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

MAYBE 82.997 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

  ↳ IFR

mainModule Main

(((*) :: 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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

mainModule Main

(((*) :: 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.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

mainModule Main

(((*) :: 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

gcd' x 0 = x

gcd' x y = gcd' y (x `rem` y)

is transformed to

gcd' x xz = gcd'2 x xz

gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x xz = x

gcd'1 yu yv yw = gcd'0 yv yw

gcd'2 x xz = gcd'1 (xz == 0) x xz

gcd'2 yx yy = gcd'0 yx yy

The following Function with conditions

gcd 0 0 = error []

gcd x y =

gcd' (abs x) (abs y)

where

gcd' x 0 = x

gcd' x y = gcd' y (x `rem` y)

is transformed to

gcd yz zu = gcd3 yz zu

gcd x y = gcd0 x y

gcd0 x y =

gcd' (abs x) (abs y)

where

gcd' x xz = gcd'2 x xz

gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x xz = x

gcd'1 yu yv yw = gcd'0 yv yw

gcd'2 x xz = gcd'1 (xz == 0) x xz

gcd'2 yx yy = gcd'0 yx yy

gcd1 True yz zu = error []

gcd1 zv zw zx = gcd0 zw zx

gcd2 True yz zu = gcd1 (zu == 0) yz zu

gcd2 zy zz vuu = gcd0 zz vuu

gcd3 yz zu = gcd2 (yz == 0) yz zu

gcd3 vuv vuw = gcd0 vuv vuw

The following Function with conditions

absReal x

| x >= 0

= x

| otherwise

= `negate` x

is transformed to

absReal x = absReal2 x

absReal0 x True = `negate` x

absReal1 x True = x

absReal1 x False = absReal0 x otherwise

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions

undefined

| False

= undefined

is transformed to

undefined = undefined1

undefined0 True = undefined

undefined1 = undefined0 False

The following Function with conditions

reduce x y

| y == 0

= error []

| otherwise

= x `quot` d :% (y `quot` d)

where

d = gcd x y

is transformed to

reduce x y = reduce2 x y

reduce2 x y =

reduce1 x y (y == 0)

where

d = gcd x y

reduce0 x y True = x `quot` d :% (y `quot` d)

reduce1 x y True = error []

reduce1 x y False = reduce0 x y otherwise

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

mainModule Main

(((*) :: 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

reduce1 x y (y == 0)

where

d = gcd x y

reduce0 x y True = x `quot` d :% (y `quot` d)

reduce1 x y True = error []

reduce1 x y False = reduce0 x y otherwise

are unpacked to the following functions on top level

reduce2D vux vuy = gcd vux vuy

reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy)

reduce2Reduce1 vux vuy x y True = error []

reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise

The bindings of the following Let/Where expression

gcd' (abs x) (abs y)

where

gcd' x xz = gcd'2 x xz

gcd' x y = gcd'0 x y

gcd'0 x y = gcd' y (x `rem` y)

gcd'1 True x xz = x

gcd'1 yu yv yw = gcd'0 yv yw

gcd'2 x xz = gcd'1 (xz == 0) x xz

gcd'2 yx yy = gcd'0 yx yy

are unpacked to the following functions on top level

gcd0Gcd'1 True x xz = x

gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw

gcd0Gcd' x xz = gcd0Gcd'2 x xz

gcd0Gcd' x y = gcd0Gcd'0 x y

gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz

gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy

gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

mainModule Main

(((*) :: 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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                      ↳ Narrow

mainModule Main

((*) :: Ratio Int -> Ratio Int -> Ratio Int)

