInt (Neg (Succ yx217))",fontsize=16,color="magenta"];3442 -> 3479[label="",style="dashed", color="magenta", weight=3];
3443[label="fromInt (Neg (Succ yx217))",fontsize=16,color="black",shape="box"];3443 -> 3480[label="",style="solid", color="black", weight=3];
3444 -> 576[label="",style="dashed", color="red", weight=0];
3444[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3444 -> 3481[label="",style="dashed", color="magenta", weight=3];
3445[label="fromInt (Pos (Succ Zero))",fontsize=16,color="black",shape="triangle"];3445 -> 3482[label="",style="solid", color="black", weight=3];
3446[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat (Succ yx21200) (Succ yx218))) (numericEnumFrom (primMinusNat (Succ yx21200) (Succ yx218)))))\n  Enum a",fontsize=16,color="black",shape="box"];3446 -> 3483[label="",style="solid", color="black", weight=3];
3447[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat Zero (Succ yx218))) (numericEnumFrom (primMinusNat Zero (Succ yx218)))))\n  Enum a",fontsize=16,color="black",shape="box"];3447 -> 3484[label="",style="solid", color="black", weight=3];
3448[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom (Neg (primPlusNat (Succ yx218) yx2120))))\n  Enum a",fontsize=16,color="black",shape="box"];3448 -> 3485[label="",style="solid", color="black", weight=3];
422[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) (Pos yx410))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) (Pos yx410)) == GT)))",fontsize=16,color="burlywood",shape="box"];4860[label="yx410/Succ yx4100",fontsize=10,color="white",style="solid",shape="box"];422 -> 4860[label="",style="solid", color="burlywood", weight=9];
4860 -> 475[label="",style="solid", color="burlywood", weight=3];
4861[label="yx410/Zero",fontsize=10,color="white",style="solid",shape="box"];422 -> 4861[label="",style="solid", color="burlywood", weight=9];
4861 -> 476[label="",style="solid", color="burlywood", weight=3];
423[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) (Neg yx410))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) (Neg yx410)) == GT)))",fontsize=16,color="burlywood",shape="box"];4862[label="yx410/Succ yx4100",fontsize=10,color="white",style="solid",shape="box"];423 -> 4862[label="",style="solid", color="burlywood", weight=9];
4862 -> 477[label="",style="solid", color="burlywood", weight=3];
4863[label="yx410/Zero",fontsize=10,color="white",style="solid",shape="box"];423 -> 4863[label="",style="solid", color="burlywood", weight=9];
4863 -> 478[label="",style="solid", color="burlywood", weight=3];
424[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) (Pos yx410))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) (Pos yx410)) == GT)))",fontsize=16,color="burlywood",shape="box"];4864[label="yx410/Succ yx4100",fontsize=10,color="white",style="solid",shape="box"];424 -> 4864[label="",style="solid", color="burlywood", weight=9];
4864 -> 479[label="",style="solid", color="burlywood", weight=3];
4865[label="yx410/Zero",fontsize=10,color="white",style="solid",shape="box"];424 -> 4865[label="",style="solid", color="burlywood", weight=9];
4865 -> 480[label="",style="solid", color="burlywood", weight=3];
425[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) (Neg yx410))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) (Neg yx410)) == GT)))",fontsize=16,color="burlywood",shape="box"];4866[label="yx410/Succ yx4100",fontsize=10,color="white",style="solid",shape="box"];425 -> 4866[label="",style="solid", color="burlywood", weight=9];
4866 -> 481[label="",style="solid", color="burlywood", weight=3];
4867[label="yx410/Zero",fontsize=10,color="white",style="solid",shape="box"];425 -> 4867[label="",style="solid", color="burlywood", weight=9];
4867 -> 482[label="",style="solid", color="burlywood", weight=3];
3187[label="primQuotInt (Pos yx7000) yx710",fontsize=16,color="burlywood",shape="box"];4868[label="yx710/Pos yx7100",fontsize=10,color="white",style="solid",shape="box"];3187 -> 4868[label="",style="solid", color="burlywood", weight=9];
4868 -> 3221[label="",style="solid", color="burlywood", weight=3];
4869[label="yx710/Neg yx7100",fontsize=10,color="white",style="solid",shape="box"];3187 -> 4869[label="",style="solid", color="burlywood", weight=9];
4869 -> 3222[label="",style="solid", color="burlywood", weight=3];
3188[label="primQuotInt (Neg yx7000) yx710",fontsize=16,color="burlywood",shape="box"];4870[label="yx710/Pos yx7100",fontsize=10,color="white",style="solid",shape="box"];3188 -> 4870[label="",style="solid", color="burlywood", weight=9];
4870 -> 3223[label="",style="solid", color="burlywood", weight=3];
4871[label="yx710/Neg yx7100",fontsize=10,color="white",style="solid",shape="box"];3188 -> 4871[label="",style="solid", color="burlywood", weight=9];
4871 -> 3224[label="",style="solid", color="burlywood", weight=3];
4546[label="yx2750",fontsize=16,color="green",shape="box"];4547[label="yx274",fontsize=16,color="green",shape="box"];4548[label="yx2750",fontsize=16,color="green",shape="box"];4549[label="yx274",fontsize=16,color="green",shape="box"];4550[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (numericEnumFrom (Pos yx278)))\n  Enum a",fontsize=16,color="black",shape="box"];4550 -> 4551[label="",style="solid", color="black", weight=3];
4053 -> 3745[label="",style="dashed", color="red", weight=0];
4053[label="primPlusNat yx2180 yx212000",fontsize=16,color="magenta"];4053 -> 4063[label="",style="dashed", color="magenta", weight=3];
4053 -> 4064[label="",style="dashed", color="magenta", weight=3];
4295[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx252) (numericEnumFrom $! Pos yx252 + yx258) (flip (<=) (Pos Zero) (Pos yx252)))\n  Enum a",fontsize=16,color="black",shape="box"];4295 -> 4304[label="",style="solid", color="black", weight=3];
3593 -> 3611[label="",style="dashed", color="red", weight=0];
3593[label="map toEnum (takeWhile (flip (<=) yx207) (Pos (Succ yx212000) : (numericEnumFrom $! Pos (Succ yx212000) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];3593 -> 3612[label="",style="dashed", color="magenta", weight=3];
3519[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom (Neg (Succ yx218))))\n  Enum a",fontsize=16,color="black",shape="box"];3519 -> 3529[label="",style="solid", color="black", weight=3];
3594 -> 3616[label="",style="dashed", color="red", weight=0];
3594[label="map toEnum (takeWhile (flip (<=) yx207) (Pos Zero : (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];3594 -> 3617[label="",style="dashed", color="magenta", weight=3];
4296[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx254) (numericEnumFrom $! Pos yx254 + yx259) (flip (<=) (Neg Zero) (Pos yx254)))\n  Enum a",fontsize=16,color="black",shape="box"];4296 -> 4305[label="",style="solid", color="black", weight=3];
3355[label="intToRatio (Neg Zero)\n  Integral a",fontsize=16,color="black",shape="box"];3355 -> 3416[label="",style="solid", color="black", weight=3];
3356[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primPlusInt (Neg Zero) yx212)) (numericEnumFrom (primPlusInt (Neg Zero) yx212))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4875[label="yx212/Pos yx2120",fontsize=10,color="white",style="solid",shape="box"];3356 -> 4875[label="",style="solid", color="burlywood", weight=9];
4875 -> 3417[label="",style="solid", color="burlywood", weight=3];
4876[label="yx212/Neg yx2120",fontsize=10,color="white",style="solid",shape="box"];3356 -> 4876[label="",style="solid", color="burlywood", weight=9];
4876 -> 3418[label="",style="solid", color="burlywood", weight=3];
3479[label="Neg (Succ yx217)",fontsize=16,color="green",shape="box"];3480[label="Integer (Neg (Succ yx217))",fontsize=16,color="green",shape="box"];3481[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3482[label="Integer (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];3485 -> 3520[label="",style="dashed", color="red", weight=0];
3485[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120) : (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];3485 -> 3521[label="",style="dashed", color="magenta", weight=3];
475[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) (Pos (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) (Pos (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];475 -> 534[label="",style="solid", color="black", weight=3];
476[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) (Pos Zero))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) (Pos Zero)) == GT)))",fontsize=16,color="black",shape="box"];476 -> 535[label="",style="solid", color="black", weight=3];
477[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) (Neg (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) (Neg (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];477 -> 536[label="",style="solid", color="black", weight=3];
478[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Pos yx400) (Neg Zero))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Pos yx400) (Neg Zero)) == GT)))",fontsize=16,color="black",shape="box"];478 -> 537[label="",style="solid", color="black", weight=3];
479[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) (Pos (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) (Pos (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];479 -> 538[label="",style="solid", color="black", weight=3];
480[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) (Pos Zero))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) (Pos Zero)) == GT)))",fontsize=16,color="black",shape="box"];480 -> 539[label="",style="solid", color="black", weight=3];
481[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) (Neg (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) (Neg (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];481 -> 540[label="",style="solid", color="black", weight=3];
482[label="map toEnum (takeWhile1 (flip (<=) (primQuotInt (Neg yx400) (Neg Zero))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (primQuotInt (Neg yx400) (Neg Zero)) == GT)))",fontsize=16,color="black",shape="box"];482 -> 541[label="",style="solid", color="black", weight=3];
3221[label="primQuotInt (Pos yx7000) (Pos yx7100)",fontsize=16,color="burlywood",shape="box"];4878[label="yx7100/Succ yx71000",fontsize=10,color="white",style="solid",shape="box"];3221 -> 4878[label="",style="solid", color="burlywood", weight=9];
4878 -> 3266[label="",style="solid", color="burlywood", weight=3];
4879[label="yx7100/Zero",fontsize=10,color="white",style="solid",shape="box"];3221 -> 4879[label="",style="solid", color="burlywood", weight=9];
4879 -> 3267[label="",style="solid", color="burlywood", weight=3];
3222[label="primQuotInt (Pos yx7000) (Neg yx7100)",fontsize=16,color="burlywood",shape="box"];4880[label="yx7100/Succ yx71000",fontsize=10,color="white",style="solid",shape="box"];3222 -> 4880[label="",style="solid", color="burlywood", weight=9];
4880 -> 3268[label="",style="solid", color="burlywood", weight=3];
4881[label="yx7100/Zero",fontsize=10,color="white",style="solid",shape="box"];3222 -> 4881[label="",style="solid", color="burlywood", weight=9];
4881 -> 3269[label="",style="solid", color="burlywood", weight=3];
3223[label="primQuotInt (Neg yx7000) (Pos yx7100)",fontsize=16,color="burlywood",shape="box"];4882[label="yx7100/Succ yx71000",fontsize=10,color="white",style="solid",shape="box"];3223 -> 4882[label="",style="solid", color="burlywood", weight=9];
4882 -> 3270[label="",style="solid", color="burlywood", weight=3];
4883[label="yx7100/Zero",fontsize=10,color="white",style="solid",shape="box"];3223 -> 4883[label="",style="solid", color="burlywood", weight=9];
4883 -> 3271[label="",style="solid", color="burlywood", weight=3];
3224[label="primQuotInt (Neg yx7000) (Neg yx7100)",fontsize=16,color="burlywood",shape="box"];4884[label="yx7100/Succ yx71000",fontsize=10,color="white",style="solid",shape="box"];3224 -> 4884[label="",style="solid", color="burlywood", weight=9];
4884 -> 3272[label="",style="solid", color="burlywood", weight=3];
4885[label="yx7100/Zero",fontsize=10,color="white",style="solid",shape="box"];3224 -> 4885[label="",style="solid", color="burlywood", weight=9];
4885 -> 3273[label="",style="solid", color="burlywood", weight=3];
4551 -> 4552[label="",style="dashed", color="red", weight=0];
4551[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (Pos yx278 : (numericEnumFrom $! Pos yx278 + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];4551 -> 4553[label="",style="dashed", color="magenta", weight=3];
4063[label="yx212000",fontsize=16,color="green",shape="box"];4064[label="yx2180",fontsize=16,color="green",shape="box"];4304[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx252) (numericEnumFrom $! Pos yx252 + yx258) ((<=) Pos yx252 Pos Zero))\n  Enum a",fontsize=16,color="black",shape="box"];4304 -> 4314[label="",style="solid", color="black", weight=3];
3612 -> 576[label="",style="dashed", color="red", weight=0];
3612[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3612 -> 3628[label="",style="dashed", color="magenta", weight=3];
3611[label="map toEnum (takeWhile (flip (<=) yx207) (Pos (Succ yx212000) : (numericEnumFrom $! Pos (Succ yx212000) + yx238)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3611 -> 3629[label="",style="solid", color="black", weight=3];
3529 -> 3554[label="",style="dashed", color="red", weight=0];
3529[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (Succ yx218) : (numericEnumFrom $! Neg (Succ yx218) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];3529 -> 3555[label="",style="dashed", color="magenta", weight=3];
3617 -> 576[label="",style="dashed", color="red", weight=0];
3617[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3617 -> 3630[label="",style="dashed", color="magenta", weight=3];
3616[label="map toEnum (takeWhile (flip (<=) yx207) (Pos Zero : (numericEnumFrom $! Pos Zero + yx239)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3616 -> 3631[label="",style="solid", color="black", weight=3];
4305[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx254) (numericEnumFrom $! Pos yx254 + yx259) ((<=) Pos yx254 Neg Zero))\n  Enum a",fontsize=16,color="black",shape="box"];4305 -> 4315[label="",style="solid", color="black", weight=3];
3416[label="fromInt (Neg Zero) :% fromInt (Pos (Succ Zero))\n  Integral a",fontsize=16,color="green",shape="box"];3416 -> 3459[label="",style="dashed", color="green", weight=3];
3416 -> 3460[label="",style="dashed", color="green", weight=3];
3417[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primPlusInt (Neg Zero) (Pos yx2120))) (numericEnumFrom (primPlusInt (Neg Zero) (Pos yx2120)))))\n  Enum a",fontsize=16,color="black",shape="box"];3417 -> 3461[label="",style="solid", color="black", weight=3];
3418[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primPlusInt (Neg Zero) (Neg yx2120))) (numericEnumFrom (primPlusInt (Neg Zero) (Neg yx2120)))))\n  Enum a",fontsize=16,color="black",shape="box"];3418 -> 3462[label="",style="solid", color="black", weight=3];
3521 -> 576[label="",style="dashed", color="red", weight=0];
3521[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3521 -> 3530[label="",style="dashed", color="magenta", weight=3];
3520[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120) : (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3520 -> 3531[label="",style="solid", color="black", weight=3];
534[label="map toEnum (takeWhile1 (flip (<=) (Pos (primDivNatS yx400 (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Pos (primDivNatS yx400 (Succ yx4100))) == GT)))",fontsize=16,color="burlywood",shape="triangle"];4891[label="yx400/Succ yx4000",fontsize=10,color="white",style="solid",shape="box"];534 -> 4891[label="",style="solid", color="burlywood", weight=9];
4891 -> 592[label="",style="solid", color="burlywood", weight=3];
4892[label="yx400/Zero",fontsize=10,color="white",style="solid",shape="box"];534 -> 4892[label="",style="solid", color="burlywood", weight=9];
4892 -> 593[label="",style="solid", color="burlywood", weight=3];
535[label="map toEnum (takeWhile1 (flip (<=) (error [])) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (error []) == GT)))",fontsize=16,color="black",shape="triangle"];535 -> 594[label="",style="solid", color="black", weight=3];
536[label="map toEnum (takeWhile1 (flip (<=) (Neg (primDivNatS yx400 (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Neg (primDivNatS yx400 (Succ yx4100))) == GT)))",fontsize=16,color="burlywood",shape="triangle"];4893[label="yx400/Succ yx4000",fontsize=10,color="white",style="solid",shape="box"];536 -> 4893[label="",style="solid", color="burlywood", weight=9];
4893 -> 595[label="",style="solid", color="burlywood", weight=3];
4894[label="yx400/Zero",fontsize=10,color="white",style="solid",shape="box"];536 -> 4894[label="",style="solid", color="burlywood", weight=9];
4894 -> 596[label="",style="solid", color="burlywood", weight=3];
537 -> 535[label="",style="dashed", color="red", weight=0];
537[label="map toEnum (takeWhile1 (flip (<=) (error [])) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (error []) == GT)))",fontsize=16,color="magenta"];538 -> 536[label="",style="dashed", color="red", weight=0];
538[label="map toEnum (takeWhile1 (flip (<=) (Neg (primDivNatS yx400 (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Neg (primDivNatS yx400 (Succ yx4100))) == GT)))",fontsize=16,color="magenta"];538 -> 597[label="",style="dashed", color="magenta", weight=3];