module Main where

import qualified Prelude

Haskell To QDPs

digraph dp_graph {
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3163 -> 5[label="",style="solid", color="burlywood", weight=3];
5[label="(*) (vuz30 :% vuz31) vuz4",fontsize=16,color="burlywood",shape="box"];3164[label="vuz4/vuz40 :% vuz41",fontsize=10,color="white",style="solid",shape="box"];5 -> 3164[label="",style="solid", color="burlywood", weight=9];
3164 -> 6[label="",style="solid", color="burlywood", weight=3];
6[label="(*) (vuz30 :% vuz31) (vuz40 :% vuz41)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
7[label="reduce (vuz30 * vuz40) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
8[label="reduce2 (vuz30 * vuz40) (vuz31 * vuz41)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9[label="reduce2Reduce1 (vuz30 * vuz40) (vuz31 * vuz41) (vuz30 * vuz40) (vuz31 * vuz41) (vuz31 * vuz41 == fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10[label="reduce2Reduce1 (vuz30 * vuz40) (vuz31 * vuz41) (vuz30 * vuz40) (vuz31 * vuz41) (primEqInt (vuz31 * vuz41) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
11[label="reduce2Reduce1 (vuz30 * vuz40) (primMulInt vuz31 vuz41) (vuz30 * vuz40) (primMulInt vuz31 vuz41) (primEqInt (primMulInt vuz31 vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];3165[label="vuz31/Pos vuz310",fontsize=10,color="white",style="solid",shape="box"];11 -> 3165[label="",style="solid", color="burlywood", weight=9];
3165 -> 12[label="",style="solid", color="burlywood", weight=3];
3166[label="vuz31/Neg vuz310",fontsize=10,color="white",style="solid",shape="box"];11 -> 3166[label="",style="solid", color="burlywood", weight=9];
3166 -> 13[label="",style="solid", color="burlywood", weight=3];
12[label="reduce2Reduce1 (vuz30 * vuz40) (primMulInt (Pos vuz310) vuz41) (vuz30 * vuz40) (primMulInt (Pos vuz310) vuz41) (primEqInt (primMulInt (Pos vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];3167[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];12 -> 3167[label="",style="solid", color="burlywood", weight=9];
3167 -> 14[label="",style="solid", color="burlywood", weight=3];
3168[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];12 -> 3168[label="",style="solid", color="burlywood", weight=9];
3168 -> 15[label="",style="solid", color="burlywood", weight=3];
13[label="reduce2Reduce1 (vuz30 * vuz40) (primMulInt (Neg vuz310) vuz41) (vuz30 * vuz40) (primMulInt (Neg vuz310) vuz41) (primEqInt (primMulInt (Neg vuz310) vuz41) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="box"];3169[label="vuz41/Pos vuz410",fontsize=10,color="white",style="solid",shape="box"];13 -> 3169[label="",style="solid", color="burlywood", weight=9];
3169 -> 16[label="",style="solid", color="burlywood", weight=3];
3170[label="vuz41/Neg vuz410",fontsize=10,color="white",style="solid",shape="box"];13 -> 3170[label="",style="solid", color="burlywood", weight=9];
3170 -> 17[label="",style="solid", color="burlywood", weight=3];
14[label="reduce2Reduce1 (vuz30 * vuz40) (primMulInt (Pos vuz310) (Pos vuz410)) (vuz30 * vuz40) (primMulInt (Pos vuz310) (Pos vuz410)) (primEqInt (primMulInt (Pos vuz310) (Pos vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
15[label="reduce2Reduce1 (vuz30 * vuz40) (primMulInt (Pos vuz310) (Neg vuz410)) (vuz30 * vuz40) (primMulInt (Pos vuz310) (Neg vuz410)) (primEqInt (primMulInt (Pos vuz310) (Neg vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
16[label="reduce2Reduce1 (vuz30 * vuz40) (primMulInt (Neg vuz310) (Pos vuz410)) (vuz30 * vuz40) (primMulInt (Neg vuz310) (Pos vuz410)) (primEqInt (primMulInt (Neg vuz310) (Pos vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
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18 -> 222[label="",style="dashed", color="red", weight=0];
18[label="reduce2Reduce1 (vuz30 * vuz40) (Pos (primMulNat vuz310 vuz410)) (vuz30 * vuz40) (Pos (primMulNat vuz310 vuz410)) (primEqInt (Pos (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];18 -> 223[label="",style="dashed", color="magenta", weight=3];
18 -> 224[label="",style="dashed", color="magenta", weight=3];
18 -> 225[label="",style="dashed", color="magenta", weight=3];
19 -> 269[label="",style="dashed", color="red", weight=0];
19[label="reduce2Reduce1 (vuz30 * vuz40) (Neg (primMulNat vuz310 vuz410)) (vuz30 * vuz40) (Neg (primMulNat vuz310 vuz410)) (primEqInt (Neg (primMulNat vuz310 vuz410)) (fromInt (Pos Zero)))",fontsize=16,color="magenta"];19 -> 270[label="",style="dashed", color="magenta", weight=3];
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20 -> 269[label="",style="dashed", color="red", weight=0];
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20 -> 275[label="",style="dashed", color="magenta", weight=3];
21 -> 222[label="",style="dashed", color="red", weight=0];
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21 -> 227[label="",style="dashed", color="magenta", weight=3];
21 -> 228[label="",style="dashed", color="magenta", weight=3];
223[label="primMulNat vuz310 vuz410",fontsize=16,color="burlywood",shape="triangle"];3175[label="vuz310/Succ vuz3100",fontsize=10,color="white",style="solid",shape="box"];223 -> 3175[label="",style="solid", color="burlywood", weight=9];
3175 -> 259[label="",style="solid", color="burlywood", weight=3];
3176[label="vuz310/Zero",fontsize=10,color="white",style="solid",shape="box"];223 -> 3176[label="",style="solid", color="burlywood", weight=9];
3176 -> 260[label="",style="solid", color="burlywood", weight=3];
224 -> 223[label="",style="dashed", color="red", weight=0];
224[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];225 -> 223[label="",style="dashed", color="red", weight=0];
225[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];222[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) (primEqInt (Pos vuz17) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];3179[label="vuz17/Succ vuz170",fontsize=10,color="white",style="solid",shape="box"];222 -> 3179[label="",style="solid", color="burlywood", weight=9];
3179 -> 261[label="",style="solid", color="burlywood", weight=3];
3180[label="vuz17/Zero",fontsize=10,color="white",style="solid",shape="box"];222 -> 3180[label="",style="solid", color="burlywood", weight=9];
3180 -> 262[label="",style="solid", color="burlywood", weight=3];
270 -> 223[label="",style="dashed", color="red", weight=0];
270[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];270 -> 306[label="",style="dashed", color="magenta", weight=3];
271 -> 223[label="",style="dashed", color="red", weight=0];
271[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];271 -> 307[label="",style="dashed", color="magenta", weight=3];
272 -> 223[label="",style="dashed", color="red", weight=0];
272[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];272 -> 308[label="",style="dashed", color="magenta", weight=3];
269[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) (primEqInt (Neg vuz20) (fromInt (Pos Zero)))",fontsize=16,color="burlywood",shape="triangle"];3184[label="vuz20/Succ vuz200",fontsize=10,color="white",style="solid",shape="box"];269 -> 3184[label="",style="solid", color="burlywood", weight=9];
3184 -> 309[label="",style="solid", color="burlywood", weight=3];
3185[label="vuz20/Zero",fontsize=10,color="white",style="solid",shape="box"];269 -> 3185[label="",style="solid", color="burlywood", weight=9];
3185 -> 310[label="",style="solid", color="burlywood", weight=3];
273 -> 223[label="",style="dashed", color="red", weight=0];
273[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];273 -> 311[label="",style="dashed", color="magenta", weight=3];
274 -> 223[label="",style="dashed", color="red", weight=0];
274[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];274 -> 312[label="",style="dashed", color="magenta", weight=3];
275 -> 223[label="",style="dashed", color="red", weight=0];
275[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];275 -> 313[label="",style="dashed", color="magenta", weight=3];
226 -> 223[label="",style="dashed", color="red", weight=0];
226[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];226 -> 263[label="",style="dashed", color="magenta", weight=3];
226 -> 264[label="",style="dashed", color="magenta", weight=3];
227 -> 223[label="",style="dashed", color="red", weight=0];
227[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];227 -> 265[label="",style="dashed", color="magenta", weight=3];
227 -> 266[label="",style="dashed", color="magenta", weight=3];
228 -> 223[label="",style="dashed", color="red", weight=0];
228[label="primMulNat vuz310 vuz410",fontsize=16,color="magenta"];228 -> 267[label="",style="dashed", color="magenta", weight=3];
228 -> 268[label="",style="dashed", color="magenta", weight=3];
259[label="primMulNat (Succ vuz3100) vuz410",fontsize=16,color="burlywood",shape="box"];3192[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];259 -> 3192[label="",style="solid", color="burlywood", weight=9];
3192 -> 314[label="",style="solid", color="burlywood", weight=3];
3193[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];259 -> 3193[label="",style="solid", color="burlywood", weight=9];
3193 -> 315[label="",style="solid", color="burlywood", weight=3];
260[label="primMulNat Zero vuz410",fontsize=16,color="burlywood",shape="box"];3194[label="vuz410/Succ vuz4100",fontsize=10,color="white",style="solid",shape="box"];260 -> 3194[label="",style="solid", color="burlywood", weight=9];
3194 -> 316[label="",style="solid", color="burlywood", weight=3];
3195[label="vuz410/Zero",fontsize=10,color="white",style="solid",shape="box"];260 -> 3195[label="",style="solid", color="burlywood", weight=9];
3195 -> 317[label="",style="solid", color="burlywood", weight=3];
261[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) (primEqInt (Pos (Succ vuz170)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];261 -> 318[label="",style="solid", color="black", weight=3];
262[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) (primEqInt (Pos Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];262 -> 319[label="",style="solid", color="black", weight=3];
306[label="vuz410",fontsize=16,color="green",shape="box"];307[label="vuz410",fontsize=16,color="green",shape="box"];308[label="vuz410",fontsize=16,color="green",shape="box"];309[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) (primEqInt (Neg (Succ vuz200)) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];309 -> 320[label="",style="solid", color="black", weight=3];
310[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) (primEqInt (Neg Zero) (fromInt (Pos Zero)))",fontsize=16,color="black",shape="box"];310 -> 321[label="",style="solid", color="black", weight=3];
311[label="vuz310",fontsize=16,color="green",shape="box"];312[label="vuz310",fontsize=16,color="green",shape="box"];313[label="vuz310",fontsize=16,color="green",shape="box"];263[label="vuz410",fontsize=16,color="green",shape="box"];264[label="vuz310",fontsize=16,color="green",shape="box"];265[label="vuz410",fontsize=16,color="green",shape="box"];266[label="vuz310",fontsize=16,color="green",shape="box"];267[label="vuz410",fontsize=16,color="green",shape="box"];268[label="vuz310",fontsize=16,color="green",shape="box"];314[label="primMulNat (Succ vuz3100) (Succ vuz4100)",fontsize=16,color="black",shape="box"];314 -> 322[label="",style="solid", color="black", weight=3];
315[label="primMulNat (Succ vuz3100) Zero",fontsize=16,color="black",shape="box"];315 -> 323[label="",style="solid", color="black", weight=3];
316[label="primMulNat Zero (Succ vuz4100)",fontsize=16,color="black",shape="box"];316 -> 324[label="",style="solid", color="black", weight=3];
317[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];317 -> 325[label="",style="solid", color="black", weight=3];
318[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) (primEqInt (Pos (Succ vuz170)) (Pos Zero))",fontsize=16,color="black",shape="box"];318 -> 326[label="",style="solid", color="black", weight=3];
319[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) (primEqInt (Pos Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];319 -> 327[label="",style="solid", color="black", weight=3];
320[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) (primEqInt (Neg (Succ vuz200)) (Pos Zero))",fontsize=16,color="black",shape="box"];320 -> 328[label="",style="solid", color="black", weight=3];
321[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) (primEqInt (Neg Zero) (Pos Zero))",fontsize=16,color="black",shape="box"];321 -> 329[label="",style="solid", color="black", weight=3];
322 -> 330[label="",style="dashed", color="red", weight=0];
322[label="primPlusNat (primMulNat vuz3100 (Succ vuz4100)) (Succ vuz4100)",fontsize=16,color="magenta"];322 -> 331[label="",style="dashed", color="magenta", weight=3];
323[label="Zero",fontsize=16,color="green",shape="box"];324[label="Zero",fontsize=16,color="green",shape="box"];325[label="Zero",fontsize=16,color="green",shape="box"];326[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) False",fontsize=16,color="black",shape="box"];326 -> 332[label="",style="solid", color="black", weight=3];
327[label="reduce2Reduce1 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) True",fontsize=16,color="black",shape="box"];327 -> 333[label="",style="solid", color="black", weight=3];
328[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) False",fontsize=16,color="black",shape="box"];328 -> 334[label="",style="solid", color="black", weight=3];
329[label="reduce2Reduce1 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) True",fontsize=16,color="black",shape="box"];329 -> 335[label="",style="solid", color="black", weight=3];
331 -> 223[label="",style="dashed", color="red", weight=0];
331[label="primMulNat vuz3100 (Succ vuz4100)",fontsize=16,color="magenta"];331 -> 336[label="",style="dashed", color="magenta", weight=3];
331 -> 337[label="",style="dashed", color="magenta", weight=3];
330[label="primPlusNat vuz21 (Succ vuz4100)",fontsize=16,color="burlywood",shape="triangle"];3198[label="vuz21/Succ vuz210",fontsize=10,color="white",style="solid",shape="box"];330 -> 3198[label="",style="solid", color="burlywood", weight=9];
3198 -> 338[label="",style="solid", color="burlywood", weight=3];
3199[label="vuz21/Zero",fontsize=10,color="white",style="solid",shape="box"];330 -> 3199[label="",style="solid", color="burlywood", weight=9];
3199 -> 339[label="",style="solid", color="burlywood", weight=3];
332[label="reduce2Reduce0 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) otherwise",fontsize=16,color="black",shape="box"];332 -> 340[label="",style="solid", color="black", weight=3];
333[label="error []",fontsize=16,color="black",shape="triangle"];333 -> 341[label="",style="solid", color="black", weight=3];
334[label="reduce2Reduce0 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) otherwise",fontsize=16,color="black",shape="box"];334 -> 342[label="",style="solid", color="black", weight=3];
335 -> 333[label="",style="dashed", color="red", weight=0];
335[label="error []",fontsize=16,color="magenta"];336[label="Succ vuz4100",fontsize=16,color="green",shape="box"];337[label="vuz3100",fontsize=16,color="green",shape="box"];338[label="primPlusNat (Succ vuz210) (Succ vuz4100)",fontsize=16,color="black",shape="box"];338 -> 343[label="",style="solid", color="black", weight=3];
339[label="primPlusNat Zero (Succ vuz4100)",fontsize=16,color="black",shape="box"];339 -> 344[label="",style="solid", color="black", weight=3];
340[label="reduce2Reduce0 (vuz30 * vuz40) (Pos vuz16) (vuz30 * vuz40) (Pos vuz15) True",fontsize=16,color="black",shape="box"];340 -> 345[label="",style="solid", color="black", weight=3];
341[label="error []",fontsize=16,color="red",shape="box"];342[label="reduce2Reduce0 (vuz30 * vuz40) (Neg vuz19) (vuz30 * vuz40) (Neg vuz18) True",fontsize=16,color="black",shape="box"];342 -> 346[label="",style="solid", color="black", weight=3];
343[label="Succ (Succ (primPlusNat vuz210 vuz4100))",fontsize=16,color="green",shape="box"];343 -> 347[label="",style="dashed", color="green", weight=3];
344[label="Succ vuz4100",fontsize=16,color="green",shape="box"];345[label="vuz30 * vuz40 `quot` reduce2D (vuz30 * vuz40) (Pos vuz16) :% (Pos vuz15 `quot` reduce2D (vuz30 * vuz40) (Pos vuz16))",fontsize=16,color="green",shape="box"];345 -> 348[label="",style="dashed", color="green", weight=3];
345 -> 349[label="",style="dashed", color="green", weight=3];
346[label="vuz30 * vuz40 `quot` reduce2D (vuz30 * vuz40) (Neg vuz19) :% (Neg vuz18 `quot` reduce2D (vuz30 * vuz40) (Neg vuz19))",fontsize=16,color="green",shape="box"];346 -> 350[label="",style="dashed", color="green", weight=3];
346 -> 351[label="",style="dashed", color="green", weight=3];
347[label="primPlusNat vuz210 vuz4100",fontsize=16,color="burlywood",shape="triangle"];3201[label="vuz210/Succ vuz2100",fontsize=10,color="white",style="solid",shape="box"];347 -> 3201[label="",style="solid", color="burlywood", weight=9];
3201 -> 352[label="",style="solid", color="burlywood", weight=3];
3202[label="vuz210/Zero",fontsize=10,color="white",style="solid",shape="box"];347 -> 3202[label="",style="solid", color="burlywood", weight=9];
3202 -> 353[label="",style="solid", color="burlywood", weight=3];
348[label="vuz30 * vuz40 `quot` reduce2D (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];348 -> 354[label="",style="solid", color="black", weight=3];
349[label="Pos vuz15 `quot` reduce2D (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];349 -> 355[label="",style="solid", color="black", weight=3];
350[label="vuz30 * vuz40 `quot` reduce2D (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];350 -> 356[label="",style="solid", color="black", weight=3];
351[label="Neg vuz18 `quot` reduce2D (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];351 -> 357[label="",style="solid", color="black", weight=3];
352[label="primPlusNat (Succ vuz2100) vuz4100",fontsize=16,color="burlywood",shape="box"];3203[label="vuz4100/Succ vuz41000",fontsize=10,color="white",style="solid",shape="box"];352 -> 3203[label="",style="solid", color="burlywood", weight=9];
3203 -> 358[label="",style="solid", color="burlywood", weight=3];
3204[label="vuz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];352 -> 3204[label="",style="solid", color="burlywood", weight=9];
3204 -> 359[label="",style="solid", color="burlywood", weight=3];
353[label="primPlusNat Zero vuz4100",fontsize=16,color="burlywood",shape="box"];3205[label="vuz4100/Succ vuz41000",fontsize=10,color="white",style="solid",shape="box"];353 -> 3205[label="",style="solid", color="burlywood", weight=9];
3205 -> 360[label="",style="solid", color="burlywood", weight=3];
3206[label="vuz4100/Zero",fontsize=10,color="white",style="solid",shape="box"];353 -> 3206[label="",style="solid", color="burlywood", weight=9];
3206 -> 361[label="",style="solid", color="burlywood", weight=3];
354[label="primQuotInt (vuz30 * vuz40) (reduce2D (vuz30 * vuz40) (Pos vuz16))",fontsize=16,color="black",shape="box"];354 -> 362[label="",style="solid", color="black", weight=3];
355 -> 2212[label="",style="dashed", color="red", weight=0];
355[label="primQuotInt (Pos vuz15) (reduce2D (vuz30 * vuz40) (Pos vuz16))",fontsize=16,color="magenta"];355 -> 2213[label="",style="dashed", color="magenta", weight=3];
356[label="primQuotInt (vuz30 * vuz40) (reduce2D (vuz30 * vuz40) (Neg vuz19))",fontsize=16,color="black",shape="box"];356 -> 364[label="",style="solid", color="black", weight=3];
357 -> 997[label="",style="dashed", color="red", weight=0];
357[label="primQuotInt (Neg vuz18) (reduce2D (vuz30 * vuz40) (Neg vuz19))",fontsize=16,color="magenta"];357 -> 998[label="",style="dashed", color="magenta", weight=3];
357 -> 999[label="",style="dashed", color="magenta", weight=3];
358[label="primPlusNat (Succ vuz2100) (Succ vuz41000)",fontsize=16,color="black",shape="box"];358 -> 366[label="",style="solid", color="black", weight=3];
359[label="primPlusNat (Succ vuz2100) Zero",fontsize=16,color="black",shape="box"];359 -> 367[label="",style="solid", color="black", weight=3];
360[label="primPlusNat Zero (Succ vuz41000)",fontsize=16,color="black",shape="box"];360 -> 368[label="",style="solid", color="black", weight=3];
361[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];361 -> 369[label="",style="solid", color="black", weight=3];
362[label="primQuotInt (primMulInt vuz30 vuz40) (reduce2D (primMulInt vuz30 vuz40) (Pos vuz16))",fontsize=16,color="burlywood",shape="box"];3209[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];362 -> 3209[label="",style="solid", color="burlywood", weight=9];
3209 -> 370[label="",style="solid", color="burlywood", weight=3];
3210[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];362 -> 3210[label="",style="solid", color="burlywood", weight=9];
3210 -> 371[label="",style="solid", color="burlywood", weight=3];
2213[label="reduce2D (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];2213 -> 2622[label="",style="solid", color="black", weight=3];
2212[label="primQuotInt (Pos vuz15) vuz83",fontsize=16,color="burlywood",shape="triangle"];3211[label="vuz83/Pos vuz830",fontsize=10,color="white",style="solid",shape="box"];2212 -> 3211[label="",style="solid", color="burlywood", weight=9];
3211 -> 2623[label="",style="solid", color="burlywood", weight=3];
3212[label="vuz83/Neg vuz830",fontsize=10,color="white",style="solid",shape="box"];2212 -> 3212[label="",style="solid", color="burlywood", weight=9];
3212 -> 2624[label="",style="solid", color="burlywood", weight=3];
364[label="primQuotInt (primMulInt vuz30 vuz40) (reduce2D (primMulInt vuz30 vuz40) (Neg vuz19))",fontsize=16,color="burlywood",shape="box"];3213[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];364 -> 3213[label="",style="solid", color="burlywood", weight=9];
3213 -> 373[label="",style="solid", color="burlywood", weight=3];
3214[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];364 -> 3214[label="",style="solid", color="burlywood", weight=9];
3214 -> 374[label="",style="solid", color="burlywood", weight=3];
998[label="reduce2D (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];998 -> 1444[label="",style="solid", color="black", weight=3];
999[label="vuz18",fontsize=16,color="green",shape="box"];997[label="primQuotInt (Neg vuz39) vuz40",fontsize=16,color="burlywood",shape="triangle"];3215[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];997 -> 3215[label="",style="solid", color="burlywood", weight=9];
3215 -> 1445[label="",style="solid", color="burlywood", weight=3];
3216[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];997 -> 3216[label="",style="solid", color="burlywood", weight=9];
3216 -> 1446[label="",style="solid", color="burlywood", weight=3];
366[label="Succ (Succ (primPlusNat vuz2100 vuz41000))",fontsize=16,color="green",shape="box"];366 -> 376[label="",style="dashed", color="green", weight=3];
367[label="Succ vuz2100",fontsize=16,color="green",shape="box"];368[label="Succ vuz41000",fontsize=16,color="green",shape="box"];369[label="Zero",fontsize=16,color="green",shape="box"];370[label="primQuotInt (primMulInt (Pos vuz300) vuz40) (reduce2D (primMulInt (Pos vuz300) vuz40) (Pos vuz16))",fontsize=16,color="burlywood",shape="box"];3217[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];370 -> 3217[label="",style="solid", color="burlywood", weight=9];
3217 -> 377[label="",style="solid", color="burlywood", weight=3];
3218[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];370 -> 3218[label="",style="solid", color="burlywood", weight=9];
3218 -> 378[label="",style="solid", color="burlywood", weight=3];
371[label="primQuotInt (primMulInt (Neg vuz300) vuz40) (reduce2D (primMulInt (Neg vuz300) vuz40) (Pos vuz16))",fontsize=16,color="burlywood",shape="box"];3219[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];371 -> 3219[label="",style="solid", color="burlywood", weight=9];
3219 -> 379[label="",style="solid", color="burlywood", weight=3];
3220[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];371 -> 3220[label="",style="solid", color="burlywood", weight=9];
3220 -> 380[label="",style="solid", color="burlywood", weight=3];
2622[label="gcd (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];2622 -> 2630[label="",style="solid", color="black", weight=3];
2623[label="primQuotInt (Pos vuz15) (Pos vuz830)",fontsize=16,color="burlywood",shape="box"];3221[label="vuz830/Succ vuz8300",fontsize=10,color="white",style="solid",shape="box"];2623 -> 3221[label="",style="solid", color="burlywood", weight=9];
3221 -> 2631[label="",style="solid", color="burlywood", weight=3];
3222[label="vuz830/Zero",fontsize=10,color="white",style="solid",shape="box"];2623 -> 3222[label="",style="solid", color="burlywood", weight=9];
3222 -> 2632[label="",style="solid", color="burlywood", weight=3];
2624[label="primQuotInt (Pos vuz15) (Neg vuz830)",fontsize=16,color="burlywood",shape="box"];3223[label="vuz830/Succ vuz8300",fontsize=10,color="white",style="solid",shape="box"];2624 -> 3223[label="",style="solid", color="burlywood", weight=9];
3223 -> 2633[label="",style="solid", color="burlywood", weight=3];
3224[label="vuz830/Zero",fontsize=10,color="white",style="solid",shape="box"];2624 -> 3224[label="",style="solid", color="burlywood", weight=9];
3224 -> 2634[label="",style="solid", color="burlywood", weight=3];
373[label="primQuotInt (primMulInt (Pos vuz300) vuz40) (reduce2D (primMulInt (Pos vuz300) vuz40) (Neg vuz19))",fontsize=16,color="burlywood",shape="box"];3225[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];373 -> 3225[label="",style="solid", color="burlywood", weight=9];
3225 -> 382[label="",style="solid", color="burlywood", weight=3];
3226[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];373 -> 3226[label="",style="solid", color="burlywood", weight=9];
3226 -> 383[label="",style="solid", color="burlywood", weight=3];
374[label="primQuotInt (primMulInt (Neg vuz300) vuz40) (reduce2D (primMulInt (Neg vuz300) vuz40) (Neg vuz19))",fontsize=16,color="burlywood",shape="box"];3227[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];374 -> 3227[label="",style="solid", color="burlywood", weight=9];
3227 -> 384[label="",style="solid", color="burlywood", weight=3];
3228[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];374 -> 3228[label="",style="solid", color="burlywood", weight=9];
3228 -> 385[label="",style="solid", color="burlywood", weight=3];
1444[label="gcd (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];1444 -> 1450[label="",style="solid", color="black", weight=3];
1445[label="primQuotInt (Neg vuz39) (Pos vuz400)",fontsize=16,color="burlywood",shape="box"];3229[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];1445 -> 3229[label="",style="solid", color="burlywood", weight=9];
3229 -> 1451[label="",style="solid", color="burlywood", weight=3];
3230[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];1445 -> 3230[label="",style="solid", color="burlywood", weight=9];
3230 -> 1452[label="",style="solid", color="burlywood", weight=3];
1446[label="primQuotInt (Neg vuz39) (Neg vuz400)",fontsize=16,color="burlywood",shape="box"];3231[label="vuz400/Succ vuz4000",fontsize=10,color="white",style="solid",shape="box"];1446 -> 3231[label="",style="solid", color="burlywood", weight=9];