538 -> 598[label="",style="dashed", color="magenta", weight=3];
539 -> 535[label="",style="dashed", color="red", weight=0];
539[label="map toEnum (takeWhile1 (flip (<=) (error [])) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (error []) == GT)))",fontsize=16,color="magenta"];540 -> 534[label="",style="dashed", color="red", weight=0];
540[label="map toEnum (takeWhile1 (flip (<=) (Pos (primDivNatS yx400 (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Pos (primDivNatS yx400 (Succ yx4100))) == GT)))",fontsize=16,color="magenta"];540 -> 599[label="",style="dashed", color="magenta", weight=3];
540 -> 600[label="",style="dashed", color="magenta", weight=3];
541 -> 535[label="",style="dashed", color="red", weight=0];
541[label="map toEnum (takeWhile1 (flip (<=) (error [])) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (error []) == GT)))",fontsize=16,color="magenta"];3266[label="primQuotInt (Pos yx7000) (Pos (Succ yx71000))",fontsize=16,color="black",shape="box"];3266 -> 3318[label="",style="solid", color="black", weight=3];
3267[label="primQuotInt (Pos yx7000) (Pos Zero)",fontsize=16,color="black",shape="box"];3267 -> 3319[label="",style="solid", color="black", weight=3];
3268[label="primQuotInt (Pos yx7000) (Neg (Succ yx71000))",fontsize=16,color="black",shape="box"];3268 -> 3320[label="",style="solid", color="black", weight=3];
3269[label="primQuotInt (Pos yx7000) (Neg Zero)",fontsize=16,color="black",shape="box"];3269 -> 3321[label="",style="solid", color="black", weight=3];
3270[label="primQuotInt (Neg yx7000) (Pos (Succ yx71000))",fontsize=16,color="black",shape="box"];3270 -> 3322[label="",style="solid", color="black", weight=3];
3271[label="primQuotInt (Neg yx7000) (Pos Zero)",fontsize=16,color="black",shape="box"];3271 -> 3323[label="",style="solid", color="black", weight=3];
3272[label="primQuotInt (Neg yx7000) (Neg (Succ yx71000))",fontsize=16,color="black",shape="box"];3272 -> 3324[label="",style="solid", color="black", weight=3];
3273[label="primQuotInt (Neg yx7000) (Neg Zero)",fontsize=16,color="black",shape="box"];3273 -> 3325[label="",style="solid", color="black", weight=3];
4553 -> 576[label="",style="dashed", color="red", weight=0];
4553[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];4553 -> 4554[label="",style="dashed", color="magenta", weight=3];
4552[label="map toEnum (takeWhile (flip (<=) (Pos (Succ yx272))) (Pos yx278 : (numericEnumFrom $! Pos yx278 + yx280)))\n  Enum a",fontsize=16,color="black",shape="triangle"];4552 -> 4555[label="",style="solid", color="black", weight=3];
4314[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx252) (numericEnumFrom $! Pos yx252 + yx258) (compare (Pos yx252) (Pos Zero) /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];4314 -> 4343[label="",style="solid", color="black", weight=3];
3628[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3629[label="map toEnum (takeWhile2 (flip (<=) yx207) (Pos (Succ yx212000) : (numericEnumFrom $! Pos (Succ yx212000) + yx238)))\n  Enum a",fontsize=16,color="black",shape="box"];3629 -> 3648[label="",style="solid", color="black", weight=3];
3555 -> 576[label="",style="dashed", color="red", weight=0];
3555[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3555 -> 3573[label="",style="dashed", color="magenta", weight=3];
3554[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (Succ yx218) : (numericEnumFrom $! Neg (Succ yx218) + yx234)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3554 -> 3574[label="",style="solid", color="black", weight=3];
3630[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3631[label="map toEnum (takeWhile2 (flip (<=) yx207) (Pos Zero : (numericEnumFrom $! Pos Zero + yx239)))\n  Enum a",fontsize=16,color="black",shape="box"];3631 -> 3649[label="",style="solid", color="black", weight=3];
4315[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx254) (numericEnumFrom $! Pos yx254 + yx259) (compare (Pos yx254) (Neg Zero) /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];4315 -> 4344[label="",style="solid", color="black", weight=3];
3459[label="fromInt (Neg Zero)\n  Integral a",fontsize=16,color="blue",shape="box"];4902[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3459 -> 4902[label="",style="solid", color="blue", weight=9];
4902 -> 3488[label="",style="solid", color="blue", weight=3];
4903[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];3459 -> 4903[label="",style="solid", color="blue", weight=9];
4903 -> 3489[label="",style="solid", color="blue", weight=3];
3460[label="fromInt (Pos (Succ Zero))\n  Integral a",fontsize=16,color="blue",shape="box"];4904[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];3460 -> 4904[label="",style="solid", color="blue", weight=9];
4904 -> 3490[label="",style="solid", color="blue", weight=3];
4905[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];3460 -> 4905[label="",style="solid", color="blue", weight=9];
4905 -> 3491[label="",style="solid", color="blue", weight=3];
3461[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat yx2120 Zero)) (numericEnumFrom (primMinusNat yx2120 Zero))))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4906[label="yx2120/Succ yx21200",fontsize=10,color="white",style="solid",shape="box"];3461 -> 4906[label="",style="solid", color="burlywood", weight=9];
4906 -> 3492[label="",style="solid", color="burlywood", weight=3];
4907[label="yx2120/Zero",fontsize=10,color="white",style="solid",shape="box"];3461 -> 4907[label="",style="solid", color="burlywood", weight=9];
4907 -> 3493[label="",style="solid", color="burlywood", weight=3];
3462[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Neg (primPlusNat Zero yx2120))) (numericEnumFrom (Neg (primPlusNat Zero yx2120)))))\n  Enum a",fontsize=16,color="black",shape="box"];3462 -> 3494[label="",style="solid", color="black", weight=3];
3530[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3531[label="map toEnum (takeWhile2 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120) : (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232)))\n  Enum a",fontsize=16,color="black",shape="box"];3531 -> 3559[label="",style="solid", color="black", weight=3];
592[label="map toEnum (takeWhile1 (flip (<=) (Pos (primDivNatS (Succ yx4000) (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Pos (primDivNatS (Succ yx4000) (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];592 -> 677[label="",style="solid", color="black", weight=3];
593[label="map toEnum (takeWhile1 (flip (<=) (Pos (primDivNatS Zero (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Pos (primDivNatS Zero (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];593 -> 678[label="",style="solid", color="black", weight=3];
594[label="error []",fontsize=16,color="red",shape="box"];595[label="map toEnum (takeWhile1 (flip (<=) (Neg (primDivNatS (Succ yx4000) (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Neg (primDivNatS (Succ yx4000) (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];595 -> 679[label="",style="solid", color="black", weight=3];
596[label="map toEnum (takeWhile1 (flip (<=) (Neg (primDivNatS Zero (Succ yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Neg (primDivNatS Zero (Succ yx4100))) == GT)))",fontsize=16,color="black",shape="box"];596 -> 680[label="",style="solid", color="black", weight=3];
597[label="yx400",fontsize=16,color="green",shape="box"];598[label="yx4100",fontsize=16,color="green",shape="box"];599[label="yx400",fontsize=16,color="green",shape="box"];600[label="yx4100",fontsize=16,color="green",shape="box"];3318[label="Pos (primDivNatS yx7000 (Succ yx71000))",fontsize=16,color="green",shape="box"];3318 -> 3363[label="",style="dashed", color="green", weight=3];
3319[label="error []",fontsize=16,color="black",shape="triangle"];3319 -> 3364[label="",style="solid", color="black", weight=3];
3320[label="Neg (primDivNatS yx7000 (Succ yx71000))",fontsize=16,color="green",shape="box"];3320 -> 3365[label="",style="dashed", color="green", weight=3];
3321 -> 3319[label="",style="dashed", color="red", weight=0];
3321[label="error []",fontsize=16,color="magenta"];3322[label="Neg (primDivNatS yx7000 (Succ yx71000))",fontsize=16,color="green",shape="box"];3322 -> 3366[label="",style="dashed", color="green", weight=3];
3323 -> 3319[label="",style="dashed", color="red", weight=0];
3323[label="error []",fontsize=16,color="magenta"];3324[label="Pos (primDivNatS yx7000 (Succ yx71000))",fontsize=16,color="green",shape="box"];3324 -> 3367[label="",style="dashed", color="green", weight=3];
3325 -> 3319[label="",style="dashed", color="red", weight=0];
3325[label="error []",fontsize=16,color="magenta"];4554[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];4555[label="map toEnum (takeWhile2 (flip (<=) (Pos (Succ yx272))) (Pos yx278 : (numericEnumFrom $! Pos yx278 + yx280)))\n  Enum a",fontsize=16,color="black",shape="box"];4555 -> 4556[label="",style="solid", color="black", weight=3];
4343[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx252) (numericEnumFrom $! Pos yx252 + yx258) (not (compare (Pos yx252) (Pos Zero) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4343 -> 4352[label="",style="solid", color="black", weight=3];
3648[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos (Succ yx212000)) (numericEnumFrom $! Pos (Succ yx212000) + yx238) (flip (<=) yx207 (Pos (Succ yx212000))))\n  Enum a",fontsize=16,color="black",shape="box"];3648 -> 3660[label="",style="solid", color="black", weight=3];
3573[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3574[label="map toEnum (takeWhile2 (flip (<=) yx207) (Neg (Succ yx218) : (numericEnumFrom $! Neg (Succ yx218) + yx234)))\n  Enum a",fontsize=16,color="black",shape="box"];3574 -> 3595[label="",style="solid", color="black", weight=3];
3649[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos Zero) (numericEnumFrom $! Pos Zero + yx239) (flip (<=) yx207 (Pos Zero)))\n  Enum a",fontsize=16,color="black",shape="box"];3649 -> 3661[label="",style="solid", color="black", weight=3];
4344[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx254) (numericEnumFrom $! Pos yx254 + yx259) (not (compare (Pos yx254) (Neg Zero) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4344 -> 4353[label="",style="solid", color="black", weight=3];
3488 -> 576[label="",style="dashed", color="red", weight=0];
3488[label="fromInt (Neg Zero)",fontsize=16,color="magenta"];3488 -> 3532[label="",style="dashed", color="magenta", weight=3];
3489[label="fromInt (Neg Zero)",fontsize=16,color="black",shape="box"];3489 -> 3533[label="",style="solid", color="black", weight=3];
3490 -> 576[label="",style="dashed", color="red", weight=0];
3490[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3490 -> 3534[label="",style="dashed", color="magenta", weight=3];
3491 -> 3445[label="",style="dashed", color="red", weight=0];
3491[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3492[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat (Succ yx21200) Zero)) (numericEnumFrom (primMinusNat (Succ yx21200) Zero))))\n  Enum a",fontsize=16,color="black",shape="box"];3492 -> 3535[label="",style="solid", color="black", weight=3];
3493[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (primMinusNat Zero Zero)) (numericEnumFrom (primMinusNat Zero Zero))))\n  Enum a",fontsize=16,color="black",shape="box"];3493 -> 3536[label="",style="solid", color="black", weight=3];
3494[label="map toEnum (takeWhile (flip (<=) yx207) (numericEnumFrom (Neg (primPlusNat Zero yx2120))))\n  Enum a",fontsize=16,color="black",shape="box"];3494 -> 3537[label="",style="solid", color="black", weight=3];
3559[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120)) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232) (flip (<=) yx207 (Neg (primPlusNat (Succ yx218) yx2120))))\n  Enum a",fontsize=16,color="black",shape="box"];3559 -> 3587[label="",style="solid", color="black", weight=3];
677 -> 856[label="",style="dashed", color="red", weight=0];
677[label="map toEnum (takeWhile1 (flip (<=) (Pos (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Pos (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))) == GT)))",fontsize=16,color="magenta"];677 -> 857[label="",style="dashed", color="magenta", weight=3];
678 -> 858[label="",style="dashed", color="red", weight=0];
678[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="magenta"];678 -> 859[label="",style="dashed", color="magenta", weight=3];
679 -> 860[label="",style="dashed", color="red", weight=0];
679[label="map toEnum (takeWhile1 (flip (<=) (Neg (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Neg (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))) == GT)))",fontsize=16,color="magenta"];679 -> 861[label="",style="dashed", color="magenta", weight=3];
680 -> 862[label="",style="dashed", color="red", weight=0];
680[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Neg Zero) (numericEnumFrom $! Neg Zero + fromInt (Pos (Succ Zero))) (not (primCmpInt (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="magenta"];680 -> 863[label="",style="dashed", color="magenta", weight=3];
3363 -> 1688[label="",style="dashed", color="red", weight=0];
3363[label="primDivNatS yx7000 (Succ yx71000)",fontsize=16,color="magenta"];3363 -> 3423[label="",style="dashed", color="magenta", weight=3];
3363 -> 3424[label="",style="dashed", color="magenta", weight=3];
3364[label="error []",fontsize=16,color="red",shape="box"];3365 -> 1688[label="",style="dashed", color="red", weight=0];
3365[label="primDivNatS yx7000 (Succ yx71000)",fontsize=16,color="magenta"];3365 -> 3425[label="",style="dashed", color="magenta", weight=3];
3365 -> 3426[label="",style="dashed", color="magenta", weight=3];
3366 -> 1688[label="",style="dashed", color="red", weight=0];
3366[label="primDivNatS yx7000 (Succ yx71000)",fontsize=16,color="magenta"];3366 -> 3427[label="",style="dashed", color="magenta", weight=3];
3366 -> 3428[label="",style="dashed", color="magenta", weight=3];
3367 -> 1688[label="",style="dashed", color="red", weight=0];
3367[label="primDivNatS yx7000 (Succ yx71000)",fontsize=16,color="magenta"];3367 -> 3429[label="",style="dashed", color="magenta", weight=3];
3367 -> 3430[label="",style="dashed", color="magenta", weight=3];
4556[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx278) (numericEnumFrom $! Pos yx278 + yx280) (flip (<=) (Pos (Succ yx272)) (Pos yx278)))\n  Enum a",fontsize=16,color="black",shape="box"];4556 -> 4557[label="",style="solid", color="black", weight=3];
4352 -> 3763[label="",style="dashed", color="red", weight=0];
4352[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Pos yx252) (numericEnumFrom $! Pos yx252 + yx258) (not (primCmpInt (Pos yx252) (Pos Zero) == GT)))\n  Enum a",fontsize=16,color="magenta"];4352 -> 4362[label="",style="dashed", color="magenta", weight=3];
4352 -> 4363[label="",style="dashed", color="magenta", weight=3];
4352 -> 4364[label="",style="dashed", color="magenta", weight=3];
4352 -> 4365[label="",style="dashed", color="magenta", weight=3];
4352 -> 4366[label="",style="dashed", color="magenta", weight=3];
3660[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos (Succ yx212000)) (numericEnumFrom $! Pos (Succ yx212000) + yx238) ((<=) Pos (Succ yx212000) yx207))\n  Enum a",fontsize=16,color="black",shape="box"];3660 -> 3672[label="",style="solid", color="black", weight=3];
3595[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx218)) (numericEnumFrom $! Neg (Succ yx218) + yx234) (flip (<=) yx207 (Neg (Succ yx218))))\n  Enum a",fontsize=16,color="black",shape="box"];3595 -> 3622[label="",style="solid", color="black", weight=3];
3661[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos Zero) (numericEnumFrom $! Pos Zero + yx239) ((<=) Pos Zero yx207))\n  Enum a",fontsize=16,color="black",shape="box"];3661 -> 3673[label="",style="solid", color="black", weight=3];
4353 -> 3763[label="",style="dashed", color="red", weight=0];
4353[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Pos yx254) (numericEnumFrom $! Pos yx254 + yx259) (not (primCmpInt (Pos yx254) (Neg Zero) == GT)))\n  Enum a",fontsize=16,color="magenta"];4353 -> 4367[label="",style="dashed", color="magenta", weight=3];
4353 -> 4368[label="",style="dashed", color="magenta", weight=3];
4353 -> 4369[label="",style="dashed", color="magenta", weight=3];
4353 -> 4370[label="",style="dashed", color="magenta", weight=3];
4353 -> 4371[label="",style="dashed", color="magenta", weight=3];
3532[label="Neg Zero",fontsize=16,color="green",shape="box"];3533[label="Integer (Neg Zero)",fontsize=16,color="green",shape="box"];3534[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3535 -> 3551[label="",style="dashed", color="red", weight=0];
3535[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Pos (Succ yx21200))) (numericEnumFrom (Pos (Succ yx21200)))))\n  Enum a",fontsize=16,color="magenta"];3535 -> 3578[label="",style="dashed", color="magenta", weight=3];
3536 -> 3553[label="",style="dashed", color="red", weight=0];
3536[label="map toEnum (takeWhile (flip (<=) yx207) (enforceWHNF (WHNF (Pos Zero)) (numericEnumFrom (Pos Zero))))\n  Enum a",fontsize=16,color="magenta"];3537 -> 3579[label="",style="dashed", color="red", weight=0];