3231 -> 1453[label="",style="solid", color="burlywood", weight=3];
3232[label="vuz400/Zero",fontsize=10,color="white",style="solid",shape="box"];1446 -> 3232[label="",style="solid", color="burlywood", weight=9];
3232 -> 1454[label="",style="solid", color="burlywood", weight=3];
376 -> 347[label="",style="dashed", color="red", weight=0];
376[label="primPlusNat vuz2100 vuz41000",fontsize=16,color="magenta"];376 -> 387[label="",style="dashed", color="magenta", weight=3];
376 -> 388[label="",style="dashed", color="magenta", weight=3];
377[label="primQuotInt (primMulInt (Pos vuz300) (Pos vuz400)) (reduce2D (primMulInt (Pos vuz300) (Pos vuz400)) (Pos vuz16))",fontsize=16,color="black",shape="box"];377 -> 389[label="",style="solid", color="black", weight=3];
378[label="primQuotInt (primMulInt (Pos vuz300) (Neg vuz400)) (reduce2D (primMulInt (Pos vuz300) (Neg vuz400)) (Pos vuz16))",fontsize=16,color="black",shape="box"];378 -> 390[label="",style="solid", color="black", weight=3];
379[label="primQuotInt (primMulInt (Neg vuz300) (Pos vuz400)) (reduce2D (primMulInt (Neg vuz300) (Pos vuz400)) (Pos vuz16))",fontsize=16,color="black",shape="box"];379 -> 391[label="",style="solid", color="black", weight=3];
380[label="primQuotInt (primMulInt (Neg vuz300) (Neg vuz400)) (reduce2D (primMulInt (Neg vuz300) (Neg vuz400)) (Pos vuz16))",fontsize=16,color="black",shape="box"];380 -> 392[label="",style="solid", color="black", weight=3];
2630[label="gcd3 (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];2630 -> 2642[label="",style="solid", color="black", weight=3];
2631[label="primQuotInt (Pos vuz15) (Pos (Succ vuz8300))",fontsize=16,color="black",shape="box"];2631 -> 2643[label="",style="solid", color="black", weight=3];
2632[label="primQuotInt (Pos vuz15) (Pos Zero)",fontsize=16,color="black",shape="box"];2632 -> 2644[label="",style="solid", color="black", weight=3];
2633[label="primQuotInt (Pos vuz15) (Neg (Succ vuz8300))",fontsize=16,color="black",shape="box"];2633 -> 2645[label="",style="solid", color="black", weight=3];
2634[label="primQuotInt (Pos vuz15) (Neg Zero)",fontsize=16,color="black",shape="box"];2634 -> 2646[label="",style="solid", color="black", weight=3];
382[label="primQuotInt (primMulInt (Pos vuz300) (Pos vuz400)) (reduce2D (primMulInt (Pos vuz300) (Pos vuz400)) (Neg vuz19))",fontsize=16,color="black",shape="box"];382 -> 394[label="",style="solid", color="black", weight=3];
383[label="primQuotInt (primMulInt (Pos vuz300) (Neg vuz400)) (reduce2D (primMulInt (Pos vuz300) (Neg vuz400)) (Neg vuz19))",fontsize=16,color="black",shape="box"];383 -> 395[label="",style="solid", color="black", weight=3];
384[label="primQuotInt (primMulInt (Neg vuz300) (Pos vuz400)) (reduce2D (primMulInt (Neg vuz300) (Pos vuz400)) (Neg vuz19))",fontsize=16,color="black",shape="box"];384 -> 396[label="",style="solid", color="black", weight=3];
385[label="primQuotInt (primMulInt (Neg vuz300) (Neg vuz400)) (reduce2D (primMulInt (Neg vuz300) (Neg vuz400)) (Neg vuz19))",fontsize=16,color="black",shape="box"];385 -> 397[label="",style="solid", color="black", weight=3];
1450[label="gcd3 (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];1450 -> 1462[label="",style="solid", color="black", weight=3];
1451[label="primQuotInt (Neg vuz39) (Pos (Succ vuz4000))",fontsize=16,color="black",shape="box"];1451 -> 1463[label="",style="solid", color="black", weight=3];
1452[label="primQuotInt (Neg vuz39) (Pos Zero)",fontsize=16,color="black",shape="box"];1452 -> 1464[label="",style="solid", color="black", weight=3];
1453[label="primQuotInt (Neg vuz39) (Neg (Succ vuz4000))",fontsize=16,color="black",shape="box"];1453 -> 1465[label="",style="solid", color="black", weight=3];
1454[label="primQuotInt (Neg vuz39) (Neg Zero)",fontsize=16,color="black",shape="box"];1454 -> 1466[label="",style="solid", color="black", weight=3];
387[label="vuz2100",fontsize=16,color="green",shape="box"];388[label="vuz41000",fontsize=16,color="green",shape="box"];389 -> 2212[label="",style="dashed", color="red", weight=0];
389[label="primQuotInt (Pos (primMulNat vuz300 vuz400)) (reduce2D (Pos (primMulNat vuz300 vuz400)) (Pos vuz16))",fontsize=16,color="magenta"];389 -> 2217[label="",style="dashed", color="magenta", weight=3];
389 -> 2218[label="",style="dashed", color="magenta", weight=3];
390 -> 997[label="",style="dashed", color="red", weight=0];
390[label="primQuotInt (Neg (primMulNat vuz300 vuz400)) (reduce2D (Neg (primMulNat vuz300 vuz400)) (Pos vuz16))",fontsize=16,color="magenta"];390 -> 1006[label="",style="dashed", color="magenta", weight=3];
390 -> 1007[label="",style="dashed", color="magenta", weight=3];
391 -> 997[label="",style="dashed", color="red", weight=0];
391[label="primQuotInt (Neg (primMulNat vuz300 vuz400)) (reduce2D (Neg (primMulNat vuz300 vuz400)) (Pos vuz16))",fontsize=16,color="magenta"];391 -> 1008[label="",style="dashed", color="magenta", weight=3];
391 -> 1009[label="",style="dashed", color="magenta", weight=3];
392 -> 2212[label="",style="dashed", color="red", weight=0];
392[label="primQuotInt (Pos (primMulNat vuz300 vuz400)) (reduce2D (Pos (primMulNat vuz300 vuz400)) (Pos vuz16))",fontsize=16,color="magenta"];392 -> 2219[label="",style="dashed", color="magenta", weight=3];
392 -> 2220[label="",style="dashed", color="magenta", weight=3];
2642[label="gcd2 (vuz30 * vuz40 == fromInt (Pos Zero)) (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];2642 -> 2669[label="",style="solid", color="black", weight=3];
2643[label="Pos (primDivNatS vuz15 (Succ vuz8300))",fontsize=16,color="green",shape="box"];2643 -> 2670[label="",style="dashed", color="green", weight=3];
2644 -> 1464[label="",style="dashed", color="red", weight=0];
2644[label="error []",fontsize=16,color="magenta"];2645[label="Neg (primDivNatS vuz15 (Succ vuz8300))",fontsize=16,color="green",shape="box"];2645 -> 2671[label="",style="dashed", color="green", weight=3];
2646 -> 1464[label="",style="dashed", color="red", weight=0];
2646[label="error []",fontsize=16,color="magenta"];394 -> 2212[label="",style="dashed", color="red", weight=0];
394[label="primQuotInt (Pos (primMulNat vuz300 vuz400)) (reduce2D (Pos (primMulNat vuz300 vuz400)) (Neg vuz19))",fontsize=16,color="magenta"];394 -> 2222[label="",style="dashed", color="magenta", weight=3];
394 -> 2223[label="",style="dashed", color="magenta", weight=3];
395 -> 997[label="",style="dashed", color="red", weight=0];
395[label="primQuotInt (Neg (primMulNat vuz300 vuz400)) (reduce2D (Neg (primMulNat vuz300 vuz400)) (Neg vuz19))",fontsize=16,color="magenta"];395 -> 1010[label="",style="dashed", color="magenta", weight=3];
395 -> 1011[label="",style="dashed", color="magenta", weight=3];
396 -> 997[label="",style="dashed", color="red", weight=0];
396[label="primQuotInt (Neg (primMulNat vuz300 vuz400)) (reduce2D (Neg (primMulNat vuz300 vuz400)) (Neg vuz19))",fontsize=16,color="magenta"];396 -> 1012[label="",style="dashed", color="magenta", weight=3];
396 -> 1013[label="",style="dashed", color="magenta", weight=3];
397 -> 2212[label="",style="dashed", color="red", weight=0];
397[label="primQuotInt (Pos (primMulNat vuz300 vuz400)) (reduce2D (Pos (primMulNat vuz300 vuz400)) (Neg vuz19))",fontsize=16,color="magenta"];397 -> 2224[label="",style="dashed", color="magenta", weight=3];
397 -> 2225[label="",style="dashed", color="magenta", weight=3];
1462[label="gcd2 (vuz30 * vuz40 == fromInt (Pos Zero)) (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];1462 -> 1487[label="",style="solid", color="black", weight=3];
1463[label="Neg (primDivNatS vuz39 (Succ vuz4000))",fontsize=16,color="green",shape="box"];1463 -> 1488[label="",style="dashed", color="green", weight=3];
1464[label="error []",fontsize=16,color="black",shape="triangle"];1464 -> 1489[label="",style="solid", color="black", weight=3];
1465[label="Pos (primDivNatS vuz39 (Succ vuz4000))",fontsize=16,color="green",shape="box"];1465 -> 1490[label="",style="dashed", color="green", weight=3];
1466 -> 1464[label="",style="dashed", color="red", weight=0];
1466[label="error []",fontsize=16,color="magenta"];2217 -> 223[label="",style="dashed", color="red", weight=0];
2217[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2217 -> 2625[label="",style="dashed", color="magenta", weight=3];
2217 -> 2626[label="",style="dashed", color="magenta", weight=3];
2218 -> 2627[label="",style="dashed", color="red", weight=0];
2218[label="reduce2D (Pos (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];2218 -> 2628[label="",style="dashed", color="magenta", weight=3];
1006 -> 1447[label="",style="dashed", color="red", weight=0];
1006[label="reduce2D (Neg (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];1006 -> 1448[label="",style="dashed", color="magenta", weight=3];
1007 -> 223[label="",style="dashed", color="red", weight=0];
1007[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1007 -> 1455[label="",style="dashed", color="magenta", weight=3];
1007 -> 1456[label="",style="dashed", color="magenta", weight=3];
1008 -> 1447[label="",style="dashed", color="red", weight=0];
1008[label="reduce2D (Neg (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];1008 -> 1449[label="",style="dashed", color="magenta", weight=3];
1009 -> 223[label="",style="dashed", color="red", weight=0];
1009[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1009 -> 1457[label="",style="dashed", color="magenta", weight=3];
1009 -> 1458[label="",style="dashed", color="magenta", weight=3];
2219 -> 223[label="",style="dashed", color="red", weight=0];
2219[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2219 -> 2635[label="",style="dashed", color="magenta", weight=3];
2219 -> 2636[label="",style="dashed", color="magenta", weight=3];
2220 -> 2627[label="",style="dashed", color="red", weight=0];
2220[label="reduce2D (Pos (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];2220 -> 2629[label="",style="dashed", color="magenta", weight=3];
2669[label="gcd2 (primEqInt (vuz30 * vuz40) (fromInt (Pos Zero))) (vuz30 * vuz40) (Pos vuz16)",fontsize=16,color="black",shape="box"];2669 -> 2685[label="",style="solid", color="black", weight=3];
2670 -> 1488[label="",style="dashed", color="red", weight=0];
2670[label="primDivNatS vuz15 (Succ vuz8300)",fontsize=16,color="magenta"];2670 -> 2686[label="",style="dashed", color="magenta", weight=3];
2670 -> 2687[label="",style="dashed", color="magenta", weight=3];
2671 -> 1488[label="",style="dashed", color="red", weight=0];
2671[label="primDivNatS vuz15 (Succ vuz8300)",fontsize=16,color="magenta"];2671 -> 2688[label="",style="dashed", color="magenta", weight=3];
2671 -> 2689[label="",style="dashed", color="magenta", weight=3];
2222 -> 223[label="",style="dashed", color="red", weight=0];
2222[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2222 -> 2637[label="",style="dashed", color="magenta", weight=3];
2222 -> 2638[label="",style="dashed", color="magenta", weight=3];
2223 -> 2639[label="",style="dashed", color="red", weight=0];
2223[label="reduce2D (Pos (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];2223 -> 2640[label="",style="dashed", color="magenta", weight=3];
1010 -> 1459[label="",style="dashed", color="red", weight=0];
1010[label="reduce2D (Neg (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];1010 -> 1460[label="",style="dashed", color="magenta", weight=3];
1011 -> 223[label="",style="dashed", color="red", weight=0];
1011[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1011 -> 1467[label="",style="dashed", color="magenta", weight=3];
1011 -> 1468[label="",style="dashed", color="magenta", weight=3];
1012 -> 1459[label="",style="dashed", color="red", weight=0];
1012[label="reduce2D (Neg (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];1012 -> 1461[label="",style="dashed", color="magenta", weight=3];
1013 -> 223[label="",style="dashed", color="red", weight=0];
1013[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1013 -> 1469[label="",style="dashed", color="magenta", weight=3];
1013 -> 1470[label="",style="dashed", color="magenta", weight=3];
2224 -> 223[label="",style="dashed", color="red", weight=0];
2224[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2224 -> 2647[label="",style="dashed", color="magenta", weight=3];
2224 -> 2648[label="",style="dashed", color="magenta", weight=3];
2225 -> 2639[label="",style="dashed", color="red", weight=0];
2225[label="reduce2D (Pos (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];2225 -> 2641[label="",style="dashed", color="magenta", weight=3];
1487[label="gcd2 (primEqInt (vuz30 * vuz40) (fromInt (Pos Zero))) (vuz30 * vuz40) (Neg vuz19)",fontsize=16,color="black",shape="box"];1487 -> 1501[label="",style="solid", color="black", weight=3];
1488[label="primDivNatS vuz39 (Succ vuz4000)",fontsize=16,color="burlywood",shape="triangle"];3263[label="vuz39/Succ vuz390",fontsize=10,color="white",style="solid",shape="box"];1488 -> 3263[label="",style="solid", color="burlywood", weight=9];
3263 -> 1502[label="",style="solid", color="burlywood", weight=3];
3264[label="vuz39/Zero",fontsize=10,color="white",style="solid",shape="box"];1488 -> 3264[label="",style="solid", color="burlywood", weight=9];
3264 -> 1503[label="",style="solid", color="burlywood", weight=3];
1489[label="error []",fontsize=16,color="red",shape="box"];1490 -> 1488[label="",style="dashed", color="red", weight=0];
1490[label="primDivNatS vuz39 (Succ vuz4000)",fontsize=16,color="magenta"];1490 -> 1504[label="",style="dashed", color="magenta", weight=3];