3537[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (primPlusNat Zero yx2120) : (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + fromInt (Pos (Succ Zero)))))\n  Enum a",fontsize=16,color="magenta"];3537 -> 3580[label="",style="dashed", color="magenta", weight=3];
3587[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120)) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232) ((<=) Neg (primPlusNat (Succ yx218) yx2120) yx207))\n  Enum a",fontsize=16,color="black",shape="box"];3587 -> 3608[label="",style="solid", color="black", weight=3];
857 -> 576[label="",style="dashed", color="red", weight=0];
857[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];857 -> 1062[label="",style="dashed", color="magenta", weight=3];
856 -> 803[label="",style="dashed", color="red", weight=0];
856[label="map toEnum (takeWhile1 (flip (<=) (Pos (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + yx64) (not (primCmpInt (Neg Zero) (Pos (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))) == GT)))",fontsize=16,color="magenta"];856 -> 1063[label="",style="dashed", color="magenta", weight=3];
856 -> 1064[label="",style="dashed", color="magenta", weight=3];
856 -> 1065[label="",style="dashed", color="magenta", weight=3];
859 -> 576[label="",style="dashed", color="red", weight=0];
859[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];859 -> 1066[label="",style="dashed", color="magenta", weight=3];
858 -> 803[label="",style="dashed", color="red", weight=0];
858[label="map toEnum (takeWhile1 (flip (<=) (Pos Zero)) (Neg Zero) (numericEnumFrom $! Neg Zero + yx65) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="magenta"];858 -> 1067[label="",style="dashed", color="magenta", weight=3];
858 -> 1068[label="",style="dashed", color="magenta", weight=3];
858 -> 1069[label="",style="dashed", color="magenta", weight=3];
861 -> 576[label="",style="dashed", color="red", weight=0];
861[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];861 -> 1070[label="",style="dashed", color="magenta", weight=3];
860 -> 803[label="",style="dashed", color="red", weight=0];
860[label="map toEnum (takeWhile1 (flip (<=) (Neg (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)))) (Neg Zero) (numericEnumFrom $! Neg Zero + yx66) (not (primCmpInt (Neg Zero) (Neg (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))) == GT)))",fontsize=16,color="magenta"];860 -> 1071[label="",style="dashed", color="magenta", weight=3];
860 -> 1072[label="",style="dashed", color="magenta", weight=3];
860 -> 1073[label="",style="dashed", color="magenta", weight=3];
863 -> 576[label="",style="dashed", color="red", weight=0];
863[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];863 -> 1074[label="",style="dashed", color="magenta", weight=3];
862 -> 803[label="",style="dashed", color="red", weight=0];
862[label="map toEnum (takeWhile1 (flip (<=) (Neg Zero)) (Neg Zero) (numericEnumFrom $! Neg Zero + yx67) (not (primCmpInt (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="magenta"];862 -> 1075[label="",style="dashed", color="magenta", weight=3];
862 -> 1076[label="",style="dashed", color="magenta", weight=3];
862 -> 1077[label="",style="dashed", color="magenta", weight=3];
3423[label="yx7000",fontsize=16,color="green",shape="box"];3424[label="yx71000",fontsize=16,color="green",shape="box"];3425[label="yx7000",fontsize=16,color="green",shape="box"];3426[label="yx71000",fontsize=16,color="green",shape="box"];3427[label="yx7000",fontsize=16,color="green",shape="box"];3428[label="yx71000",fontsize=16,color="green",shape="box"];3429[label="yx7000",fontsize=16,color="green",shape="box"];3430[label="yx71000",fontsize=16,color="green",shape="box"];4557[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx278) (numericEnumFrom $! Pos yx278 + yx280) ((<=) Pos yx278 Pos (Succ yx272)))\n  Enum a",fontsize=16,color="black",shape="box"];4557 -> 4558[label="",style="solid", color="black", weight=3];
4362[label="yx252",fontsize=16,color="green",shape="box"];4363[label="yx258",fontsize=16,color="green",shape="box"];4364[label="Pos Zero",fontsize=16,color="green",shape="box"];4365[label="yx252",fontsize=16,color="green",shape="box"];4366[label="yx252",fontsize=16,color="green",shape="box"];3672[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos (Succ yx212000)) (numericEnumFrom $! Pos (Succ yx212000) + yx238) (compare (Pos (Succ yx212000)) yx207 /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];3672 -> 3694[label="",style="solid", color="black", weight=3];
3622[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx218)) (numericEnumFrom $! Neg (Succ yx218) + yx234) ((<=) Neg (Succ yx218) yx207))\n  Enum a",fontsize=16,color="black",shape="box"];3622 -> 3643[label="",style="solid", color="black", weight=3];
3673[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos Zero) (numericEnumFrom $! Pos Zero + yx239) (compare (Pos Zero) yx207 /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];3673 -> 3695[label="",style="solid", color="black", weight=3];
4367[label="yx254",fontsize=16,color="green",shape="box"];4368[label="yx259",fontsize=16,color="green",shape="box"];4369[label="Neg Zero",fontsize=16,color="green",shape="box"];4370[label="yx254",fontsize=16,color="green",shape="box"];4371[label="yx254",fontsize=16,color="green",shape="box"];3578[label="yx21200",fontsize=16,color="green",shape="box"];3580 -> 576[label="",style="dashed", color="red", weight=0];
3580[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3580 -> 3598[label="",style="dashed", color="magenta", weight=3];
3579[label="map toEnum (takeWhile (flip (<=) yx207) (Neg (primPlusNat Zero yx2120) : (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235)))\n  Enum a",fontsize=16,color="black",shape="triangle"];3579 -> 3599[label="",style="solid", color="black", weight=3];
3608[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120)) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232) (compare (Neg (primPlusNat (Succ yx218) yx2120)) yx207 /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];3608 -> 3623[label="",style="solid", color="black", weight=3];
1062[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];1063[label="Pos (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))",fontsize=16,color="green",shape="box"];1063 -> 1217[label="",style="dashed", color="green", weight=3];
1064[label="Pos (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))",fontsize=16,color="green",shape="box"];1064 -> 1218[label="",style="dashed", color="green", weight=3];
1065[label="yx64",fontsize=16,color="green",shape="box"];803[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) yx27 == GT)))",fontsize=16,color="burlywood",shape="triangle"];4936[label="yx27/Pos yx270",fontsize=10,color="white",style="solid",shape="box"];803 -> 4936[label="",style="solid", color="burlywood", weight=9];
4936 -> 972[label="",style="solid", color="burlywood", weight=3];
4937[label="yx27/Neg yx270",fontsize=10,color="white",style="solid",shape="box"];803 -> 4937[label="",style="solid", color="burlywood", weight=9];
4937 -> 973[label="",style="solid", color="burlywood", weight=3];
1066[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];1067[label="Pos Zero",fontsize=16,color="green",shape="box"];1068[label="Pos Zero",fontsize=16,color="green",shape="box"];1069[label="yx65",fontsize=16,color="green",shape="box"];1070[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];1071[label="Neg (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))",fontsize=16,color="green",shape="box"];1071 -> 1219[label="",style="dashed", color="green", weight=3];
1072[label="Neg (primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100))",fontsize=16,color="green",shape="box"];1072 -> 1220[label="",style="dashed", color="green", weight=3];
1073[label="yx66",fontsize=16,color="green",shape="box"];1074[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];1075[label="Neg Zero",fontsize=16,color="green",shape="box"];1076[label="Neg Zero",fontsize=16,color="green",shape="box"];1077[label="yx67",fontsize=16,color="green",shape="box"];4558[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx278) (numericEnumFrom $! Pos yx278 + yx280) (compare (Pos yx278) (Pos (Succ yx272)) /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];4558 -> 4559[label="",style="solid", color="black", weight=3];
3694[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos (Succ yx212000)) (numericEnumFrom $! Pos (Succ yx212000) + yx238) (not (compare (Pos (Succ yx212000)) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3694 -> 3753[label="",style="solid", color="black", weight=3];
3643[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx218)) (numericEnumFrom $! Neg (Succ yx218) + yx234) (compare (Neg (Succ yx218)) yx207 /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];3643 -> 3654[label="",style="solid", color="black", weight=3];
3695[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos Zero) (numericEnumFrom $! Pos Zero + yx239) (not (compare (Pos Zero) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3695 -> 3754[label="",style="solid", color="black", weight=3];
3598[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3599[label="map toEnum (takeWhile2 (flip (<=) yx207) (Neg (primPlusNat Zero yx2120) : (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235)))\n  Enum a",fontsize=16,color="black",shape="box"];3599 -> 3627[label="",style="solid", color="black", weight=3];
3623[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120)) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232) (not (compare (Neg (primPlusNat (Succ yx218) yx2120)) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3623 -> 3644[label="",style="solid", color="black", weight=3];
1217 -> 1151[label="",style="dashed", color="red", weight=0];
1217[label="primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)",fontsize=16,color="magenta"];1218 -> 1151[label="",style="dashed", color="red", weight=0];
1218[label="primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)",fontsize=16,color="magenta"];972[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) (Pos yx270) == GT)))",fontsize=16,color="burlywood",shape="box"];4940[label="yx270/Succ yx2700",fontsize=10,color="white",style="solid",shape="box"];972 -> 4940[label="",style="solid", color="burlywood", weight=9];
4940 -> 1161[label="",style="solid", color="burlywood", weight=3];
4941[label="yx270/Zero",fontsize=10,color="white",style="solid",shape="box"];972 -> 4941[label="",style="solid", color="burlywood", weight=9];
4941 -> 1162[label="",style="solid", color="burlywood", weight=3];
973[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) (Neg yx270) == GT)))",fontsize=16,color="burlywood",shape="box"];4942[label="yx270/Succ yx2700",fontsize=10,color="white",style="solid",shape="box"];973 -> 4942[label="",style="solid", color="burlywood", weight=9];
4942 -> 1163[label="",style="solid", color="burlywood", weight=3];
4943[label="yx270/Zero",fontsize=10,color="white",style="solid",shape="box"];973 -> 4943[label="",style="solid", color="burlywood", weight=9];
4943 -> 1164[label="",style="solid", color="burlywood", weight=3];
1219 -> 1151[label="",style="dashed", color="red", weight=0];
1219[label="primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)",fontsize=16,color="magenta"];1219 -> 1342[label="",style="dashed", color="magenta", weight=3];
1220 -> 1151[label="",style="dashed", color="red", weight=0];
1220[label="primDivNatS0 yx4000 yx4100 (primGEqNatS yx4000 yx4100)",fontsize=16,color="magenta"];1220 -> 1343[label="",style="dashed", color="magenta", weight=3];
4559[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx278) (numericEnumFrom $! Pos yx278 + yx280) (not (compare (Pos yx278) (Pos (Succ yx272)) == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];4559 -> 4560[label="",style="solid", color="black", weight=3];
3753 -> 3763[label="",style="dashed", color="red", weight=0];
3753[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos (Succ yx212000)) (numericEnumFrom $! Pos (Succ yx212000) + yx238) (not (primCmpInt (Pos (Succ yx212000)) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];3753 -> 3981[label="",style="dashed", color="magenta", weight=3];
3753 -> 3982[label="",style="dashed", color="magenta", weight=3];
3753 -> 3983[label="",style="dashed", color="magenta", weight=3];
3753 -> 3984[label="",style="dashed", color="magenta", weight=3];
3753 -> 3985[label="",style="dashed", color="magenta", weight=3];
3654[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx218)) (numericEnumFrom $! Neg (Succ yx218) + yx234) (not (compare (Neg (Succ yx218)) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3654 -> 3666[label="",style="solid", color="black", weight=3];
3754 -> 3763[label="",style="dashed", color="red", weight=0];
3754[label="map toEnum (takeWhile1 (flip (<=) yx207) (Pos Zero) (numericEnumFrom $! Pos Zero + yx239) (not (primCmpInt (Pos Zero) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];3754 -> 3986[label="",style="dashed", color="magenta", weight=3];
3754 -> 3987[label="",style="dashed", color="magenta", weight=3];
3754 -> 3988[label="",style="dashed", color="magenta", weight=3];
3754 -> 3989[label="",style="dashed", color="magenta", weight=3];
3754 -> 3990[label="",style="dashed", color="magenta", weight=3];
3627[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero yx2120)) (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235) (flip (<=) yx207 (Neg (primPlusNat Zero yx2120))))\n  Enum a",fontsize=16,color="black",shape="box"];3627 -> 3647[label="",style="solid", color="black", weight=3];
3644[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) yx2120)) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) yx2120) + yx232) (not (primCmpInt (Neg (primPlusNat (Succ yx218) yx2120)) yx207 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4948[label="yx2120/Succ yx21200",fontsize=10,color="white",style="solid",shape="box"];3644 -> 4948[label="",style="solid", color="burlywood", weight=9];
4948 -> 3655[label="",style="solid", color="burlywood", weight=3];
4949[label="yx2120/Zero",fontsize=10,color="white",style="solid",shape="box"];3644 -> 4949[label="",style="solid", color="burlywood", weight=9];
4949 -> 3656[label="",style="solid", color="burlywood", weight=3];
1161[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) (Pos (Succ yx2700)) == GT)))",fontsize=16,color="black",shape="box"];1161 -> 1288[label="",style="solid", color="black", weight=3];
1162[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) (Pos Zero) == GT)))",fontsize=16,color="black",shape="box"];1162 -> 1289[label="",style="solid", color="black", weight=3];
1163[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) (Neg (Succ yx2700)) == GT)))",fontsize=16,color="black",shape="box"];1163 -> 1290[label="",style="solid", color="black", weight=3];
1164[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpInt (Neg Zero) (Neg Zero) == GT)))",fontsize=16,color="black",shape="box"];1164 -> 1291[label="",style="solid", color="black", weight=3];
1342[label="yx4100",fontsize=16,color="green",shape="box"];1343[label="yx4100",fontsize=16,color="green",shape="box"];4560 -> 3763[label="",style="dashed", color="red", weight=0];
4560[label="map toEnum (takeWhile1 (flip (<=) (Pos (Succ yx272))) (Pos yx278) (numericEnumFrom $! Pos yx278 + yx280) (not (primCmpInt (Pos yx278) (Pos (Succ yx272)) == GT)))\n  Enum a",fontsize=16,color="magenta"];4560 -> 4561[label="",style="dashed", color="magenta", weight=3];
4560 -> 4562[label="",style="dashed", color="magenta", weight=3];
4560 -> 4563[label="",style="dashed", color="magenta", weight=3];
4560 -> 4564[label="",style="dashed", color="magenta", weight=3];
4560 -> 4565[label="",style="dashed", color="magenta", weight=3];
3981[label="Succ yx212000",fontsize=16,color="green",shape="box"];3982[label="yx238",fontsize=16,color="green",shape="box"];3983[label="yx207",fontsize=16,color="green",shape="box"];3984[label="Succ yx212000",fontsize=16,color="green",shape="box"];3985[label="Succ yx212000",fontsize=16,color="green",shape="box"];3666 -> 2774[label="",style="dashed", color="red", weight=0];
3666[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx218)) (numericEnumFrom $! Neg (Succ yx218) + yx234) (not (primCmpInt (Neg (Succ yx218)) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];3666 -> 3678[label="",style="dashed", color="magenta", weight=3];
3666 -> 3679[label="",style="dashed", color="magenta", weight=3];
3666 -> 3680[label="",style="dashed", color="magenta", weight=3];
3666 -> 3681[label="",style="dashed", color="magenta", weight=3];
3986[label="Zero",fontsize=16,color="green",shape="box"];3987[label="yx239",fontsize=16,color="green",shape="box"];3988[label="yx207",fontsize=16,color="green",shape="box"];3989[label="Zero",fontsize=16,color="green",shape="box"];3990[label="Zero",fontsize=16,color="green",shape="box"];3647[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero yx2120)) (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235) ((<=) Neg (primPlusNat Zero yx2120) yx207))\n  Enum a",fontsize=16,color="black",shape="box"];3647 -> 3659[label="",style="solid", color="black", weight=3];
3655[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) (Succ yx21200))) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) (Succ yx21200)) + yx232) (not (primCmpInt (Neg (primPlusNat (Succ yx218) (Succ yx21200))) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3655 -> 3667[label="",style="solid", color="black", weight=3];