2625[label="vuz400",fontsize=16,color="green",shape="box"];2626[label="vuz300",fontsize=16,color="green",shape="box"];2628 -> 223[label="",style="dashed", color="red", weight=0];
2628[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2628 -> 2649[label="",style="dashed", color="magenta", weight=3];
2628 -> 2650[label="",style="dashed", color="magenta", weight=3];
2627[label="reduce2D (Pos vuz84) (Pos vuz16)",fontsize=16,color="black",shape="triangle"];2627 -> 2651[label="",style="solid", color="black", weight=3];
1448 -> 223[label="",style="dashed", color="red", weight=0];
1448[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1448 -> 1471[label="",style="dashed", color="magenta", weight=3];
1448 -> 1472[label="",style="dashed", color="magenta", weight=3];
1447[label="reduce2D (Neg vuz41) (Pos vuz16)",fontsize=16,color="black",shape="triangle"];1447 -> 1473[label="",style="solid", color="black", weight=3];
1455[label="vuz400",fontsize=16,color="green",shape="box"];1456[label="vuz300",fontsize=16,color="green",shape="box"];1449 -> 223[label="",style="dashed", color="red", weight=0];
1449[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1449 -> 1474[label="",style="dashed", color="magenta", weight=3];
1449 -> 1475[label="",style="dashed", color="magenta", weight=3];
1457[label="vuz400",fontsize=16,color="green",shape="box"];1458[label="vuz300",fontsize=16,color="green",shape="box"];2635[label="vuz400",fontsize=16,color="green",shape="box"];2636[label="vuz300",fontsize=16,color="green",shape="box"];2629 -> 223[label="",style="dashed", color="red", weight=0];
2629[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2629 -> 2652[label="",style="dashed", color="magenta", weight=3];
2629 -> 2653[label="",style="dashed", color="magenta", weight=3];
2685[label="gcd2 (primEqInt (primMulInt vuz30 vuz40) (fromInt (Pos Zero))) (primMulInt vuz30 vuz40) (Pos vuz16)",fontsize=16,color="burlywood",shape="box"];3270[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];2685 -> 3270[label="",style="solid", color="burlywood", weight=9];
3270 -> 2701[label="",style="solid", color="burlywood", weight=3];
3271[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];2685 -> 3271[label="",style="solid", color="burlywood", weight=9];
3271 -> 2702[label="",style="solid", color="burlywood", weight=3];
2686[label="vuz8300",fontsize=16,color="green",shape="box"];2687[label="vuz15",fontsize=16,color="green",shape="box"];2688[label="vuz8300",fontsize=16,color="green",shape="box"];2689[label="vuz15",fontsize=16,color="green",shape="box"];2637[label="vuz400",fontsize=16,color="green",shape="box"];2638[label="vuz300",fontsize=16,color="green",shape="box"];2640 -> 223[label="",style="dashed", color="red", weight=0];
2640[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2640 -> 2654[label="",style="dashed", color="magenta", weight=3];
2640 -> 2655[label="",style="dashed", color="magenta", weight=3];
2639[label="reduce2D (Pos vuz85) (Neg vuz19)",fontsize=16,color="black",shape="triangle"];2639 -> 2656[label="",style="solid", color="black", weight=3];
1460 -> 223[label="",style="dashed", color="red", weight=0];
1460[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1460 -> 1476[label="",style="dashed", color="magenta", weight=3];
1460 -> 1477[label="",style="dashed", color="magenta", weight=3];
1459[label="reduce2D (Neg vuz42) (Neg vuz19)",fontsize=16,color="black",shape="triangle"];1459 -> 1478[label="",style="solid", color="black", weight=3];
1467[label="vuz400",fontsize=16,color="green",shape="box"];1468[label="vuz300",fontsize=16,color="green",shape="box"];1461 -> 223[label="",style="dashed", color="red", weight=0];
1461[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1461 -> 1479[label="",style="dashed", color="magenta", weight=3];
1461 -> 1480[label="",style="dashed", color="magenta", weight=3];
1469[label="vuz400",fontsize=16,color="green",shape="box"];1470[label="vuz300",fontsize=16,color="green",shape="box"];2647[label="vuz400",fontsize=16,color="green",shape="box"];2648[label="vuz300",fontsize=16,color="green",shape="box"];2641 -> 223[label="",style="dashed", color="red", weight=0];
2641[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2641 -> 2657[label="",style="dashed", color="magenta", weight=3];
2641 -> 2658[label="",style="dashed", color="magenta", weight=3];
1501[label="gcd2 (primEqInt (primMulInt vuz30 vuz40) (fromInt (Pos Zero))) (primMulInt vuz30 vuz40) (Neg vuz19)",fontsize=16,color="burlywood",shape="box"];3276[label="vuz30/Pos vuz300",fontsize=10,color="white",style="solid",shape="box"];1501 -> 3276[label="",style="solid", color="burlywood", weight=9];
3276 -> 1513[label="",style="solid", color="burlywood", weight=3];
3277[label="vuz30/Neg vuz300",fontsize=10,color="white",style="solid",shape="box"];1501 -> 3277[label="",style="solid", color="burlywood", weight=9];
3277 -> 1514[label="",style="solid", color="burlywood", weight=3];
1502[label="primDivNatS (Succ vuz390) (Succ vuz4000)",fontsize=16,color="black",shape="box"];1502 -> 1515[label="",style="solid", color="black", weight=3];
1503[label="primDivNatS Zero (Succ vuz4000)",fontsize=16,color="black",shape="box"];1503 -> 1516[label="",style="solid", color="black", weight=3];
1504[label="vuz4000",fontsize=16,color="green",shape="box"];2649[label="vuz400",fontsize=16,color="green",shape="box"];2650[label="vuz300",fontsize=16,color="green",shape="box"];2651[label="gcd (Pos vuz84) (Pos vuz16)",fontsize=16,color="black",shape="box"];2651 -> 2672[label="",style="solid", color="black", weight=3];
1471[label="vuz400",fontsize=16,color="green",shape="box"];1472[label="vuz300",fontsize=16,color="green",shape="box"];1473[label="gcd (Neg vuz41) (Pos vuz16)",fontsize=16,color="black",shape="box"];1473 -> 1491[label="",style="solid", color="black", weight=3];
1474[label="vuz400",fontsize=16,color="green",shape="box"];1475[label="vuz300",fontsize=16,color="green",shape="box"];2652[label="vuz400",fontsize=16,color="green",shape="box"];2653[label="vuz300",fontsize=16,color="green",shape="box"];2701[label="gcd2 (primEqInt (primMulInt (Pos vuz300) vuz40) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) vuz40) (Pos vuz16)",fontsize=16,color="burlywood",shape="box"];3278[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];2701 -> 3278[label="",style="solid", color="burlywood", weight=9];
3278 -> 2712[label="",style="solid", color="burlywood", weight=3];
3279[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];2701 -> 3279[label="",style="solid", color="burlywood", weight=9];
3279 -> 2713[label="",style="solid", color="burlywood", weight=3];
2702[label="gcd2 (primEqInt (primMulInt (Neg vuz300) vuz40) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) vuz40) (Pos vuz16)",fontsize=16,color="burlywood",shape="box"];3280[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];2702 -> 3280[label="",style="solid", color="burlywood", weight=9];
3280 -> 2714[label="",style="solid", color="burlywood", weight=3];
3281[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];2702 -> 3281[label="",style="solid", color="burlywood", weight=9];
3281 -> 2715[label="",style="solid", color="burlywood", weight=3];
2654[label="vuz400",fontsize=16,color="green",shape="box"];2655[label="vuz300",fontsize=16,color="green",shape="box"];2656[label="gcd (Pos vuz85) (Neg vuz19)",fontsize=16,color="black",shape="box"];2656 -> 2673[label="",style="solid", color="black", weight=3];
1476[label="vuz400",fontsize=16,color="green",shape="box"];1477[label="vuz300",fontsize=16,color="green",shape="box"];1478[label="gcd (Neg vuz42) (Neg vuz19)",fontsize=16,color="black",shape="box"];1478 -> 1492[label="",style="solid", color="black", weight=3];
1479[label="vuz400",fontsize=16,color="green",shape="box"];1480[label="vuz300",fontsize=16,color="green",shape="box"];2657[label="vuz400",fontsize=16,color="green",shape="box"];2658[label="vuz300",fontsize=16,color="green",shape="box"];1513[label="gcd2 (primEqInt (primMulInt (Pos vuz300) vuz40) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) vuz40) (Neg vuz19)",fontsize=16,color="burlywood",shape="box"];3282[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];1513 -> 3282[label="",style="solid", color="burlywood", weight=9];
3282 -> 1525[label="",style="solid", color="burlywood", weight=3];
3283[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];1513 -> 3283[label="",style="solid", color="burlywood", weight=9];
3283 -> 1526[label="",style="solid", color="burlywood", weight=3];
1514[label="gcd2 (primEqInt (primMulInt (Neg vuz300) vuz40) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) vuz40) (Neg vuz19)",fontsize=16,color="burlywood",shape="box"];3284[label="vuz40/Pos vuz400",fontsize=10,color="white",style="solid",shape="box"];1514 -> 3284[label="",style="solid", color="burlywood", weight=9];
3284 -> 1527[label="",style="solid", color="burlywood", weight=3];
3285[label="vuz40/Neg vuz400",fontsize=10,color="white",style="solid",shape="box"];1514 -> 3285[label="",style="solid", color="burlywood", weight=9];
3285 -> 1528[label="",style="solid", color="burlywood", weight=3];
1515[label="primDivNatS0 vuz390 vuz4000 (primGEqNatS vuz390 vuz4000)",fontsize=16,color="burlywood",shape="box"];3286[label="vuz390/Succ vuz3900",fontsize=10,color="white",style="solid",shape="box"];1515 -> 3286[label="",style="solid", color="burlywood", weight=9];
3286 -> 1529[label="",style="solid", color="burlywood", weight=3];
3287[label="vuz390/Zero",fontsize=10,color="white",style="solid",shape="box"];1515 -> 3287[label="",style="solid", color="burlywood", weight=9];
3287 -> 1530[label="",style="solid", color="burlywood", weight=3];
1516[label="Zero",fontsize=16,color="green",shape="box"];2672[label="gcd3 (Pos vuz84) (Pos vuz16)",fontsize=16,color="black",shape="box"];2672 -> 2690[label="",style="solid", color="black", weight=3];
1491[label="gcd3 (Neg vuz41) (Pos vuz16)",fontsize=16,color="black",shape="box"];1491 -> 1505[label="",style="solid", color="black", weight=3];
2712[label="gcd2 (primEqInt (primMulInt (Pos vuz300) (Pos vuz400)) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (Pos vuz400)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2712 -> 2728[label="",style="solid", color="black", weight=3];
2713[label="gcd2 (primEqInt (primMulInt (Pos vuz300) (Neg vuz400)) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (Neg vuz400)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2713 -> 2729[label="",style="solid", color="black", weight=3];
2714[label="gcd2 (primEqInt (primMulInt (Neg vuz300) (Pos vuz400)) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (Pos vuz400)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2714 -> 2730[label="",style="solid", color="black", weight=3];
2715[label="gcd2 (primEqInt (primMulInt (Neg vuz300) (Neg vuz400)) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (Neg vuz400)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2715 -> 2731[label="",style="solid", color="black", weight=3];
2673[label="gcd3 (Pos vuz85) (Neg vuz19)",fontsize=16,color="black",shape="box"];2673 -> 2691[label="",style="solid", color="black", weight=3];
1492[label="gcd3 (Neg vuz42) (Neg vuz19)",fontsize=16,color="black",shape="box"];1492 -> 1506[label="",style="solid", color="black", weight=3];
1525[label="gcd2 (primEqInt (primMulInt (Pos vuz300) (Pos vuz400)) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (Pos vuz400)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1525 -> 1542[label="",style="solid", color="black", weight=3];
1526[label="gcd2 (primEqInt (primMulInt (Pos vuz300) (Neg vuz400)) (fromInt (Pos Zero))) (primMulInt (Pos vuz300) (Neg vuz400)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1526 -> 1543[label="",style="solid", color="black", weight=3];
1527[label="gcd2 (primEqInt (primMulInt (Neg vuz300) (Pos vuz400)) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (Pos vuz400)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1527 -> 1544[label="",style="solid", color="black", weight=3];
1528[label="gcd2 (primEqInt (primMulInt (Neg vuz300) (Neg vuz400)) (fromInt (Pos Zero))) (primMulInt (Neg vuz300) (Neg vuz400)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1528 -> 1545[label="",style="solid", color="black", weight=3];
1529[label="primDivNatS0 (Succ vuz3900) vuz4000 (primGEqNatS (Succ vuz3900) vuz4000)",fontsize=16,color="burlywood",shape="box"];3288[label="vuz4000/Succ vuz40000",fontsize=10,color="white",style="solid",shape="box"];1529 -> 3288[label="",style="solid", color="burlywood", weight=9];
3288 -> 1546[label="",style="solid", color="burlywood", weight=3];
3289[label="vuz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];1529 -> 3289[label="",style="solid", color="burlywood", weight=9];
3289 -> 1547[label="",style="solid", color="burlywood", weight=3];
1530[label="primDivNatS0 Zero vuz4000 (primGEqNatS Zero vuz4000)",fontsize=16,color="burlywood",shape="box"];3290[label="vuz4000/Succ vuz40000",fontsize=10,color="white",style="solid",shape="box"];1530 -> 3290[label="",style="solid", color="burlywood", weight=9];
3290 -> 1548[label="",style="solid", color="burlywood", weight=3];
3291[label="vuz4000/Zero",fontsize=10,color="white",style="solid",shape="box"];1530 -> 3291[label="",style="solid", color="burlywood", weight=9];
3291 -> 1549[label="",style="solid", color="burlywood", weight=3];
2690[label="gcd2 (Pos vuz84 == fromInt (Pos Zero)) (Pos vuz84) (Pos vuz16)",fontsize=16,color="black",shape="box"];2690 -> 2703[label="",style="solid", color="black", weight=3];
1505[label="gcd2 (Neg vuz41 == fromInt (Pos Zero)) (Neg vuz41) (Pos vuz16)",fontsize=16,color="black",shape="box"];1505 -> 1517[label="",style="solid", color="black", weight=3];
2728 -> 2703[label="",style="dashed", color="red", weight=0];
2728[label="gcd2 (primEqInt (Pos (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Pos (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];2728 -> 2743[label="",style="dashed", color="magenta", weight=3];
2729 -> 1517[label="",style="dashed", color="red", weight=0];
2729[label="gcd2 (primEqInt (Neg (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Neg (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];2729 -> 2744[label="",style="dashed", color="magenta", weight=3];
2730 -> 1517[label="",style="dashed", color="red", weight=0];
2730[label="gcd2 (primEqInt (Neg (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Neg (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];2730 -> 2745[label="",style="dashed", color="magenta", weight=3];
2731 -> 2703[label="",style="dashed", color="red", weight=0];
2731[label="gcd2 (primEqInt (Pos (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Pos (primMulNat vuz300 vuz400)) (Pos vuz16)",fontsize=16,color="magenta"];2731 -> 2746[label="",style="dashed", color="magenta", weight=3];
2691[label="gcd2 (Pos vuz85 == fromInt (Pos Zero)) (Pos vuz85) (Neg vuz19)",fontsize=16,color="black",shape="box"];2691 -> 2704[label="",style="solid", color="black", weight=3];
1506[label="gcd2 (Neg vuz42 == fromInt (Pos Zero)) (Neg vuz42) (Neg vuz19)",fontsize=16,color="black",shape="box"];1506 -> 1518[label="",style="solid", color="black", weight=3];
1542 -> 1559[label="",style="dashed", color="red", weight=0];
1542[label="gcd2 (primEqInt (Pos (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Pos (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];1542 -> 1560[label="",style="dashed", color="magenta", weight=3];
1542 -> 1561[label="",style="dashed", color="magenta", weight=3];
1543 -> 1518[label="",style="dashed", color="red", weight=0];
1543[label="gcd2 (primEqInt (Neg (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Neg (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];1543 -> 1564[label="",style="dashed", color="magenta", weight=3];
1544 -> 1518[label="",style="dashed", color="red", weight=0];
1544[label="gcd2 (primEqInt (Neg (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Neg (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];1544 -> 1565[label="",style="dashed", color="magenta", weight=3];
1545 -> 1559[label="",style="dashed", color="red", weight=0];
1545[label="gcd2 (primEqInt (Pos (primMulNat vuz300 vuz400)) (fromInt (Pos Zero))) (Pos (primMulNat vuz300 vuz400)) (Neg vuz19)",fontsize=16,color="magenta"];1545 -> 1562[label="",style="dashed", color="magenta", weight=3];
1545 -> 1563[label="",style="dashed", color="magenta", weight=3];
1546[label="primDivNatS0 (Succ vuz3900) (Succ vuz40000) (primGEqNatS (Succ vuz3900) (Succ vuz40000))",fontsize=16,color="black",shape="box"];1546 -> 1566[label="",style="solid", color="black", weight=3];
1547[label="primDivNatS0 (Succ vuz3900) Zero (primGEqNatS (Succ vuz3900) Zero)",fontsize=16,color="black",shape="box"];1547 -> 1567[label="",style="solid", color="black", weight=3];
1548[label="primDivNatS0 Zero (Succ vuz40000) (primGEqNatS Zero (Succ vuz40000))",fontsize=16,color="black",shape="box"];1548 -> 1568[label="",style="solid", color="black", weight=3];
1549[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1549 -> 1569[label="",style="solid", color="black", weight=3];
2703[label="gcd2 (primEqInt (Pos vuz84) (fromInt (Pos Zero))) (Pos vuz84) (Pos vuz16)",fontsize=16,color="burlywood",shape="triangle"];3300[label="vuz84/Succ vuz840",fontsize=10,color="white",style="solid",shape="box"];2703 -> 3300[label="",style="solid", color="burlywood", weight=9];
3300 -> 2716[label="",style="solid", color="burlywood", weight=3];
3301[label="vuz84/Zero",fontsize=10,color="white",style="solid",shape="box"];2703 -> 3301[label="",style="solid", color="burlywood", weight=9];
3301 -> 2717[label="",style="solid", color="burlywood", weight=3];
1517[label="gcd2 (primEqInt (Neg vuz41) (fromInt (Pos Zero))) (Neg vuz41) (Pos vuz16)",fontsize=16,color="burlywood",shape="triangle"];3302[label="vuz41/Succ vuz410",fontsize=10,color="white",style="solid",shape="box"];1517 -> 3302[label="",style="solid", color="burlywood", weight=9];
3302 -> 1531[label="",style="solid", color="burlywood", weight=3];
3303[label="vuz41/Zero",fontsize=10,color="white",style="solid",shape="box"];1517 -> 3303[label="",style="solid", color="burlywood", weight=9];
3303 -> 1532[label="",style="solid", color="burlywood", weight=3];
2743 -> 223[label="",style="dashed", color="red", weight=0];
2743[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2743 -> 2759[label="",style="dashed", color="magenta", weight=3];
2743 -> 2760[label="",style="dashed", color="magenta", weight=3];
2744 -> 223[label="",style="dashed", color="red", weight=0];
2744[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2744 -> 2761[label="",style="dashed", color="magenta", weight=3];
2744 -> 2762[label="",style="dashed", color="magenta", weight=3];
2745 -> 223[label="",style="dashed", color="red", weight=0];
2745[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2745 -> 2763[label="",style="dashed", color="magenta", weight=3];
2745 -> 2764[label="",style="dashed", color="magenta", weight=3];
2746 -> 223[label="",style="dashed", color="red", weight=0];
2746[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];2746 -> 2765[label="",style="dashed", color="magenta", weight=3];
2746 -> 2766[label="",style="dashed", color="magenta", weight=3];
2704 -> 1559[label="",style="dashed", color="red", weight=0];
2704[label="gcd2 (primEqInt (Pos vuz85) (fromInt (Pos Zero))) (Pos vuz85) (Neg vuz19)",fontsize=16,color="magenta"];2704 -> 2718[label="",style="dashed", color="magenta", weight=3];
2704 -> 2719[label="",style="dashed", color="magenta", weight=3];
1518[label="gcd2 (primEqInt (Neg vuz42) (fromInt (Pos Zero))) (Neg vuz42) (Neg vuz19)",fontsize=16,color="burlywood",shape="triangle"];3309[label="vuz42/Succ vuz420",fontsize=10,color="white",style="solid",shape="box"];1518 -> 3309[label="",style="solid", color="burlywood", weight=9];
3309 -> 1533[label="",style="solid", color="burlywood", weight=3];
3310[label="vuz42/Zero",fontsize=10,color="white",style="solid",shape="box"];1518 -> 3310[label="",style="solid", color="burlywood", weight=9];
3310 -> 1534[label="",style="solid", color="burlywood", weight=3];
1560 -> 223[label="",style="dashed", color="red", weight=0];
1560[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1560 -> 1570[label="",style="dashed", color="magenta", weight=3];
1560 -> 1571[label="",style="dashed", color="magenta", weight=3];
1561 -> 223[label="",style="dashed", color="red", weight=0];
1561[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1561 -> 1572[label="",style="dashed", color="magenta", weight=3];
1561 -> 1573[label="",style="dashed", color="magenta", weight=3];
1559[label="gcd2 (primEqInt (Pos vuz44) (fromInt (Pos Zero))) (Pos vuz43) (Neg vuz19)",fontsize=16,color="burlywood",shape="triangle"];3313[label="vuz44/Succ vuz440",fontsize=10,color="white",style="solid",shape="box"];1559 -> 3313[label="",style="solid", color="burlywood", weight=9];
3313 -> 1574[label="",style="solid", color="burlywood", weight=3];
3314[label="vuz44/Zero",fontsize=10,color="white",style="solid",shape="box"];1559 -> 3314[label="",style="solid", color="burlywood", weight=9];
3314 -> 1575[label="",style="solid", color="burlywood", weight=3];
1564 -> 223[label="",style="dashed", color="red", weight=0];
1564[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1564 -> 1588[label="",style="dashed", color="magenta", weight=3];
1564 -> 1589[label="",style="dashed", color="magenta", weight=3];
1565 -> 223[label="",style="dashed", color="red", weight=0];
1565[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1565 -> 1590[label="",style="dashed", color="magenta", weight=3];
1565 -> 1591[label="",style="dashed", color="magenta", weight=3];
1562 -> 223[label="",style="dashed", color="red", weight=0];
1562[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1562 -> 1576[label="",style="dashed", color="magenta", weight=3];
1562 -> 1577[label="",style="dashed", color="magenta", weight=3];
1563 -> 223[label="",style="dashed", color="red", weight=0];
1563[label="primMulNat vuz300 vuz400",fontsize=16,color="magenta"];1563 -> 1578[label="",style="dashed", color="magenta", weight=3];
1563 -> 1579[label="",style="dashed", color="magenta", weight=3];
1566 -> 2163[label="",style="dashed", color="red", weight=0];
1566[label="primDivNatS0 (Succ vuz3900) (Succ vuz40000) (primGEqNatS vuz3900 vuz40000)",fontsize=16,color="magenta"];1566 -> 2164[label="",style="dashed", color="magenta", weight=3];
1566 -> 2165[label="",style="dashed", color="magenta", weight=3];
1566 -> 2166[label="",style="dashed", color="magenta", weight=3];
1566 -> 2167[label="",style="dashed", color="magenta", weight=3];
1567[label="primDivNatS0 (Succ vuz3900) Zero True",fontsize=16,color="black",shape="box"];1567 -> 1594[label="",style="solid", color="black", weight=3];
1568[label="primDivNatS0 Zero (Succ vuz40000) False",fontsize=16,color="black",shape="box"];1568 -> 1595[label="",style="solid", color="black", weight=3];
1569[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];1569 -> 1596[label="",style="solid", color="black", weight=3];
2716[label="gcd2 (primEqInt (Pos (Succ vuz840)) (fromInt (Pos Zero))) (Pos (Succ vuz840)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2716 -> 2732[label="",style="solid", color="black", weight=3];
2717[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];2717 -> 2733[label="",style="solid", color="black", weight=3];
1531[label="gcd2 (primEqInt (Neg (Succ vuz410)) (fromInt (Pos Zero))) (Neg (Succ vuz410)) (Pos vuz16)",fontsize=16,color="black",shape="box"];1531 -> 1550[label="",style="solid", color="black", weight=3];
1532[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];1532 -> 1551[label="",style="solid", color="black", weight=3];
2759[label="vuz400",fontsize=16,color="green",shape="box"];2760[label="vuz300",fontsize=16,color="green",shape="box"];2761[label="vuz400",fontsize=16,color="green",shape="box"];2762[label="vuz300",fontsize=16,color="green",shape="box"];2763[label="vuz400",fontsize=16,color="green",shape="box"];2764[label="vuz300",fontsize=16,color="green",shape="box"];2765[label="vuz400",fontsize=16,color="green",shape="box"];2766[label="vuz300",fontsize=16,color="green",shape="box"];2718[label="vuz85",fontsize=16,color="green",shape="box"];2719[label="vuz85",fontsize=16,color="green",shape="box"];1533[label="gcd2 (primEqInt (Neg (Succ vuz420)) (fromInt (Pos Zero))) (Neg (Succ vuz420)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1533 -> 1552[label="",style="solid", color="black", weight=3];
1534[label="gcd2 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz19)",fontsize=16,color="black",shape="box"];1534 -> 1553[label="",style="solid", color="black", weight=3];
1570[label="vuz400",fontsize=16,color="green",shape="box"];1571[label="vuz300",fontsize=16,color="green",shape="box"];1572[label="vuz400",fontsize=16,color="green",shape="box"];1573[label="vuz300",fontsize=16,color="green",shape="box"];1574[label="gcd2 (primEqInt (Pos (Succ vuz440)) (fromInt (Pos Zero))) (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1574 -> 1597[label="",style="solid", color="black", weight=3];
1575[label="gcd2 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1575 -> 1598[label="",style="solid", color="black", weight=3];
1588[label="vuz400",fontsize=16,color="green",shape="box"];1589[label="vuz300",fontsize=16,color="green",shape="box"];1590[label="vuz400",fontsize=16,color="green",shape="box"];1591[label="vuz300",fontsize=16,color="green",shape="box"];1576[label="vuz400",fontsize=16,color="green",shape="box"];1577[label="vuz300",fontsize=16,color="green",shape="box"];1578[label="vuz400",fontsize=16,color="green",shape="box"];1579[label="vuz300",fontsize=16,color="green",shape="box"];2164[label="vuz40000",fontsize=16,color="green",shape="box"];2165[label="vuz40000",fontsize=16,color="green",shape="box"];2166[label="vuz3900",fontsize=16,color="green",shape="box"];2167[label="vuz3900",fontsize=16,color="green",shape="box"];2163[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS vuz81 vuz82)",fontsize=16,color="burlywood",shape="triangle"];3320[label="vuz81/Succ vuz810",fontsize=10,color="white",style="solid",shape="box"];2163 -> 3320[label="",style="solid", color="burlywood", weight=9];
3320 -> 2204[label="",style="solid", color="burlywood", weight=3];
3321[label="vuz81/Zero",fontsize=10,color="white",style="solid",shape="box"];2163 -> 3321[label="",style="solid", color="burlywood", weight=9];
3321 -> 2205[label="",style="solid", color="burlywood", weight=3];
1594[label="Succ (primDivNatS (primMinusNatS (Succ vuz3900) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1594 -> 1611[label="",style="dashed", color="green", weight=3];
1595[label="Zero",fontsize=16,color="green",shape="box"];1596[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];1596 -> 1612[label="",style="dashed", color="green", weight=3];
2732[label="gcd2 (primEqInt (Pos (Succ vuz840)) (Pos Zero)) (Pos (Succ vuz840)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2732 -> 2747[label="",style="solid", color="black", weight=3];
2733[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];2733 -> 2748[label="",style="solid", color="black", weight=3];