3656[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat (Succ yx218) Zero)) (numericEnumFrom $! Neg (primPlusNat (Succ yx218) Zero) + yx232) (not (primCmpInt (Neg (primPlusNat (Succ yx218) Zero)) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3656 -> 3668[label="",style="solid", color="black", weight=3];
1288[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (LT == GT)))",fontsize=16,color="black",shape="box"];1288 -> 1432[label="",style="solid", color="black", weight=3];
1289[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (EQ == GT)))",fontsize=16,color="black",shape="triangle"];1289 -> 1433[label="",style="solid", color="black", weight=3];
1290[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (primCmpNat (Succ yx2700) Zero == GT)))",fontsize=16,color="black",shape="box"];1290 -> 1434[label="",style="solid", color="black", weight=3];
1291 -> 1289[label="",style="dashed", color="red", weight=0];
1291[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (EQ == GT)))",fontsize=16,color="magenta"];4561[label="yx278",fontsize=16,color="green",shape="box"];4562[label="yx280",fontsize=16,color="green",shape="box"];4563[label="Pos (Succ yx272)",fontsize=16,color="green",shape="box"];4564[label="yx278",fontsize=16,color="green",shape="box"];4565[label="yx278",fontsize=16,color="green",shape="box"];3678[label="yx218",fontsize=16,color="green",shape="box"];3679[label="yx218",fontsize=16,color="green",shape="box"];3680[label="yx234",fontsize=16,color="green",shape="box"];3681[label="yx207",fontsize=16,color="green",shape="box"];3659[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero yx2120)) (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235) (compare (Neg (primPlusNat Zero yx2120)) yx207 /= GT))\n  Enum a",fontsize=16,color="black",shape="box"];3659 -> 3671[label="",style="solid", color="black", weight=3];
3667 -> 2774[label="",style="dashed", color="red", weight=0];
3667[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ (Succ (primPlusNat yx218 yx21200)))) (numericEnumFrom $! Neg (Succ (Succ (primPlusNat yx218 yx21200))) + yx232) (not (primCmpInt (Neg (Succ (Succ (primPlusNat yx218 yx21200)))) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];3667 -> 3682[label="",style="dashed", color="magenta", weight=3];
3667 -> 3683[label="",style="dashed", color="magenta", weight=3];
3667 -> 3684[label="",style="dashed", color="magenta", weight=3];
3667 -> 3685[label="",style="dashed", color="magenta", weight=3];
3667 -> 3686[label="",style="dashed", color="magenta", weight=3];
3668 -> 2774[label="",style="dashed", color="red", weight=0];
3668[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx218)) (numericEnumFrom $! Neg (Succ yx218) + yx232) (not (primCmpInt (Neg (Succ yx218)) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];3668 -> 3687[label="",style="dashed", color="magenta", weight=3];
3668 -> 3688[label="",style="dashed", color="magenta", weight=3];
3668 -> 3689[label="",style="dashed", color="magenta", weight=3];
3668 -> 3690[label="",style="dashed", color="magenta", weight=3];
1432[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not False))",fontsize=16,color="black",shape="triangle"];1432 -> 1570[label="",style="solid", color="black", weight=3];
1433 -> 1432[label="",style="dashed", color="red", weight=0];
1433[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not False))",fontsize=16,color="magenta"];1434[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not (GT == GT)))",fontsize=16,color="black",shape="box"];1434 -> 1571[label="",style="solid", color="black", weight=3];
3671[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero yx2120)) (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235) (not (compare (Neg (primPlusNat Zero yx2120)) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3671 -> 3693[label="",style="solid", color="black", weight=3];
3682[label="Succ (primPlusNat yx218 yx21200)",fontsize=16,color="green",shape="box"];3682 -> 3745[label="",style="dashed", color="green", weight=3];
3683[label="Succ (primPlusNat yx218 yx21200)",fontsize=16,color="green",shape="box"];3683 -> 3746[label="",style="dashed", color="green", weight=3];
3684[label="yx232",fontsize=16,color="green",shape="box"];3685[label="Succ (primPlusNat yx218 yx21200)",fontsize=16,color="green",shape="box"];3685 -> 3747[label="",style="dashed", color="green", weight=3];
3686[label="yx207",fontsize=16,color="green",shape="box"];3687[label="yx218",fontsize=16,color="green",shape="box"];3688[label="yx218",fontsize=16,color="green",shape="box"];3689[label="yx232",fontsize=16,color="green",shape="box"];3690[label="yx207",fontsize=16,color="green",shape="box"];1570[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) True)",fontsize=16,color="black",shape="box"];1570 -> 1784[label="",style="solid", color="black", weight=3];
1571[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) (not True))",fontsize=16,color="black",shape="box"];1571 -> 1785[label="",style="solid", color="black", weight=3];
3693[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero yx2120)) (numericEnumFrom $! Neg (primPlusNat Zero yx2120) + yx235) (not (primCmpInt (Neg (primPlusNat Zero yx2120)) yx207 == GT)))\n  Enum a",fontsize=16,color="burlywood",shape="box"];4956[label="yx2120/Succ yx21200",fontsize=10,color="white",style="solid",shape="box"];3693 -> 4956[label="",style="solid", color="burlywood", weight=9];
4956 -> 3751[label="",style="solid", color="burlywood", weight=3];
4957[label="yx2120/Zero",fontsize=10,color="white",style="solid",shape="box"];3693 -> 4957[label="",style="solid", color="burlywood", weight=9];
4957 -> 3752[label="",style="solid", color="burlywood", weight=3];
3746 -> 3745[label="",style="dashed", color="red", weight=0];
3746[label="primPlusNat yx218 yx21200",fontsize=16,color="magenta"];3747 -> 3745[label="",style="dashed", color="red", weight=0];
3747[label="primPlusNat yx218 yx21200",fontsize=16,color="magenta"];1784[label="map toEnum (Neg Zero : takeWhile (flip (<=) yx26) (numericEnumFrom $! Neg Zero + yx57))",fontsize=16,color="black",shape="box"];1784 -> 2345[label="",style="solid", color="black", weight=3];
1785[label="map toEnum (takeWhile1 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) False)",fontsize=16,color="black",shape="box"];1785 -> 2346[label="",style="solid", color="black", weight=3];
3751[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero (Succ yx21200))) (numericEnumFrom $! Neg (primPlusNat Zero (Succ yx21200)) + yx235) (not (primCmpInt (Neg (primPlusNat Zero (Succ yx21200))) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3751 -> 4021[label="",style="solid", color="black", weight=3];
3752[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (primPlusNat Zero Zero)) (numericEnumFrom $! Neg (primPlusNat Zero Zero) + yx235) (not (primCmpInt (Neg (primPlusNat Zero Zero)) yx207 == GT)))\n  Enum a",fontsize=16,color="black",shape="box"];3752 -> 4022[label="",style="solid", color="black", weight=3];
2345[label="toEnum (Neg Zero) : map toEnum (takeWhile (flip (<=) yx26) (numericEnumFrom $! Neg Zero + yx57))",fontsize=16,color="green",shape="box"];2345 -> 2381[label="",style="dashed", color="green", weight=3];
2345 -> 2382[label="",style="dashed", color="green", weight=3];
2346[label="map toEnum (takeWhile0 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) otherwise)",fontsize=16,color="black",shape="box"];2346 -> 2383[label="",style="solid", color="black", weight=3];
4021 -> 2774[label="",style="dashed", color="red", weight=0];
4021[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg (Succ yx21200)) (numericEnumFrom $! Neg (Succ yx21200) + yx235) (not (primCmpInt (Neg (Succ yx21200)) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];4021 -> 4035[label="",style="dashed", color="magenta", weight=3];
4021 -> 4036[label="",style="dashed", color="magenta", weight=3];
4021 -> 4037[label="",style="dashed", color="magenta", weight=3];
4021 -> 4038[label="",style="dashed", color="magenta", weight=3];
4021 -> 4039[label="",style="dashed", color="magenta", weight=3];
4022 -> 2423[label="",style="dashed", color="red", weight=0];
4022[label="map toEnum (takeWhile1 (flip (<=) yx207) (Neg Zero) (numericEnumFrom $! Neg Zero + yx235) (not (primCmpInt (Neg Zero) yx207 == GT)))\n  Enum a",fontsize=16,color="magenta"];4022 -> 4040[label="",style="dashed", color="magenta", weight=3];
4022 -> 4041[label="",style="dashed", color="magenta", weight=3];
2381[label="toEnum (Neg Zero)",fontsize=16,color="black",shape="box"];2381 -> 2417[label="",style="solid", color="black", weight=3];
2382[label="map toEnum (takeWhile (flip (<=) yx26) (numericEnumFrom $! Neg Zero + yx57))",fontsize=16,color="black",shape="box"];2382 -> 2418[label="",style="solid", color="black", weight=3];
2383[label="map toEnum (takeWhile0 (flip (<=) yx26) (Neg Zero) (numericEnumFrom $! Neg Zero + yx57) True)",fontsize=16,color="black",shape="box"];2383 -> 2419[label="",style="solid", color="black", weight=3];
4035[label="yx21200",fontsize=16,color="green",shape="box"];4036[label="yx21200",fontsize=16,color="green",shape="box"];4037[label="yx235",fontsize=16,color="green",shape="box"];4038[label="yx21200",fontsize=16,color="green",shape="box"];4039[label="yx207",fontsize=16,color="green",shape="box"];4040[label="yx235",fontsize=16,color="green",shape="box"];4041[label="yx207",fontsize=16,color="green",shape="box"];2417[label="fromInt (Neg Zero)",fontsize=16,color="black",shape="box"];2417 -> 3046[label="",style="solid", color="black", weight=3];
2418[label="map toEnum (takeWhile (flip (<=) yx26) (Neg Zero + yx57 `seq` numericEnumFrom (Neg Zero + yx57)))",fontsize=16,color="black",shape="box"];2418 -> 3047[label="",style="solid", color="black", weight=3];
2419 -> 2377[label="",style="dashed", color="red", weight=0];
2419[label="map toEnum []",fontsize=16,color="magenta"];3046[label="intToRatio (Neg Zero)",fontsize=16,color="black",shape="box"];3046 -> 3081[label="",style="solid", color="black", weight=3];
3047[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (Neg Zero + yx57)) (numericEnumFrom (Neg Zero + yx57))))",fontsize=16,color="black",shape="box"];3047 -> 3082[label="",style="solid", color="black", weight=3];
2377[label="map toEnum []",fontsize=16,color="black",shape="triangle"];2377 -> 2414[label="",style="solid", color="black", weight=3];
3081[label="fromInt (Neg Zero) :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];3081 -> 3110[label="",style="dashed", color="green", weight=3];
3081 -> 3111[label="",style="dashed", color="green", weight=3];
3082[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (primPlusInt (Neg Zero) yx57)) (numericEnumFrom (primPlusInt (Neg Zero) yx57))))",fontsize=16,color="burlywood",shape="box"];4963[label="yx57/Pos yx570",fontsize=10,color="white",style="solid",shape="box"];3082 -> 4963[label="",style="solid", color="burlywood", weight=9];
4963 -> 3112[label="",style="solid", color="burlywood", weight=3];
4964[label="yx57/Neg yx570",fontsize=10,color="white",style="solid",shape="box"];3082 -> 4964[label="",style="solid", color="burlywood", weight=9];
4964 -> 3113[label="",style="solid", color="burlywood", weight=3];
2414[label="[]",fontsize=16,color="green",shape="box"];3110 -> 576[label="",style="dashed", color="red", weight=0];
3110[label="fromInt (Neg Zero)",fontsize=16,color="magenta"];3110 -> 3144[label="",style="dashed", color="magenta", weight=3];
3111 -> 576[label="",style="dashed", color="red", weight=0];
3111[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3111 -> 3145[label="",style="dashed", color="magenta", weight=3];
3112[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (primPlusInt (Neg Zero) (Pos yx570))) (numericEnumFrom (primPlusInt (Neg Zero) (Pos yx570)))))",fontsize=16,color="black",shape="box"];3112 -> 3146[label="",style="solid", color="black", weight=3];
3113[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (primPlusInt (Neg Zero) (Neg yx570))) (numericEnumFrom (primPlusInt (Neg Zero) (Neg yx570)))))",fontsize=16,color="black",shape="box"];3113 -> 3147[label="",style="solid", color="black", weight=3];
3144[label="Neg Zero",fontsize=16,color="green",shape="box"];3145[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3146[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (primMinusNat yx570 Zero)) (numericEnumFrom (primMinusNat yx570 Zero))))",fontsize=16,color="burlywood",shape="box"];4967[label="yx570/Succ yx5700",fontsize=10,color="white",style="solid",shape="box"];3146 -> 4967[label="",style="solid", color="burlywood", weight=9];
4967 -> 3201[label="",style="solid", color="burlywood", weight=3];
4968[label="yx570/Zero",fontsize=10,color="white",style="solid",shape="box"];3146 -> 4968[label="",style="solid", color="burlywood", weight=9];
4968 -> 3202[label="",style="solid", color="burlywood", weight=3];
3147[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (Neg (primPlusNat Zero yx570))) (numericEnumFrom (Neg (primPlusNat Zero yx570)))))",fontsize=16,color="black",shape="box"];3147 -> 3203[label="",style="solid", color="black", weight=3];
3201[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (primMinusNat (Succ yx5700) Zero)) (numericEnumFrom (primMinusNat (Succ yx5700) Zero))))",fontsize=16,color="black",shape="box"];3201 -> 3234[label="",style="solid", color="black", weight=3];
3202[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (primMinusNat Zero Zero)) (numericEnumFrom (primMinusNat Zero Zero))))",fontsize=16,color="black",shape="box"];3202 -> 3235[label="",style="solid", color="black", weight=3];
3203[label="map toEnum (takeWhile (flip (<=) yx26) (numericEnumFrom (Neg (primPlusNat Zero yx570))))",fontsize=16,color="black",shape="box"];3203 -> 3236[label="",style="solid", color="black", weight=3];
3234[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (Pos (Succ yx5700))) (numericEnumFrom (Pos (Succ yx5700)))))",fontsize=16,color="black",shape="box"];3234 -> 3437[label="",style="solid", color="black", weight=3];
3235 -> 3233[label="",style="dashed", color="red", weight=0];
3235[label="map toEnum (takeWhile (flip (<=) yx26) (enforceWHNF (WHNF (Pos Zero)) (numericEnumFrom (Pos Zero))))",fontsize=16,color="magenta"];3235 -> 3438[label="",style="dashed", color="magenta", weight=3];
3236 -> 3579[label="",style="dashed", color="red", weight=0];
3236[label="map toEnum (takeWhile (flip (<=) yx26) (Neg (primPlusNat Zero yx570) : (numericEnumFrom $! Neg (primPlusNat Zero yx570) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];3236 -> 3581[label="",style="dashed", color="magenta", weight=3];
3236 -> 3582[label="",style="dashed", color="magenta", weight=3];
3236 -> 3583[label="",style="dashed", color="magenta", weight=3];
3437[label="map toEnum (takeWhile (flip (<=) yx26) (numericEnumFrom (Pos (Succ yx5700))))",fontsize=16,color="black",shape="box"];3437 -> 3512[label="",style="solid", color="black", weight=3];
3438[label="yx26",fontsize=16,color="green",shape="box"];3233[label="map toEnum (takeWhile (flip (<=) yx18) (enforceWHNF (WHNF (Pos Zero)) (numericEnumFrom (Pos Zero))))",fontsize=16,color="black",shape="triangle"];3233 -> 3436[label="",style="solid", color="black", weight=3];
3581[label="yx26",fontsize=16,color="green",shape="box"];3582 -> 576[label="",style="dashed", color="red", weight=0];
3582[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3582 -> 3605[label="",style="dashed", color="magenta", weight=3];
3583[label="yx570",fontsize=16,color="green",shape="box"];3512 -> 3611[label="",style="dashed", color="red", weight=0];
3512[label="map toEnum (takeWhile (flip (<=) yx26) (Pos (Succ yx5700) : (numericEnumFrom $! Pos (Succ yx5700) + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];3512 -> 3613[label="",style="dashed", color="magenta", weight=3];
3512 -> 3614[label="",style="dashed", color="magenta", weight=3];
3512 -> 3615[label="",style="dashed", color="magenta", weight=3];
3436[label="map toEnum (takeWhile (flip (<=) yx18) (numericEnumFrom (Pos Zero)))",fontsize=16,color="black",shape="box"];3436 -> 3511[label="",style="solid", color="black", weight=3];
3605[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3613[label="yx26",fontsize=16,color="green",shape="box"];3614 -> 576[label="",style="dashed", color="red", weight=0];
3614[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3614 -> 3642[label="",style="dashed", color="magenta", weight=3];
3615[label="yx5700",fontsize=16,color="green",shape="box"];3511 -> 3616[label="",style="dashed", color="red", weight=0];
3511[label="map toEnum (takeWhile (flip (<=) yx18) (Pos Zero : (numericEnumFrom $! Pos Zero + fromInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];3511 -> 3618[label="",style="dashed", color="magenta", weight=3];
3511 -> 3619[label="",style="dashed", color="magenta", weight=3];
3642[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];3618 -> 576[label="",style="dashed", color="red", weight=0];
3618[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];3618 -> 3641[label="",style="dashed", color="magenta", weight=3];
3619[label="yx18",fontsize=16,color="green",shape="box"];3641[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];}

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                                ↳ QDPSizeChangeProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primMinusNatS(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS(yx2000, yx2010)

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:

new_primMinusNatS(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS(yx2000, yx2010)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(new_primMinusNatS0(yx40000), Zero)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS0(Zero, Zero) → new_primDivNatS(new_primMinusNatS1, Zero)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)
new_primMinusNatS1 → Zero
new_primMinusNatS0(yx30000) → Succ(yx30000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS0(x0)
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS1
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(new_primMinusNatS0(yx40000), Zero)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)
new_primMinusNatS1 → Zero
new_primMinusNatS0(yx30000) → Succ(yx30000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS0(x0)
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS1
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(new_primMinusNatS0(yx40000), Zero)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)
new_primMinusNatS0(yx30000) → Succ(yx30000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS0(x0)
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS1
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

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

new_primMinusNatS1

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(new_primMinusNatS0(yx40000), Zero)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)
new_primMinusNatS0(yx30000) → Succ(yx30000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS0(x0)
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(new_primMinusNatS0(yx40000), Zero) at position [0] we obtained the following new rules:

new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)
new_primMinusNatS0(yx30000) → Succ(yx30000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS0(x0)
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS0(x0)
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

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

new_primMinusNatS0(x0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246)) at position [0] we obtained the following new rules:

new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246))

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(Succ(yx245), Succ(yx246)), Succ(yx246)) at position [0] we obtained the following new rules:

new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ QDPOrderProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

new_primDivNatS0(Succ(yx40000), Succ(yx41000)) → new_primDivNatS00(yx40000, yx41000, yx40000, yx41000)
new_primDivNatS0(Succ(yx40000), Zero) → new_primDivNatS(Succ(yx40000), Zero)

The remaining pairs can at least be oriented weakly.

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

Used ordering: Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + x₁
POL(Zero) = 0
POL(new_primDivNatS(x₁, x₂)) = x₁
POL(new_primDivNatS0(x₁, x₂)) = 1 + x₁
POL(new_primDivNatS00(x₁, x₂, x₃, x₄)) = x₁
POL(new_primDivNatS01(x₁, x₂)) = x₁
POL(new_primMinusNatS2(x₁, x₂)) = x₁

The following usable rules [17] were oriented:

new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ QDPOrderProof

                                                                  ↳ QDP

                                                                    ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS(Succ(yx4000), yx4100) → new_primDivNatS0(yx4000, yx4100)
new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
new_primDivNatS01(yx245, yx246) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS00(yx245, yx246, Succ(yx2470), Zero) → new_primDivNatS(new_primMinusNatS2(yx245, yx246), Succ(yx246))
new_primDivNatS00(yx245, yx246, Zero, Zero) → new_primDivNatS01(yx245, yx246)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 4 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ QDPOrderProof

                                                                  ↳ QDP

                                                                    ↳ DependencyGraphProof

                                                                      ↳ QDP

                                                                        ↳ UsableRulesProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)

The TRS R consists of the following rules:

new_primMinusNatS2(Succ(yx2000), Succ(yx2010)) → new_primMinusNatS2(yx2000, yx2010)
new_primMinusNatS2(Zero, Succ(yx2010)) → Zero
new_primMinusNatS2(Zero, Zero) → Zero
new_primMinusNatS2(Succ(yx2000), Zero) → Succ(yx2000)

The set Q consists of the following terms:

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ QDPOrderProof

                                                                  ↳ QDP

                                                                    ↳ DependencyGraphProof

                                                                      ↳ QDP

                                                                        ↳ UsableRulesProof

                                                                          ↳ QDP

                                                                            ↳ QReductionProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)

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

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

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

new_primMinusNatS2(Zero, Succ(x0))
new_primMinusNatS2(Zero, Zero)
new_primMinusNatS2(Succ(x0), Zero)
new_primMinusNatS2(Succ(x0), Succ(x1))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ UsableRulesProof

                                      ↳ QDP

                                        ↳ QReductionProof

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ UsableRulesProof

                                                  ↳ QDP

                                                    ↳ QReductionProof

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ QDPOrderProof

                                                                  ↳ QDP

                                                                    ↳ DependencyGraphProof

                                                                      ↳ QDP

                                                                        ↳ UsableRulesProof

                                                                          ↳ QDP

                                                                            ↳ QReductionProof

                                                                              ↳ QDP

                                                                                ↳ QDPSizeChangeProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)

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

new_primDivNatS00(yx245, yx246, Succ(yx2470), Succ(yx2480)) → new_primDivNatS00(yx245, yx246, yx2470, yx2480)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ QDPSizeChangeProof

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_primPlusNat(Succ(yx2180), Succ(yx212000)) → new_primPlusNat(yx2180, yx212000)

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

new_primPlusNat(Succ(yx2180), Succ(yx212000)) → new_primPlusNat(yx2180, yx212000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map11(yx207, yx212000, bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map18(yx207, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 2 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc) at position [1] we obtained the following new rules:

new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc) at position [1] we obtained the following new rules:

new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, new_fromInt(Pos(Succ(Zero))), ba) at position [2] we obtained the following new rules:

new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map5(yx253, yx252, bb) → new_map7(yx252, new_fromInt(Pos(Succ(Zero))), bb) at position [1] we obtained the following new rules:

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map6(yx255, yx254, bb) → new_map19(yx254, new_fromInt(Pos(Succ(Zero))), bb) at position [1] we obtained the following new rules:

new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc) at position [3] we obtained the following new rules:

new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc) at position [3] we obtained the following new rules:

new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc) at position [1] we obtained the following new rules:

new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

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                                                                                          ↳ QDP

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                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, new_fromInt(Pos(Succ(Zero))), bc) at position [3] we obtained the following new rules:

new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

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                                                            ↳ Rewriting

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                                                                ↳ Rewriting

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                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

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                                          ↳ QDP

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                                              ↳ QDP

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                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, new_fromInt(Pos(Succ(Zero))), bc) at position [2] we obtained the following new rules:

new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

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                                          ↳ QDP

                                            ↳ Rewriting

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                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, new_fromInt(Pos(Succ(Zero))), bc) at position [1] we obtained the following new rules:

new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

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                                                                                                            ↳ UsableRulesProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_fromInt(yx8) → yx8
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(x0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

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                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_fromInt(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_fromInt(x0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

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                                          ↳ QDP

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                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Succ(yx213000))), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc) we obtained the following new rules:

new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

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                                                                                    ↳ Rewriting

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                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

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                                                                                              ↳ QDP

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                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map14(yx207, yx218, Succ(yx21200), yx232, bc) → new_map13(yx207, Succ(new_primPlusNat0(yx218, yx21200)), Succ(new_primPlusNat0(yx218, yx21200)), yx232, Succ(new_primPlusNat0(yx218, yx21200)), yx207, bc) we obtained the following new rules:

new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

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                                          ↳ QDP

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                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, yx218, Neg(yx2120), yx219, Pos(yx2130), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc) we obtained the following new rules:

new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

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                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Succ(yx2510), bb) → new_map(yx19900, yx249, yx250, yx237, yx2510, yx19900, bb) we obtained the following new rules:

new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

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                                          ↳ QDP

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                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc) we obtained the following new rules:

new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

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                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Neg(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Neg(Zero), yx250, yx2370, bb) we obtained the following new rules:

new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

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                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map10(yx207, yx239, bc) → new_map4(yx207, Zero, Zero, yx239, Zero, bc) we obtained the following new rules:

new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

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                                          ↳ QDP