1550[label="gcd2 (primEqInt (Neg (Succ vuz410)) (Pos Zero)) (Neg (Succ vuz410)) (Pos vuz16)",fontsize=16,color="black",shape="box"];1550 -> 1580[label="",style="solid", color="black", weight=3];
1551[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];1551 -> 1581[label="",style="solid", color="black", weight=3];
1552[label="gcd2 (primEqInt (Neg (Succ vuz420)) (Pos Zero)) (Neg (Succ vuz420)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1552 -> 1582[label="",style="solid", color="black", weight=3];
1553[label="gcd2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg vuz19)",fontsize=16,color="black",shape="box"];1553 -> 1583[label="",style="solid", color="black", weight=3];
1597[label="gcd2 (primEqInt (Pos (Succ vuz440)) (Pos Zero)) (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1597 -> 1613[label="",style="solid", color="black", weight=3];
1598[label="gcd2 (primEqInt (Pos Zero) (Pos Zero)) (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1598 -> 1614[label="",style="solid", color="black", weight=3];
2204[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS (Succ vuz810) vuz82)",fontsize=16,color="burlywood",shape="box"];3322[label="vuz82/Succ vuz820",fontsize=10,color="white",style="solid",shape="box"];2204 -> 3322[label="",style="solid", color="burlywood", weight=9];
3322 -> 2659[label="",style="solid", color="burlywood", weight=3];
3323[label="vuz82/Zero",fontsize=10,color="white",style="solid",shape="box"];2204 -> 3323[label="",style="solid", color="burlywood", weight=9];
3323 -> 2660[label="",style="solid", color="burlywood", weight=3];
2205[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS Zero vuz82)",fontsize=16,color="burlywood",shape="box"];3324[label="vuz82/Succ vuz820",fontsize=10,color="white",style="solid",shape="box"];2205 -> 3324[label="",style="solid", color="burlywood", weight=9];
3324 -> 2661[label="",style="solid", color="burlywood", weight=3];
3325[label="vuz82/Zero",fontsize=10,color="white",style="solid",shape="box"];2205 -> 3325[label="",style="solid", color="burlywood", weight=9];
3325 -> 2662[label="",style="solid", color="burlywood", weight=3];
1611 -> 1488[label="",style="dashed", color="red", weight=0];
1611[label="primDivNatS (primMinusNatS (Succ vuz3900) Zero) (Succ Zero)",fontsize=16,color="magenta"];1611 -> 1627[label="",style="dashed", color="magenta", weight=3];
1611 -> 1628[label="",style="dashed", color="magenta", weight=3];
1612 -> 1488[label="",style="dashed", color="red", weight=0];
1612[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];1612 -> 1629[label="",style="dashed", color="magenta", weight=3];
1612 -> 1630[label="",style="dashed", color="magenta", weight=3];
2747[label="gcd2 False (Pos (Succ vuz840)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2747 -> 2767[label="",style="solid", color="black", weight=3];
2748[label="gcd2 True (Pos Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];2748 -> 2768[label="",style="solid", color="black", weight=3];
1580[label="gcd2 False (Neg (Succ vuz410)) (Pos vuz16)",fontsize=16,color="black",shape="box"];1580 -> 1599[label="",style="solid", color="black", weight=3];
1581[label="gcd2 True (Neg Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];1581 -> 1600[label="",style="solid", color="black", weight=3];
1582[label="gcd2 False (Neg (Succ vuz420)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1582 -> 1601[label="",style="solid", color="black", weight=3];
1583[label="gcd2 True (Neg Zero) (Neg vuz19)",fontsize=16,color="black",shape="box"];1583 -> 1602[label="",style="solid", color="black", weight=3];
1613[label="gcd2 False (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1613 -> 1631[label="",style="solid", color="black", weight=3];
1614[label="gcd2 True (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1614 -> 1632[label="",style="solid", color="black", weight=3];
2659[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS (Succ vuz810) (Succ vuz820))",fontsize=16,color="black",shape="box"];2659 -> 2674[label="",style="solid", color="black", weight=3];
2660[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS (Succ vuz810) Zero)",fontsize=16,color="black",shape="box"];2660 -> 2675[label="",style="solid", color="black", weight=3];
2661[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS Zero (Succ vuz820))",fontsize=16,color="black",shape="box"];2661 -> 2676[label="",style="solid", color="black", weight=3];
2662[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2662 -> 2677[label="",style="solid", color="black", weight=3];
1627[label="Zero",fontsize=16,color="green",shape="box"];1628[label="primMinusNatS (Succ vuz3900) Zero",fontsize=16,color="black",shape="triangle"];1628 -> 1648[label="",style="solid", color="black", weight=3];
1629[label="Zero",fontsize=16,color="green",shape="box"];1630[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="triangle"];1630 -> 1649[label="",style="solid", color="black", weight=3];
2767[label="gcd0 (Pos (Succ vuz840)) (Pos vuz16)",fontsize=16,color="black",shape="box"];2767 -> 2783[label="",style="solid", color="black", weight=3];
2768[label="gcd1 (Pos vuz16 == fromInt (Pos Zero)) (Pos Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];2768 -> 2784[label="",style="solid", color="black", weight=3];
1599[label="gcd0 (Neg (Succ vuz410)) (Pos vuz16)",fontsize=16,color="black",shape="box"];1599 -> 1615[label="",style="solid", color="black", weight=3];
1600[label="gcd1 (Pos vuz16 == fromInt (Pos Zero)) (Neg Zero) (Pos vuz16)",fontsize=16,color="black",shape="box"];1600 -> 1616[label="",style="solid", color="black", weight=3];
1601[label="gcd0 (Neg (Succ vuz420)) (Neg vuz19)",fontsize=16,color="black",shape="box"];1601 -> 1617[label="",style="solid", color="black", weight=3];
1602[label="gcd1 (Neg vuz19 == fromInt (Pos Zero)) (Neg Zero) (Neg vuz19)",fontsize=16,color="black",shape="box"];1602 -> 1618[label="",style="solid", color="black", weight=3];
1631[label="gcd0 (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="triangle"];1631 -> 1650[label="",style="solid", color="black", weight=3];
1632[label="gcd1 (Neg vuz19 == fromInt (Pos Zero)) (Pos vuz43) (Neg vuz19)",fontsize=16,color="black",shape="box"];1632 -> 1651[label="",style="solid", color="black", weight=3];
2674 -> 2163[label="",style="dashed", color="red", weight=0];
2674[label="primDivNatS0 (Succ vuz79) (Succ vuz80) (primGEqNatS vuz810 vuz820)",fontsize=16,color="magenta"];2674 -> 2692[label="",style="dashed", color="magenta", weight=3];
2674 -> 2693[label="",style="dashed", color="magenta", weight=3];
2675[label="primDivNatS0 (Succ vuz79) (Succ vuz80) True",fontsize=16,color="black",shape="triangle"];2675 -> 2694[label="",style="solid", color="black", weight=3];
2676[label="primDivNatS0 (Succ vuz79) (Succ vuz80) False",fontsize=16,color="black",shape="box"];2676 -> 2695[label="",style="solid", color="black", weight=3];
2677 -> 2675[label="",style="dashed", color="red", weight=0];
2677[label="primDivNatS0 (Succ vuz79) (Succ vuz80) True",fontsize=16,color="magenta"];1648[label="Succ vuz3900",fontsize=16,color="green",shape="box"];1649[label="Zero",fontsize=16,color="green",shape="box"];2783 -> 2802[label="",style="dashed", color="red", weight=0];
2783[label="gcd0Gcd' (abs (Pos (Succ vuz840))) (abs (Pos vuz16))",fontsize=16,color="magenta"];2783 -> 2803[label="",style="dashed", color="magenta", weight=3];
2783 -> 2804[label="",style="dashed", color="magenta", weight=3];
2784[label="gcd1 (primEqInt (Pos vuz16) (fromInt (Pos Zero))) (Pos Zero) (Pos vuz16)",fontsize=16,color="burlywood",shape="box"];3331[label="vuz16/Succ vuz160",fontsize=10,color="white",style="solid",shape="box"];2784 -> 3331[label="",style="solid", color="burlywood", weight=9];
3331 -> 2817[label="",style="solid", color="burlywood", weight=3];
3332[label="vuz16/Zero",fontsize=10,color="white",style="solid",shape="box"];2784 -> 3332[label="",style="solid", color="burlywood", weight=9];
3332 -> 2818[label="",style="solid", color="burlywood", weight=3];
1615 -> 2802[label="",style="dashed", color="red", weight=0];
1615[label="gcd0Gcd' (abs (Neg (Succ vuz410))) (abs (Pos vuz16))",fontsize=16,color="magenta"];1615 -> 2805[label="",style="dashed", color="magenta", weight=3];
1615 -> 2806[label="",style="dashed", color="magenta", weight=3];
1616[label="gcd1 (primEqInt (Pos vuz16) (fromInt (Pos Zero))) (Neg Zero) (Pos vuz16)",fontsize=16,color="burlywood",shape="box"];3334[label="vuz16/Succ vuz160",fontsize=10,color="white",style="solid",shape="box"];1616 -> 3334[label="",style="solid", color="burlywood", weight=9];
3334 -> 1634[label="",style="solid", color="burlywood", weight=3];
3335[label="vuz16/Zero",fontsize=10,color="white",style="solid",shape="box"];1616 -> 3335[label="",style="solid", color="burlywood", weight=9];
3335 -> 1635[label="",style="solid", color="burlywood", weight=3];
1617 -> 2802[label="",style="dashed", color="red", weight=0];
1617[label="gcd0Gcd' (abs (Neg (Succ vuz420))) (abs (Neg vuz19))",fontsize=16,color="magenta"];1617 -> 2807[label="",style="dashed", color="magenta", weight=3];
1617 -> 2808[label="",style="dashed", color="magenta", weight=3];
1618[label="gcd1 (primEqInt (Neg vuz19) (fromInt (Pos Zero))) (Neg Zero) (Neg vuz19)",fontsize=16,color="burlywood",shape="box"];3337[label="vuz19/Succ vuz190",fontsize=10,color="white",style="solid",shape="box"];1618 -> 3337[label="",style="solid", color="burlywood", weight=9];
3337 -> 1637[label="",style="solid", color="burlywood", weight=3];
3338[label="vuz19/Zero",fontsize=10,color="white",style="solid",shape="box"];1618 -> 3338[label="",style="solid", color="burlywood", weight=9];
3338 -> 1638[label="",style="solid", color="burlywood", weight=3];
1650 -> 2802[label="",style="dashed", color="red", weight=0];
1650[label="gcd0Gcd' (abs (Pos vuz43)) (abs (Neg vuz19))",fontsize=16,color="magenta"];1650 -> 2809[label="",style="dashed", color="magenta", weight=3];
1650 -> 2810[label="",style="dashed", color="magenta", weight=3];
1651[label="gcd1 (primEqInt (Neg vuz19) (fromInt (Pos Zero))) (Pos vuz43) (Neg vuz19)",fontsize=16,color="burlywood",shape="box"];3340[label="vuz19/Succ vuz190",fontsize=10,color="white",style="solid",shape="box"];1651 -> 3340[label="",style="solid", color="burlywood", weight=9];
3340 -> 1670[label="",style="solid", color="burlywood", weight=3];
3341[label="vuz19/Zero",fontsize=10,color="white",style="solid",shape="box"];1651 -> 3341[label="",style="solid", color="burlywood", weight=9];
3341 -> 1671[label="",style="solid", color="burlywood", weight=3];
2692[label="vuz820",fontsize=16,color="green",shape="box"];2693[label="vuz810",fontsize=16,color="green",shape="box"];2694[label="Succ (primDivNatS (primMinusNatS (Succ vuz79) (Succ vuz80)) (Succ (Succ vuz80)))",fontsize=16,color="green",shape="box"];2694 -> 2705[label="",style="dashed", color="green", weight=3];
2695[label="Zero",fontsize=16,color="green",shape="box"];2803[label="abs (Pos (Succ vuz840))",fontsize=16,color="black",shape="box"];2803 -> 2819[label="",style="solid", color="black", weight=3];
2804[label="abs (Pos vuz16)",fontsize=16,color="black",shape="triangle"];2804 -> 2820[label="",style="solid", color="black", weight=3];
2802[label="gcd0Gcd' vuz87 vuz86",fontsize=16,color="black",shape="triangle"];2802 -> 2821[label="",style="solid", color="black", weight=3];
2817[label="gcd1 (primEqInt (Pos (Succ vuz160)) (fromInt (Pos Zero))) (Pos Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];2817 -> 2832[label="",style="solid", color="black", weight=3];
2818[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];2818 -> 2833[label="",style="solid", color="black", weight=3];
2805[label="abs (Neg (Succ vuz410))",fontsize=16,color="black",shape="triangle"];2805 -> 2822[label="",style="solid", color="black", weight=3];
2806 -> 2804[label="",style="dashed", color="red", weight=0];
2806[label="abs (Pos vuz16)",fontsize=16,color="magenta"];1634[label="gcd1 (primEqInt (Pos (Succ vuz160)) (fromInt (Pos Zero))) (Neg Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];1634 -> 1653[label="",style="solid", color="black", weight=3];
1635[label="gcd1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1635 -> 1654[label="",style="solid", color="black", weight=3];
2807 -> 2805[label="",style="dashed", color="red", weight=0];
2807[label="abs (Neg (Succ vuz420))",fontsize=16,color="magenta"];2807 -> 2823[label="",style="dashed", color="magenta", weight=3];
2808[label="abs (Neg vuz19)",fontsize=16,color="black",shape="triangle"];2808 -> 2824[label="",style="solid", color="black", weight=3];
1637[label="gcd1 (primEqInt (Neg (Succ vuz190)) (fromInt (Pos Zero))) (Neg Zero) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1637 -> 1656[label="",style="solid", color="black", weight=3];
1638[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1638 -> 1657[label="",style="solid", color="black", weight=3];
2809 -> 2804[label="",style="dashed", color="red", weight=0];
2809[label="abs (Pos vuz43)",fontsize=16,color="magenta"];2809 -> 2825[label="",style="dashed", color="magenta", weight=3];
2810 -> 2808[label="",style="dashed", color="red", weight=0];
2810[label="abs (Neg vuz19)",fontsize=16,color="magenta"];1670[label="gcd1 (primEqInt (Neg (Succ vuz190)) (fromInt (Pos Zero))) (Pos vuz43) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1670 -> 1694[label="",style="solid", color="black", weight=3];
1671[label="gcd1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) (Pos vuz43) (Neg Zero)",fontsize=16,color="black",shape="box"];1671 -> 1695[label="",style="solid", color="black", weight=3];