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                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

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                                                                                                                                    ↳ Instantiation

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                                                                                                                                        ↳ Instantiation

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                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), yx219, Pos(yx2130), bc) → new_map1(yx207, yx212000, yx2180, bc) we obtained the following new rules:

new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

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                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, yx218, yx212, Zero, Neg(Succ(Zero)), bc) → new_map17(yx207, yx217, yx218, yx212, bc) we obtained the following new rules:

new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

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                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map7(yx252, yx258, bb) → new_map4(Pos(Zero), yx252, yx252, yx258, yx252, bb) we obtained the following new rules:

new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Zero), yx249, yx250, Neg(yx2370), Zero, bb) → new_map1(Pos(Zero), yx250, yx2370, bb)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 1 less node.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Pos(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map5(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb) we obtained the following new rules:

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1) at position [0] we obtained the following new rules:

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)
new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1) at position [1] we obtained the following new rules:

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), Succ(Zero), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ UsableRulesProof

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), Succ(Zero), z1)
new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ UsableRulesProof

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ QReductionProof

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), Succ(Zero), z1)
new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)

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

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

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

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ UsableRulesProof

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ QReductionProof

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), Succ(Zero), z1)
new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map5(yx253, yx252, bb) → new_map7(yx252, Pos(Succ(Zero)), bb) we obtained the following new rules:

new_map5(Succ(Zero), Succ(Zero), z0) → new_map7(Succ(Zero), Pos(Succ(Zero)), z0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ UsableRulesProof

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ QReductionProof

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), Succ(Zero), z1)
new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map5(Succ(Zero), Succ(Zero), z0) → new_map7(Succ(Zero), Pos(Succ(Zero)), z0)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map7(z1, Pos(Succ(Zero)), z2) → new_map4(Pos(Zero), z1, z1, Pos(Succ(Zero)), z1, z2) we obtained the following new rules:

new_map7(Succ(Zero), Pos(Succ(Zero)), z0) → new_map4(Pos(Zero), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), z0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ UsableRulesProof

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ QReductionProof

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map5(Succ(Zero), Succ(Zero), z1)
new_map7(Succ(Zero), Pos(Succ(Zero)), z0) → new_map4(Pos(Zero), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), z0)
new_map5(Succ(Zero), Succ(Zero), z0) → new_map7(Succ(Zero), Pos(Succ(Zero)), z0)

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 0 SCCs with 3 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Pos(Succ(yx19900)), yx249, yx250, yx237, Zero, bb) → new_map(yx19900, yx249, yx250, yx237, Zero, Succ(yx19900), bb) we obtained the following new rules:

new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map12(yx207, yx218, yx234, bc) → new_map13(yx207, yx218, yx218, yx234, yx218, yx207, bc) we obtained the following new rules:

new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, yx218, yx212, yx219, Neg(Zero), bc) → new_map16(yx207, yx217, yx218, yx212, bc) we obtained the following new rules:

new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map8(yx207, yx212000, yx238, bc) → new_map4(yx207, Succ(yx212000), Succ(yx212000), yx238, Succ(yx212000), bc) we obtained the following new rules:

new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map3(yx272, yx278, yx280, ba) → new_map4(Pos(Succ(yx272)), yx278, yx278, yx280, yx278, ba) we obtained the following new rules:

new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Pos(Succ(z0)), Succ(x4), Succ(x4), z2, Succ(x4), z3) → new_map(z0, Succ(x4), Succ(x4), z2, x4, z0, z3) we obtained the following new rules:

new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Neg(Zero), yx249, yx250, Pos(yx2370), Zero, bb) → new_map6(new_primPlusNat0(yx250, yx2370), new_primPlusNat0(yx250, yx2370), bb) we obtained the following new rules:

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1) at position [0] we obtained the following new rules:

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1) at position [1] we obtained the following new rules:

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map19(yx254, yx259, bb) → new_map4(Neg(Zero), yx254, yx254, yx259, yx254, bb) we obtained the following new rules:

new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map4(Neg(Zero), Zero, Zero, Neg(x2), Zero, z2) → new_map1(Neg(Zero), Zero, x2, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 1 less node.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)
new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Neg(Zero), Zero, Zero, Pos(x2), Zero, z2) → new_map6(new_primPlusNat0(Zero, x2), new_primPlusNat0(Zero, x2), z2) we obtained the following new rules:

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(new_primPlusNat0(Zero, Succ(Zero)), new_primPlusNat0(Zero, Succ(Zero)), z1)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ Rewriting

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), new_primPlusNat0(Zero, Succ(Zero)), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ Rewriting

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ UsableRulesProof

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ Rewriting

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ UsableRulesProof

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ QReductionProof

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

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

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

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

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ Rewriting

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ UsableRulesProof

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ QReductionProof

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map6(yx255, yx254, bb) → new_map19(yx254, Pos(Succ(Zero)), bb) we obtained the following new rules:

new_map6(Succ(Zero), Succ(Zero), z0) → new_map19(Succ(Zero), Pos(Succ(Zero)), z0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ Rewriting

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ UsableRulesProof

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ QReductionProof

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2)
new_map6(Succ(Zero), Succ(Zero), z0) → new_map19(Succ(Zero), Pos(Succ(Zero)), z0)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map19(z1, Pos(Succ(Zero)), z2) → new_map4(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, z2) we obtained the following new rules:

new_map19(Succ(Zero), Pos(Succ(Zero)), z0) → new_map4(Neg(Zero), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), z0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ UsableRulesProof

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ UsableRulesProof

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Rewriting

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ Rewriting

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ UsableRulesProof

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ QReductionProof

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ DependencyGraphProof

                                                                                                                                                                                                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map19(Succ(Zero), Pos(Succ(Zero)), z0) → new_map4(Neg(Zero), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), z0)
new_map4(Neg(Zero), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map6(Succ(Zero), Succ(Zero), z1)
new_map6(Succ(Zero), Succ(Zero), z0) → new_map19(Succ(Zero), Pos(Succ(Zero)), z0)

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 0 SCCs with 3 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map9(yx207, yx2180, bc) we obtained the following new rules:

new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, yx218, yx212, Succ(yx2190), Neg(Succ(Zero)), bc) → new_map16(yx207, yx217, yx218, yx212, bc) we obtained the following new rules:

new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map4(Pos(Succ(z0)), Zero, Zero, z2, Zero, z3) → new_map(z0, Zero, Zero, z2, Zero, Succ(z0), z3) we obtained the following new rules:

new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map14(yx207, yx218, Zero, yx232, bc) → new_map13(yx207, yx218, yx218, yx232, yx218, yx207, bc) we obtained the following new rules:

new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Pos(x5), Succ(x2), Succ(x2), Pos(Succ(Succ(x3))), Succ(x2), Pos(x5), z3) → new_map1(Pos(x5), x3, x2, z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(yx207, yx217, yx218, Pos(Zero), yx219, Pos(yx2130), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x5), z1, z1, Neg(x3), z1, Pos(x5), z3) → new_map14(Pos(x5), z1, x3, Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map13(Pos(x4), Zero, Zero, Pos(Succ(Succ(x2))), Zero, Pos(x4), z3) → new_map8(Pos(x4), x2, Pos(Succ(Zero)), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 4 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(yx207, yx217, Zero, Pos(Succ(Zero)), yx219, Pos(yx2130), bc) → new_map10(yx207, Pos(Succ(Zero)), bc) we obtained the following new rules:

new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Succ(x5))), z3) → new_map15(Neg(Succ(Succ(x5))), Succ(x4), Succ(x4), z2, x5, x4, z3) we obtained the following new rules:

new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, Succ(y_2), Neg(Succ(Succ(x5))), z4) → new_map15(Neg(Succ(Succ(x5))), Succ(y_0), Succ(y_1), z3, x5, y_2, z4) we obtained the following new rules:

new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Succ(Zero)), Zero, Zero, z2, Zero, Neg(Succ(Zero)), z3) → new_map17(Neg(Succ(Zero)), Zero, Zero, z2, z3) we obtained the following new rules:

new_map13(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), Zero, Neg(Succ(Zero)), z2) → new_map17(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), Zero, Neg(Succ(Zero)), z2) → new_map17(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Zero), z1, z1, z2, z1, Neg(Zero), z3) → new_map16(Neg(Zero), z1, z1, z2, z3) we obtained the following new rules:

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), Zero, Neg(Succ(Zero)), z2) → new_map17(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), z2)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, Succ(x4), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), z2, z3) we obtained the following new rules:

new_map13(Neg(Succ(Zero)), Succ(x0), Succ(x0), Pos(Succ(Zero)), Succ(x0), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x0), Succ(x0), Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), Zero, Neg(Succ(Zero)), z2) → new_map17(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), z2)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

new_map(yx272, yx273, yx274, Neg(yx2750), Zero, Succ(yx2770), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)
new_map16(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, yx218, Neg(yx2120), bc) → new_map14(yx207, yx218, yx2120, Pos(Succ(Zero)), bc)
new_map2(yx272, yx273, yx274, Neg(yx2750), ba) → new_map1(Pos(Succ(yx272)), yx274, yx2750, ba)

The remaining pairs can at least be oriented weakly.

new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), Zero, Neg(Succ(Zero)), z2) → new_map17(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), z2)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

Used ordering: Polynomial interpretation [25]:

POL(Neg(x₁)) = 1
POL(Pos(x₁)) = 0
POL(Succ(x₁)) = 0
POL(Zero) = 0
POL(new_map(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₂ + x₄
POL(new_map0(x₁, x₂, x₃, x₄)) = 0
POL(new_map1(x₁, x₂, x₃, x₄)) = 0
POL(new_map10(x₁, x₂, x₃)) = 0
POL(new_map12(x₁, x₂, x₃, x₄)) = 0
POL(new_map13(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = 0
POL(new_map14(x₁, x₂, x₃, x₄, x₅)) = 0
POL(new_map15(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₂ + x₃ + x₄
POL(new_map16(x₁, x₂, x₃, x₄, x₅)) = x₄
POL(new_map17(x₁, x₂, x₃, x₄, x₅)) = x₄
POL(new_map2(x₁, x₂, x₃, x₄, x₅)) = x₄
POL(new_map3(x₁, x₂, x₃, x₄)) = 0
POL(new_map4(x₁, x₂, x₃, x₄, x₅, x₆)) = 0
POL(new_map8(x₁, x₂, x₃, x₄)) = 0
POL(new_map9(x₁, x₂, x₃)) = 0
POL(new_primPlusNat0(x₁, x₂)) = 0

The following usable rules [17] were oriented: none

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Pos(x3), Zero, Zero, Pos(Succ(Zero)), Zero, Pos(x3), z2) → new_map10(Pos(x3), Pos(Succ(Zero)), z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map10(z0, Pos(Succ(Zero)), z2) → new_map4(z0, Zero, Zero, Pos(Succ(Zero)), Zero, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), Zero, Neg(Succ(Zero)), z2) → new_map17(Neg(Succ(Zero)), Zero, Zero, Pos(Succ(Zero)), z2)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map14(z0, z2, Succ(x2), Pos(Succ(Zero)), z6) → new_map13(z0, Succ(new_primPlusNat0(z2, x2)), Succ(new_primPlusNat0(z2, x2)), Pos(Succ(Zero)), Succ(new_primPlusNat0(z2, x2)), z0, z6)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map8(z0, z1, Pos(Succ(Zero)), z2) → new_map4(z0, Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map16(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map14(z0, z2, Zero, Pos(Succ(Zero)), z4) → new_map13(z0, z2, z2, Pos(Succ(Zero)), z2, z0, z4)
new_map14(Pos(z0), z1, Zero, Pos(Succ(Zero)), z3) → new_map13(Pos(z0), z1, z1, Pos(Succ(Zero)), z1, Pos(z0), z3)
new_map16(yx207, yx217, Zero, Pos(Succ(Zero)), bc) → new_map10(yx207, Pos(Succ(Zero)), bc)
new_map17(yx207, yx217, Zero, Pos(Succ(Succ(yx212000))), bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Zero, bc) → new_map8(yx207, yx212000, Pos(Succ(Zero)), bc)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map8(Pos(z0), z1, Pos(Succ(Zero)), z2) → new_map4(Pos(z0), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Zero, Zero, bc) → new_map10(yx207, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 14 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

new_map4(Pos(Succ(x0)), Zero, Zero, Pos(Succ(Zero)), Zero, z1) → new_map(x0, Zero, Zero, Pos(Succ(Zero)), Zero, Succ(x0), z1)

The remaining pairs can at least be oriented weakly.

new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)

Used ordering: Polynomial interpretation [25]:

POL(Pos(x₁)) = x₁
POL(Succ(x₁)) = 0
POL(Zero) = 1
POL(new_map(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₄
POL(new_map0(x₁, x₂, x₃, x₄)) = x₃
POL(new_map2(x₁, x₂, x₃, x₄, x₅)) = x₄
POL(new_map3(x₁, x₂, x₃, x₄)) = x₂
POL(new_map4(x₁, x₂, x₃, x₄, x₅, x₆)) = x₃
POL(new_primPlusNat0(x₁, x₂)) = x₂

The following usable rules [17] were oriented:

new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
In the following pairs the term without variables Pos(Succ(Zero)) is replaced by the fresh variable x_removed.
Pair: new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2)
Positions in right side of the pair:

Pair: new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
Positions in right side of the pair:

Pair: new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
Positions in right side of the pair:

The new variable was added to all pairs as a new argument[13].

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(yx272, yx279, yx278, ba, x_removed) → new_map3(yx272, yx278, x_removed, ba, x_removed)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba, x_removed) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba, x_removed)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2, x_removed) → new_map(x0, Succ(z1), Succ(z1), x_removed, z1, x0, z2, x_removed)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba, x_removed) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba, x_removed)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba, x_removed) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba, x_removed)
new_map3(z0, z2, Pos(Succ(Zero)), z3, x_removed) → new_map4(Pos(Succ(z0)), z2, z2, x_removed, z2, z3, x_removed)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba, x_removed) → new_map2(yx272, yx273, yx274, yx275, ba, x_removed)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

Pair: new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
Positions in right side of the pair:

Pair: new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
Positions in right side of the pair:

The new variable was added to all pairs as a new argument[13].

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(yx272, yx279, yx278, ba, x_removed) → new_map3(yx272, yx278, x_removed, ba, x_removed)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba, x_removed) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba, x_removed)
new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2, x_removed) → new_map(x0, Succ(z1), Succ(z1), x_removed, z1, x0, z2, x_removed)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba, x_removed) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba, x_removed)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba, x_removed) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba, x_removed)
new_map3(z0, z2, Pos(Succ(Zero)), z3, x_removed) → new_map4(Pos(Succ(z0)), z2, z2, x_removed, z2, z3, x_removed)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba, x_removed) → new_map2(yx272, yx273, yx274, yx275, ba, x_removed)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map4(Pos(Succ(x0)), Succ(z1), Succ(z1), Pos(Succ(Zero)), Succ(z1), z2) → new_map(x0, Succ(z1), Succ(z1), Pos(Succ(Zero)), z1, x0, z2) we obtained the following new rules:

new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map3(z0, z2, Pos(Succ(Zero)), z3) → new_map4(Pos(Succ(z0)), z2, z2, Pos(Succ(Zero)), z2, z3) we obtained the following new rules:

new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map(yx272, yx273, yx274, yx275, Succ(yx2760), Succ(yx2770), ba) → new_map(yx272, yx273, yx274, yx275, yx2760, yx2770, ba) we obtained the following new rules:

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map0(yx272, yx279, yx278, ba) → new_map3(yx272, yx278, Pos(Succ(Zero)), ba) we obtained the following new rules:

new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_map(yx272, yx273, yx274, Pos(yx2750), Zero, Succ(yx2770), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba) at position [2] we obtained the following new rules:

new_map(y0, y1, Zero, Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Zero), Zero, y5)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y5)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y5)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(y0, y1, Zero, Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Zero), Zero, y5)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y5)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y5)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y5)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y5) at position [1] we obtained the following new rules:

new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y5)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y5) at position [1] we obtained the following new rules:

new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y5)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y5) at position [1] we obtained the following new rules:

new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_map2(yx272, yx273, yx274, Pos(yx2750), ba) → new_map0(yx272, new_primPlusNat0(yx274, yx2750), new_primPlusNat0(yx274, yx2750), ba) at position [2] we obtained the following new rules:

new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y4)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y4)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map2(y0, y1, Zero, Pos(Zero), y4) → new_map0(y0, new_primPlusNat0(Zero, Zero), Zero, y4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y4)
new_map2(y0, y1, Zero, Pos(Zero), y4) → new_map0(y0, new_primPlusNat0(Zero, Zero), Zero, y4)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y4)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Zero), Succ(x0), y4) at position [1] we obtained the following new rules:

new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y4)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, new_primPlusNat0(Zero, Succ(x0)), Succ(x0), y4) at position [1] we obtained the following new rules:

new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, new_primPlusNat0(Succ(x0), Succ(x1)), Succ(Succ(new_primPlusNat0(x0, x1))), y4) at position [1] we obtained the following new rules:

new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map0(Succ(y_0), x1, Succ(Succ(y_1)), x3) → new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x3) we obtained the following new rules:

new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map0(Succ(y_0), x1, Succ(Zero), x3) → new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x3) we obtained the following new rules:

new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map0(Zero, x1, Succ(Zero), x3) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x3) we obtained the following new rules:

new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map(y0, y1, Zero, Pos(Succ(x0)), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5) we obtained the following new rules:

new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map(yx272, yx273, yx274, yx275, Zero, Zero, ba) → new_map2(yx272, yx273, yx274, yx275, ba) we obtained the following new rules:

new_map(x0, x1, Succ(y_2), Pos(Zero), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Zero), x4)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map(x0, x1, Zero, Pos(Succ(y_2)), Zero, Zero, x4) → new_map2(x0, x1, Zero, Pos(Succ(y_2)), x4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, Succ(y_2), Pos(Zero), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Zero), x4)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map(x0, x1, Zero, Pos(Succ(y_2)), Zero, Zero, x4) → new_map2(x0, x1, Zero, Pos(Succ(y_2)), x4)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map(y0, y1, Succ(x0), Pos(Zero), Zero, Succ(y4), y5) → new_map0(y0, Succ(x0), Succ(x0), y5) we obtained the following new rules:

new_map(Succ(y_0), x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(Zero, x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, Succ(y_2), Pos(Zero), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Zero), x4)
new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map(x0, x1, Zero, Pos(Succ(y_2)), Zero, Zero, x4) → new_map2(x0, x1, Zero, Pos(Succ(y_2)), x4)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(Succ(y_0), x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(Zero, x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map2(y0, y1, Succ(x0), Pos(Zero), y4) → new_map0(y0, Succ(x0), Succ(x0), y4) we obtained the following new rules:

new_map2(Zero, x1, Succ(Zero), Pos(Zero), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map2(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map2(Succ(y_0), x1, Succ(Zero), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map2(Zero, x1, Succ(Zero), Pos(Zero), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map(x0, x1, Succ(y_2), Pos(Zero), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Zero), x4)
new_map2(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map2(Succ(y_0), x1, Succ(Zero), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map(x0, x1, Zero, Pos(Succ(y_2)), Zero, Zero, x4) → new_map2(x0, x1, Zero, Pos(Succ(y_2)), x4)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(Succ(y_0), x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(Zero, x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By forward instantiating [14] the rule new_map2(y0, y1, Zero, Pos(Succ(x0)), y4) → new_map0(y0, Succ(x0), Succ(x0), y4) we obtained the following new rules:

new_map2(Succ(y_0), x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map2(Zero, x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, Succ(y_2), Pos(Zero), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Zero), x4)
new_map2(Zero, x1, Succ(Zero), Pos(Zero), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map2(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map2(Zero, x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map(x0, x1, Zero, Pos(Succ(y_2)), Zero, Zero, x4) → new_map2(x0, x1, Zero, Pos(Succ(y_2)), x4)
new_map2(Succ(y_0), x1, Succ(Zero), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(Succ(y_0), x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(Zero, x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

new_map(x0, x1, Succ(y_2), Pos(Zero), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Zero), x4)
new_map(x0, x1, Zero, Pos(Succ(y_2)), Zero, Zero, x4) → new_map2(x0, x1, Zero, Pos(Succ(y_2)), x4)
new_map(Zero, x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Zero)), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x4)
new_map(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x4)
new_map(Zero, x1, Succ(Zero), Pos(Zero), Zero, Succ(x3), x4) → new_map0(Zero, Succ(Zero), Succ(Zero), x4)

The remaining pairs can at least be oriented weakly.

new_map2(Zero, x1, Succ(Zero), Pos(Zero), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map2(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map2(Zero, x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map2(Succ(y_0), x1, Succ(Zero), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)

Used ordering: Polynomial interpretation [25]:

POL(Pos(x₁)) = x₁
POL(Succ(x₁)) = 0
POL(Zero) = 1
POL(new_map(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₂ + x₃ + x₄
POL(new_map0(x₁, x₂, x₃, x₄)) = 0
POL(new_map2(x₁, x₂, x₃, x₄, x₅)) = x₂
POL(new_map3(x₁, x₂, x₃, x₄)) = 0
POL(new_map4(x₁, x₂, x₃, x₄, x₅, x₆)) = 0
POL(new_primPlusNat0(x₁, x₂)) = 1 + x₂

The following usable rules [17] were oriented: none

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map2(Zero, x1, Succ(Zero), Pos(Zero), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Succ(y_1))), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map3(Succ(y_0), Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map2(Succ(y_0), x1, Succ(Succ(y_1)), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Succ(y_1)), Succ(Succ(y_1)), x3)
new_map0(Succ(x0), Succ(Zero), Succ(Zero), z4) → new_map3(Succ(x0), Succ(Zero), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(Zero, x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Zero, Succ(Zero), Succ(Zero), x3)
new_map0(Zero, Succ(Zero), Succ(Zero), z4) → new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), z4)
new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Zero, Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Zero, x2)
new_map2(Succ(y_0), x1, Zero, Pos(Succ(Zero)), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map3(Zero, Succ(Zero), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Zero)), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map2(Succ(y_0), x1, Succ(Zero), Pos(Zero), x3) → new_map0(Succ(y_0), Succ(Zero), Succ(Zero), x3)
new_map4(Pos(Succ(Succ(y_4))), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Succ(Zero), x2) → new_map(Succ(y_4), Succ(Zero), Succ(Zero), Pos(Succ(Zero)), Zero, Succ(y_4), x2)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 12 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                          ↳ MNOCProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
In the following pairs the term without variables Pos(Succ(Zero)) is replaced by the fresh variable x_removed.
Pair: new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
Positions in right side of the pair:

Pair: new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
Positions in right side of the pair:

Pair: new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
Positions in right side of the pair:

Pair: new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
Positions in right side of the pair:

The new variable was added to all pairs as a new argument[13].

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                          ↳ MNOCProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4, x_removed) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4, x_removed)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2, x_removed) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), x_removed, Succ(y_4), Succ(y_5), x2, x_removed)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5, x_removed) → new_map3(Succ(x0), Succ(Succ(y_1)), x_removed, z5, x_removed)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4, x_removed) → new_map3(Succ(x0), Succ(Succ(x2)), x_removed, z4, x_removed)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4, x_removed) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4, x_removed)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5, x_removed) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5, x_removed)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6, x_removed) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6, x_removed)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6, x_removed) → new_map(x0, x1, x2, x3, Zero, Zero, x6, x_removed)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2, x_removed) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), x_removed, Succ(Succ(y_1)), x2, x_removed)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6, x_removed) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6, x_removed)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

Pair: new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
Positions in right side of the pair:

The new variable was added to all pairs as a new argument[13].

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                          ↳ MNOCProof

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4, x_removed) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4, x_removed)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2, x_removed) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), x_removed, Succ(y_4), Succ(y_5), x2, x_removed)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5, x_removed) → new_map3(Succ(x0), Succ(Succ(y_1)), x_removed, z5, x_removed)
new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4, x_removed) → new_map3(Succ(x0), Succ(Succ(x2)), x_removed, z4, x_removed)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4, x_removed) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4, x_removed)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5, x_removed) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5, x_removed)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6, x_removed) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6, x_removed)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6, x_removed) → new_map(x0, x1, x2, x3, Zero, Zero, x6, x_removed)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2, x_removed) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), x_removed, Succ(Succ(y_1)), x2, x_removed)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6, x_removed) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6, x_removed)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
We use the modular non-overlap check [17] to decrease Q to the empty set.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ QDPOrderProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Narrowing

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                              ↳ Narrowing

                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                      ↳ Rewriting

                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                          ↳ Rewriting

                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                  ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                      ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                          ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                                                                                              ↳ ForwardInstantiation

                                                                                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                      ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                          ↳ RemovalProof

                                                                                                                                                                                                                                                                                                                                                                          ↳ MNOCProof

                                                                                                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map0(Succ(x0), Succ(Succ(x2)), Succ(Succ(x2)), z4) → new_map3(Succ(x0), Succ(Succ(x2)), Pos(Succ(Zero)), z4)
new_map(x0, x1, x2, Pos(y_3), Succ(Zero), Succ(Succ(y_4)), x6) → new_map(x0, x1, x2, Pos(y_3), Zero, Succ(y_4), x6)
new_map(y0, y1, Succ(x0), Pos(Succ(x1)), Zero, Succ(y4), y5) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y5)
new_map(x0, x1, x2, x3, Succ(Succ(y_4)), Succ(Succ(y_5)), x6) → new_map(x0, x1, x2, x3, Succ(y_4), Succ(y_5), x6)
new_map0(Succ(x0), Succ(Succ(y_0)), Succ(Succ(y_1)), z5) → new_map3(Succ(x0), Succ(Succ(y_1)), Pos(Succ(Zero)), z5)
new_map4(Pos(Succ(Succ(y_5))), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(Succ(y_4)), x2) → new_map(Succ(y_5), Succ(Succ(y_4)), Succ(Succ(y_4)), Pos(Succ(Zero)), Succ(y_4), Succ(y_5), x2)
new_map(x0, x1, Succ(y_2), Pos(Succ(y_3)), Zero, Zero, x4) → new_map2(x0, x1, Succ(y_2), Pos(Succ(y_3)), x4)
new_map3(Succ(y_0), Succ(Succ(y_1)), Pos(Succ(Zero)), x2) → new_map4(Pos(Succ(Succ(y_0))), Succ(Succ(y_1)), Succ(Succ(y_1)), Pos(Succ(Zero)), Succ(Succ(y_1)), x2)
new_map(x0, x1, x2, x3, Succ(Zero), Succ(Zero), x6) → new_map(x0, x1, x2, x3, Zero, Zero, x6)
new_map2(y0, y1, Succ(x0), Pos(Succ(x1)), y4) → new_map0(y0, Succ(Succ(new_primPlusNat0(x0, x1))), Succ(Succ(new_primPlusNat0(x0, x1))), y4)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

Q is empty.
We have to consider all (P,Q,R)-chains.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(yx2180), Zero) → Succ(yx2180)
new_primPlusNat0(Zero, Succ(yx212000)) → Succ(yx212000)
new_primPlusNat0(Succ(yx2180), Succ(yx212000)) → Succ(Succ(new_primPlusNat0(yx2180, yx212000)))

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

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

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

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

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

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Zero)), z3) → new_map16(Neg(Succ(Zero)), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3) we obtained the following new rules:

new_map13(Neg(Succ(Zero)), Succ(x0), Succ(x0), Pos(Succ(Zero)), Succ(x0), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x0), Succ(x0), Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), z3) we obtained the following new rules:

new_map13(Neg(Zero), Succ(x0), Succ(x0), Pos(Succ(Zero)), Succ(x0), Neg(Zero), z2) → new_map16(Neg(Zero), Succ(x0), Succ(x0), Pos(Succ(Zero)), z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Pos(x4), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Pos(x4), z3) → new_map9(Pos(x4), y_1, z3) we obtained the following new rules:

new_map13(Pos(x0), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Pos(x0), z2) → new_map9(Pos(x0), x1, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Instantiation

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map13(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), Succ(y_2), Neg(Succ(Succ(x0))), z3) → new_map15(Neg(Succ(Succ(x0))), Succ(y_0), Succ(y_1), Pos(Succ(Zero)), x0, y_2, z3) we obtained the following new rules:

new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ QDPOrderProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

new_map16(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The remaining pairs can at least be oriented weakly.

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

Used ordering: Polynomial interpretation [25]:

POL(Neg(x₁)) = 0
POL(Pos(x₁)) = x₁
POL(Succ(x₁)) = 0
POL(Zero) = 1
POL(new_map1(x₁, x₂, x₃, x₄)) = x₁
POL(new_map12(x₁, x₂, x₃, x₄)) = 0
POL(new_map13(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = 0
POL(new_map15(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₁ + x₂ + x₃ + x₄
POL(new_map16(x₁, x₂, x₃, x₄, x₅)) = x₁ + x₄
POL(new_map17(x₁, x₂, x₃, x₄, x₅)) = x₁
POL(new_map9(x₁, x₂, x₃)) = 0

The following usable rules [17] were oriented: none

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
We use the reduction pair processor [15].

The following pairs can be oriented strictly and are deleted.

new_map17(yx207, yx217, yx218, Pos(Zero), bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

The remaining pairs can at least be oriented weakly.

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

Used ordering: Polynomial interpretation [25]:

POL(Neg(x₁)) = 0
POL(Pos(x₁)) = x₁
POL(Succ(x₁)) = 0
POL(Zero) = 1
POL(new_map1(x₁, x₂, x₃, x₄)) = 0
POL(new_map12(x₁, x₂, x₃, x₄)) = 0
POL(new_map13(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = 0
POL(new_map15(x₁, x₂, x₃, x₄, x₅, x₆, x₇)) = x₄
POL(new_map16(x₁, x₂, x₃, x₄, x₅)) = 0
POL(new_map17(x₁, x₂, x₃, x₄, x₅)) = x₄
POL(new_map9(x₁, x₂, x₃)) = 0

The following usable rules [17] were oriented: none

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ Rewriting

                                          ↳ QDP

                                            ↳ Rewriting

                                              ↳ QDP

                                                ↳ Rewriting

                                                  ↳ QDP

                                                    ↳ Rewriting

                                                      ↳ QDP

                                                        ↳ Rewriting

                                                          ↳ QDP

                                                            ↳ Rewriting

                                                              ↳ QDP

                                                                ↳ Rewriting

                                                                  ↳ QDP

                                                                    ↳ Rewriting

                                                                      ↳ QDP

                                                                        ↳ Rewriting

                                                                          ↳ QDP

                                                                            ↳ Rewriting

                                                                              ↳ QDP

                                                                                ↳ Rewriting

                                                                                  ↳ QDP

                                                                                    ↳ Rewriting

                                                                                      ↳ QDP

                                                                                        ↳ Rewriting

                                                                                          ↳ QDP

                                                                                            ↳ Rewriting

                                                                                              ↳ QDP

                                                                                                ↳ Rewriting

                                                                                                  ↳ QDP

                                                                                                    ↳ Rewriting

                                                                                                      ↳ QDP

                                                                                                        ↳ Rewriting

                                                                                                          ↳ QDP

                                                                                                            ↳ UsableRulesProof

                                                                                                              ↳ QDP

                                                                                                                ↳ QReductionProof

                                                                                                                  ↳ QDP

                                                                                                                    ↳ Instantiation

                                                                                                                      ↳ QDP

                                                                                                                        ↳ Instantiation

                                                                                                                          ↳ QDP

                                                                                                                            ↳ Instantiation

                                                                                                                              ↳ QDP

                                                                                                                                ↳ Instantiation

                                                                                                                                  ↳ QDP

                                                                                                                                    ↳ Instantiation

                                                                                                                                      ↳ QDP

                                                                                                                                        ↳ Instantiation

                                                                                                                                          ↳ QDP

                                                                                                                                            ↳ Instantiation

                                                                                                                                              ↳ QDP

                                                                                                                                                ↳ Instantiation

                                                                                                                                                  ↳ QDP

                                                                                                                                                    ↳ Instantiation

                                                                                                                                                      ↳ QDP

                                                                                                                                                        ↳ Instantiation

                                                                                                                                                          ↳ QDP

                                                                                                                                                            ↳ DependencyGraphProof

                                                                                                                                                              ↳ AND

                                                                                                                                                                ↳ QDP

                                                                                                                                                                ↳ QDP

                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                    ↳ QDP

                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                        ↳ QDP

                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                            ↳ QDP

                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                              ↳ Rewriting

                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                  ↳ Rewriting

                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                          ↳ DependencyGraphProof

                                                                                                                                                                                                            ↳ AND

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                            ↳ Instantiation

                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                ↳ Instantiation

                                                                                                                                                                                                                                                  ↳ QDP

                                                                                                                                                                                                                                                    ↳ Instantiation

                                                                                                                                                                                                                                                      ↳ QDP

                                                                                                                                                                                                                                                        ↳ Instantiation

                                                                                                                                                                                                                                                          ↳ QDP

                                                                                                                                                                                                                                                            ↳ QDPOrderProof

                                                                                                                                                                                                                                                              ↳ QDP

                                                                                                                                                                                                                                                                ↳ DependencyGraphProof

                                                                                                                                                                                                                                                                  ↳ AND

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                      ↳ UsableRulesProof

                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                          ↳ QReductionProof

                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                              ↳ Instantiation

                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                  ↳ Instantiation

                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                      ↳ Instantiation

                                                                                                                                                                                                                                                                                        ↳ QDP

                                                                                                                                                                                                                                                                                          ↳ Instantiation

                                                                                                                                                                                                                                                                                            ↳ QDP

                                                                                                                                                                                                                                                                                              ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                ↳ QDP

                                                                                                                                                                                                                                                                                                  ↳ QDPOrderProof

                                                                                                                                                                                                                                                                                                    ↳ QDP

                                                                                                                                                                                                                                                                                                      ↳ QDPSizeChangeProof

                              ↳ QDP

                              ↳ QDP

                          ↳ Narrow

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

new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)

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

new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
new_map12(z0, z1, Pos(Succ(Zero)), z2) → new_map13(z0, z1, z1, Pos(Succ(Zero)), z1, z0, z2)
The graph contains the following edges 1 >= 1, 2 >= 2, 2 >= 3, 3 >= 4, 2 >= 5, 1 >= 6, 4 >= 7
new_map9(yx207, yx218, bc) → new_map12(yx207, yx218, Pos(Succ(Zero)), bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 4
new_map13(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), Succ(x1), Neg(Succ(Succ(x0))), z2) → new_map15(Neg(Succ(Succ(x0))), Succ(x1), Succ(x1), Pos(Succ(Zero)), x0, x1, z2)
The graph contains the following edges 1 >= 1, 6 >= 1, 2 >= 2, 3 >= 2, 5 >= 2, 2 >= 3, 3 >= 3, 5 >= 3, 4 >= 4, 1 > 5, 6 > 5, 2 > 6, 3 > 6, 5 > 6, 7 >= 7
new_map16(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
The graph contains the following edges 1 >= 1, 4 > 2, 3 > 3, 5 >= 4
new_map15(yx207, yx217, yx218, yx212, Succ(yx213000), Succ(yx2190), bc) → new_map15(yx207, yx217, yx218, yx212, yx213000, yx2190, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 > 5, 6 > 6, 7 >= 7
new_map15(yx207, yx217, yx218, yx212, Zero, Succ(yx2190), bc) → new_map16(yx207, yx217, yx218, yx212, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
new_map15(yx207, yx217, yx218, yx212, Zero, Zero, bc) → new_map17(yx207, yx217, yx218, yx212, bc)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 7 >= 5
new_map1(yx207, Succ(yx212000), Succ(yx2180), bc) → new_map1(yx207, yx212000, yx2180, bc)
The graph contains the following edges 1 >= 1, 2 > 2, 3 > 3, 4 >= 4
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Succ(yx212000))), bc) → new_map1(yx207, yx212000, yx2180, bc)
The graph contains the following edges 1 >= 1, 4 > 2, 3 > 3, 5 >= 4
new_map1(yx207, Zero, Succ(yx2180), bc) → new_map9(yx207, yx2180, bc)
The graph contains the following edges 1 >= 1, 3 > 2, 4 >= 3
new_map17(yx207, yx217, Succ(yx2180), Pos(Succ(Zero)), bc) → new_map9(yx207, yx2180, bc)
The graph contains the following edges 1 >= 1, 3 > 2, 5 >= 3
new_map13(Pos(x4), Succ(x2), Succ(x2), Pos(Succ(Zero)), Succ(x2), Pos(x4), z2) → new_map9(Pos(x4), x2, z2)
The graph contains the following edges 1 >= 1, 6 >= 1, 2 > 2, 3 > 2, 5 > 2, 7 >= 3
new_map13(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), Succ(y_0), Neg(Zero), z3) → new_map16(Neg(Zero), Succ(y_0), Succ(y_0), Pos(Succ(Zero)), z3)
The graph contains the following edges 1 >= 1, 6 >= 1, 2 >= 2, 3 >= 2, 5 >= 2, 2 >= 3, 3 >= 3, 5 >= 3, 4 >= 4, 7 >= 5
new_map13(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), Succ(x4), Neg(Succ(Zero)), z2) → new_map16(Neg(Succ(Zero)), Succ(x4), Succ(x4), Pos(Succ(Zero)), z2)
The graph contains the following edges 1 >= 1, 6 >= 1, 2 >= 2, 3 >= 2, 5 >= 2, 2 >= 3, 3 >= 3, 5 >= 3, 4 >= 4, 7 >= 5
new_map13(Neg(Zero), z1, z1, Pos(Succ(Zero)), z1, Neg(Zero), z2) → new_map16(Neg(Zero), z1, z1, Pos(Succ(Zero)), z2)
The graph contains the following edges 1 >= 1, 6 >= 1, 2 >= 2, 3 >= 2, 5 >= 2, 2 >= 3, 3 >= 3, 5 >= 3, 4 >= 4, 7 >= 5

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, new_fromInt(Pos(Succ(Zero))), ba)
new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, new_fromInt(Pos(Succ(Zero))), ba)
new_map21(yx207, Zero, yx235, ba) → new_map20(yx207, yx235, yx207, ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

The TRS R consists of the following rules:

new_fromInt(yx8) → yx8

The set Q consists of the following terms:

new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, new_fromInt(Pos(Succ(Zero))), ba) at position [2] we obtained the following new rules:

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map21(yx207, Zero, yx235, ba) → new_map20(yx207, yx235, yx207, ba)
new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, new_fromInt(Pos(Succ(Zero))), ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

The TRS R consists of the following rules:

new_fromInt(yx8) → yx8

The set Q consists of the following terms:

new_fromInt(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, new_fromInt(Pos(Succ(Zero))), ba) at position [2] we obtained the following new rules:

new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map21(yx207, Zero, yx235, ba) → new_map20(yx207, yx235, yx207, ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

The TRS R consists of the following rules:

new_fromInt(yx8) → yx8

The set Q consists of the following terms:

new_fromInt(x0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map21(yx207, Zero, yx235, ba) → new_map20(yx207, yx235, yx207, ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

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

new_fromInt(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_fromInt(x0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map21(yx207, Zero, yx235, ba) → new_map20(yx207, yx235, yx207, ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)
new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map21(yx207, Zero, yx235, ba) → new_map20(yx207, yx235, yx207, ba) we obtained the following new rules:

new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                                                  ↳ QDP

                                                    ↳ DependencyGraphProof

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, Neg(yx2120), Pos(Succ(yx21300)), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

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 1 less node.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                                                  ↳ QDP

                                                    ↳ DependencyGraphProof

                                                      ↳ QDP

                                                        ↳ Instantiation

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)
new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map20(yx207, yx212, Neg(Zero), ba) → new_map23(yx207, yx212, ba) we obtained the following new rules:

new_map20(Neg(Zero), Pos(Succ(Zero)), Neg(Zero), z1) → new_map23(Neg(Zero), Pos(Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                                                  ↳ QDP

                                                    ↳ DependencyGraphProof

                                                      ↳ QDP

                                                        ↳ Instantiation

                                                          ↳ QDP

                                                            ↳ Instantiation

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map20(Neg(Zero), Pos(Succ(Zero)), Neg(Zero), z1) → new_map23(Neg(Zero), Pos(Succ(Zero)), z1)
new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba)
new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map23(yx207, yx212, ba) → new_map22(yx207, yx212, ba) we obtained the following new rules:

new_map23(Neg(Zero), Pos(Succ(Zero)), z0) → new_map22(Neg(Zero), Pos(Succ(Zero)), z0)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                                                  ↳ QDP

                                                    ↳ DependencyGraphProof

                                                      ↳ QDP

                                                        ↳ Instantiation

                                                          ↳ QDP

                                                            ↳ Instantiation

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                              ↳ QDP

                          ↳ Narrow

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

new_map23(Neg(Zero), Pos(Succ(Zero)), z0) → new_map22(Neg(Zero), Pos(Succ(Zero)), z0)
new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map20(Neg(Zero), Pos(Succ(Zero)), Neg(Zero), z1) → new_map23(Neg(Zero), Pos(Succ(Zero)), z1)
new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

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 2 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                                                  ↳ QDP

                                                    ↳ DependencyGraphProof

                                                      ↳ QDP

                                                        ↳ Instantiation

                                                          ↳ QDP

                                                            ↳ Instantiation

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)
new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_map20(yx207, yx212, Pos(Zero), ba) → new_map22(yx207, yx212, ba) we obtained the following new rules:

new_map20(Pos(Zero), Pos(Succ(Zero)), Pos(Zero), z1) → new_map22(Pos(Zero), Pos(Succ(Zero)), z1)

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ Rewriting

                                  ↳ QDP

                                    ↳ Rewriting

                                      ↳ QDP

                                        ↳ UsableRulesProof

                                          ↳ QDP

                                            ↳ QReductionProof

                                              ↳ QDP

                                                ↳ Instantiation

                                                  ↳ QDP

                                                    ↳ DependencyGraphProof

                                                      ↳ QDP

                                                        ↳ Instantiation

                                                          ↳ QDP

                                                            ↳ Instantiation

                                                              ↳ QDP

                                                                ↳ DependencyGraphProof

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                                                                      ↳ QDP

                                                                        ↳ DependencyGraphProof

                              ↳ QDP

                          ↳ Narrow

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

new_map22(yx207, Neg(yx2120), ba) → new_map21(yx207, yx2120, Pos(Succ(Zero)), ba)
new_map20(Pos(Zero), Pos(Succ(Zero)), Pos(Zero), z1) → new_map22(Pos(Zero), Pos(Succ(Zero)), z1)
new_map21(z0, Zero, Pos(Succ(Zero)), z2) → new_map20(z0, Pos(Succ(Zero)), z0, z2)

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 0 SCCs with 3 less nodes.

↳ HASKELL

  ↳ LR

    ↳ HASKELL

      ↳ IFR

        ↳ HASKELL

          ↳ BR

            ↳ HASKELL

              ↳ COR

                ↳ HASKELL

                  ↳ LetRed

                    ↳ HASKELL

                      ↳ NumRed

                        ↳ HASKELL

                          ↳ Narrow

                            ↳ AND

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                              ↳ QDP

                                ↳ QDPSizeChangeProof

                          ↳ Narrow

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

new_map24(yx207, yx208, yx209, Succ(yx2100), Succ(yx2110), yx212, yx213, ba) → new_map24(yx207, yx208, yx209, yx2100, yx2110, yx212, yx213, ba)

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

new_map24(yx207, yx208, yx209, Succ(yx2100), Succ(yx2110), yx212, yx213, ba) → new_map24(yx207, yx208, yx209, yx2100, yx2110, yx212, yx213, ba)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 > 4, 5 > 5, 6 >= 6, 7 >= 7, 8 >= 8

Haskell To QDPs

primDivNatS0	x y True	= Succ (primDivNatS (primMinusNatS x y) (Succ y))
primDivNatS0	x y False	= Zero

primModNatS0	x y True	= primModNatS (primMinusNatS x y) (Succ y)
primModNatS0	x y False	= Succ x

takeWhile	p []	= takeWhile3 p []
takeWhile	p (x : xs)	= takeWhile2 p (x : xs)

takeWhile1	p x xs True	= x : takeWhile p xs
takeWhile1	p x xs False	= takeWhile0 p x xs otherwise