2705 -> 1488[label="",style="dashed", color="red", weight=0];
2705[label="primDivNatS (primMinusNatS (Succ vuz79) (Succ vuz80)) (Succ (Succ vuz80))",fontsize=16,color="magenta"];2705 -> 2720[label="",style="dashed", color="magenta", weight=3];
2705 -> 2721[label="",style="dashed", color="magenta", weight=3];
2819[label="absReal (Pos (Succ vuz840))",fontsize=16,color="black",shape="box"];2819 -> 2834[label="",style="solid", color="black", weight=3];
2820[label="absReal (Pos vuz16)",fontsize=16,color="black",shape="box"];2820 -> 2835[label="",style="solid", color="black", weight=3];
2821[label="gcd0Gcd'2 vuz87 vuz86",fontsize=16,color="black",shape="box"];2821 -> 2836[label="",style="solid", color="black", weight=3];
2832[label="gcd1 (primEqInt (Pos (Succ vuz160)) (Pos Zero)) (Pos Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];2832 -> 2839[label="",style="solid", color="black", weight=3];
2833[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];2833 -> 2840[label="",style="solid", color="black", weight=3];
2822[label="absReal (Neg (Succ vuz410))",fontsize=16,color="black",shape="box"];2822 -> 2837[label="",style="solid", color="black", weight=3];
1653[label="gcd1 (primEqInt (Pos (Succ vuz160)) (Pos Zero)) (Neg Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];1653 -> 1673[label="",style="solid", color="black", weight=3];
1654[label="gcd1 (primEqInt (Pos Zero) (Pos Zero)) (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1654 -> 1674[label="",style="solid", color="black", weight=3];
2823[label="vuz420",fontsize=16,color="green",shape="box"];2824[label="absReal (Neg vuz19)",fontsize=16,color="black",shape="box"];2824 -> 2838[label="",style="solid", color="black", weight=3];
1656[label="gcd1 (primEqInt (Neg (Succ vuz190)) (Pos Zero)) (Neg Zero) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1656 -> 1676[label="",style="solid", color="black", weight=3];
1657[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1657 -> 1677[label="",style="solid", color="black", weight=3];
2825[label="vuz43",fontsize=16,color="green",shape="box"];1694[label="gcd1 (primEqInt (Neg (Succ vuz190)) (Pos Zero)) (Pos vuz43) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1694 -> 1716[label="",style="solid", color="black", weight=3];
1695[label="gcd1 (primEqInt (Neg Zero) (Pos Zero)) (Pos vuz43) (Neg Zero)",fontsize=16,color="black",shape="box"];1695 -> 1717[label="",style="solid", color="black", weight=3];
2720[label="Succ vuz80",fontsize=16,color="green",shape="box"];2721[label="primMinusNatS (Succ vuz79) (Succ vuz80)",fontsize=16,color="black",shape="box"];2721 -> 2734[label="",style="solid", color="black", weight=3];
2834[label="absReal2 (Pos (Succ vuz840))",fontsize=16,color="black",shape="box"];2834 -> 2841[label="",style="solid", color="black", weight=3];
2835[label="absReal2 (Pos vuz16)",fontsize=16,color="black",shape="box"];2835 -> 2842[label="",style="solid", color="black", weight=3];
2836[label="gcd0Gcd'1 (vuz86 == fromInt (Pos Zero)) vuz87 vuz86",fontsize=16,color="black",shape="box"];2836 -> 2843[label="",style="solid", color="black", weight=3];
2839[label="gcd1 False (Pos Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];2839 -> 2846[label="",style="solid", color="black", weight=3];
2840[label="gcd1 True (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];2840 -> 2847[label="",style="solid", color="black", weight=3];
2837[label="absReal2 (Neg (Succ vuz410))",fontsize=16,color="black",shape="box"];2837 -> 2844[label="",style="solid", color="black", weight=3];
1673[label="gcd1 False (Neg Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];1673 -> 1697[label="",style="solid", color="black", weight=3];
1674[label="gcd1 True (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];1674 -> 1698[label="",style="solid", color="black", weight=3];
2838[label="absReal2 (Neg vuz19)",fontsize=16,color="black",shape="box"];2838 -> 2845[label="",style="solid", color="black", weight=3];
1676[label="gcd1 False (Neg Zero) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1676 -> 1700[label="",style="solid", color="black", weight=3];
1677[label="gcd1 True (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];1677 -> 1701[label="",style="solid", color="black", weight=3];
1716[label="gcd1 False (Pos vuz43) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1716 -> 1735[label="",style="solid", color="black", weight=3];
1717[label="gcd1 True (Pos vuz43) (Neg Zero)",fontsize=16,color="black",shape="box"];1717 -> 1736[label="",style="solid", color="black", weight=3];
2734[label="primMinusNatS vuz79 vuz80",fontsize=16,color="burlywood",shape="triangle"];3347[label="vuz79/Succ vuz790",fontsize=10,color="white",style="solid",shape="box"];2734 -> 3347[label="",style="solid", color="burlywood", weight=9];
3347 -> 2749[label="",style="solid", color="burlywood", weight=3];
3348[label="vuz79/Zero",fontsize=10,color="white",style="solid",shape="box"];2734 -> 3348[label="",style="solid", color="burlywood", weight=9];
3348 -> 2750[label="",style="solid", color="burlywood", weight=3];
2841[label="absReal1 (Pos (Succ vuz840)) (Pos (Succ vuz840) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];2841 -> 2848[label="",style="solid", color="black", weight=3];
2842[label="absReal1 (Pos vuz16) (Pos vuz16 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];2842 -> 2849[label="",style="solid", color="black", weight=3];
2843[label="gcd0Gcd'1 (primEqInt vuz86 (fromInt (Pos Zero))) vuz87 vuz86",fontsize=16,color="burlywood",shape="box"];3349[label="vuz86/Pos vuz860",fontsize=10,color="white",style="solid",shape="box"];2843 -> 3349[label="",style="solid", color="burlywood", weight=9];
3349 -> 2850[label="",style="solid", color="burlywood", weight=3];
3350[label="vuz86/Neg vuz860",fontsize=10,color="white",style="solid",shape="box"];2843 -> 3350[label="",style="solid", color="burlywood", weight=9];
3350 -> 2851[label="",style="solid", color="burlywood", weight=3];
2846[label="gcd0 (Pos Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];2846 -> 2854[label="",style="solid", color="black", weight=3];
2847 -> 1464[label="",style="dashed", color="red", weight=0];
2847[label="error []",fontsize=16,color="magenta"];2844[label="absReal1 (Neg (Succ vuz410)) (Neg (Succ vuz410) >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];2844 -> 2852[label="",style="solid", color="black", weight=3];
1697[label="gcd0 (Neg Zero) (Pos (Succ vuz160))",fontsize=16,color="black",shape="box"];1697 -> 1719[label="",style="solid", color="black", weight=3];
1698 -> 1464[label="",style="dashed", color="red", weight=0];
1698[label="error []",fontsize=16,color="magenta"];2845[label="absReal1 (Neg vuz19) (Neg vuz19 >= fromInt (Pos Zero))",fontsize=16,color="black",shape="box"];2845 -> 2853[label="",style="solid", color="black", weight=3];
1700[label="gcd0 (Neg Zero) (Neg (Succ vuz190))",fontsize=16,color="black",shape="box"];1700 -> 1721[label="",style="solid", color="black", weight=3];
1701 -> 1464[label="",style="dashed", color="red", weight=0];
1701[label="error []",fontsize=16,color="magenta"];1735 -> 1631[label="",style="dashed", color="red", weight=0];
1735[label="gcd0 (Pos vuz43) (Neg (Succ vuz190))",fontsize=16,color="magenta"];1735 -> 1759[label="",style="dashed", color="magenta", weight=3];
1736 -> 1464[label="",style="dashed", color="red", weight=0];
1736[label="error []",fontsize=16,color="magenta"];2749[label="primMinusNatS (Succ vuz790) vuz80",fontsize=16,color="burlywood",shape="box"];3356[label="vuz80/Succ vuz800",fontsize=10,color="white",style="solid",shape="box"];2749 -> 3356[label="",style="solid", color="burlywood", weight=9];
3356 -> 2769[label="",style="solid", color="burlywood", weight=3];
3357[label="vuz80/Zero",fontsize=10,color="white",style="solid",shape="box"];2749 -> 3357[label="",style="solid", color="burlywood", weight=9];
3357 -> 2770[label="",style="solid", color="burlywood", weight=3];
2750[label="primMinusNatS Zero vuz80",fontsize=16,color="burlywood",shape="box"];3358[label="vuz80/Succ vuz800",fontsize=10,color="white",style="solid",shape="box"];2750 -> 3358[label="",style="solid", color="burlywood", weight=9];
3358 -> 2771[label="",style="solid", color="burlywood", weight=3];
3359[label="vuz80/Zero",fontsize=10,color="white",style="solid",shape="box"];2750 -> 3359[label="",style="solid", color="burlywood", weight=9];
3359 -> 2772[label="",style="solid", color="burlywood", weight=3];
2848[label="absReal1 (Pos (Succ vuz840)) (compare (Pos (Succ vuz840)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];2848 -> 2855[label="",style="solid", color="black", weight=3];
2849[label="absReal1 (Pos vuz16) (compare (Pos vuz16) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];2849 -> 2856[label="",style="solid", color="black", weight=3];
2850[label="gcd0Gcd'1 (primEqInt (Pos vuz860) (fromInt (Pos Zero))) vuz87 (Pos vuz860)",fontsize=16,color="burlywood",shape="box"];3360[label="vuz860/Succ vuz8600",fontsize=10,color="white",style="solid",shape="box"];2850 -> 3360[label="",style="solid", color="burlywood", weight=9];
3360 -> 2857[label="",style="solid", color="burlywood", weight=3];
3361[label="vuz860/Zero",fontsize=10,color="white",style="solid",shape="box"];2850 -> 3361[label="",style="solid", color="burlywood", weight=9];
3361 -> 2858[label="",style="solid", color="burlywood", weight=3];
2851[label="gcd0Gcd'1 (primEqInt (Neg vuz860) (fromInt (Pos Zero))) vuz87 (Neg vuz860)",fontsize=16,color="burlywood",shape="box"];3362[label="vuz860/Succ vuz8600",fontsize=10,color="white",style="solid",shape="box"];2851 -> 3362[label="",style="solid", color="burlywood", weight=9];
3362 -> 2859[label="",style="solid", color="burlywood", weight=3];
3363[label="vuz860/Zero",fontsize=10,color="white",style="solid",shape="box"];2851 -> 3363[label="",style="solid", color="burlywood", weight=9];
3363 -> 2860[label="",style="solid", color="burlywood", weight=3];
2854 -> 2802[label="",style="dashed", color="red", weight=0];
2854[label="gcd0Gcd' (abs (Pos Zero)) (abs (Pos (Succ vuz160)))",fontsize=16,color="magenta"];2854 -> 2863[label="",style="dashed", color="magenta", weight=3];
2854 -> 2864[label="",style="dashed", color="magenta", weight=3];
2852[label="absReal1 (Neg (Succ vuz410)) (compare (Neg (Succ vuz410)) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];2852 -> 2861[label="",style="solid", color="black", weight=3];
1719 -> 2802[label="",style="dashed", color="red", weight=0];
1719[label="gcd0Gcd' (abs (Neg Zero)) (abs (Pos (Succ vuz160)))",fontsize=16,color="magenta"];1719 -> 2811[label="",style="dashed", color="magenta", weight=3];
1719 -> 2812[label="",style="dashed", color="magenta", weight=3];
2853[label="absReal1 (Neg vuz19) (compare (Neg vuz19) (fromInt (Pos Zero)) /= LT)",fontsize=16,color="black",shape="box"];2853 -> 2862[label="",style="solid", color="black", weight=3];
1721 -> 2802[label="",style="dashed", color="red", weight=0];
1721[label="gcd0Gcd' (abs (Neg Zero)) (abs (Neg (Succ vuz190)))",fontsize=16,color="magenta"];1721 -> 2813[label="",style="dashed", color="magenta", weight=3];
1721 -> 2814[label="",style="dashed", color="magenta", weight=3];
1759[label="Succ vuz190",fontsize=16,color="green",shape="box"];2769[label="primMinusNatS (Succ vuz790) (Succ vuz800)",fontsize=16,color="black",shape="box"];2769 -> 2785[label="",style="solid", color="black", weight=3];
2770[label="primMinusNatS (Succ vuz790) Zero",fontsize=16,color="black",shape="box"];2770 -> 2786[label="",style="solid", color="black", weight=3];
2771[label="primMinusNatS Zero (Succ vuz800)",fontsize=16,color="black",shape="box"];2771 -> 2787[label="",style="solid", color="black", weight=3];
2772[label="primMinusNatS Zero Zero",fontsize=16,color="black",shape="box"];2772 -> 2788[label="",style="solid", color="black", weight=3];
2855[label="absReal1 (Pos (Succ vuz840)) (not (compare (Pos (Succ vuz840)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2855 -> 2865[label="",style="solid", color="black", weight=3];
2856[label="absReal1 (Pos vuz16) (not (compare (Pos vuz16) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2856 -> 2866[label="",style="solid", color="black", weight=3];
2857[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz8600)) (fromInt (Pos Zero))) vuz87 (Pos (Succ vuz8600))",fontsize=16,color="black",shape="box"];2857 -> 2867[label="",style="solid", color="black", weight=3];
2858[label="gcd0Gcd'1 (primEqInt (Pos Zero) (fromInt (Pos Zero))) vuz87 (Pos Zero)",fontsize=16,color="black",shape="box"];2858 -> 2868[label="",style="solid", color="black", weight=3];
2859[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz8600)) (fromInt (Pos Zero))) vuz87 (Neg (Succ vuz8600))",fontsize=16,color="black",shape="box"];2859 -> 2869[label="",style="solid", color="black", weight=3];
2860[label="gcd0Gcd'1 (primEqInt (Neg Zero) (fromInt (Pos Zero))) vuz87 (Neg Zero)",fontsize=16,color="black",shape="box"];2860 -> 2870[label="",style="solid", color="black", weight=3];
2863 -> 2804[label="",style="dashed", color="red", weight=0];
2863[label="abs (Pos Zero)",fontsize=16,color="magenta"];2863 -> 2873[label="",style="dashed", color="magenta", weight=3];
2864 -> 2804[label="",style="dashed", color="red", weight=0];
2864[label="abs (Pos (Succ vuz160))",fontsize=16,color="magenta"];2864 -> 2874[label="",style="dashed", color="magenta", weight=3];
2861[label="absReal1 (Neg (Succ vuz410)) (not (compare (Neg (Succ vuz410)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2861 -> 2871[label="",style="solid", color="black", weight=3];
2811 -> 2808[label="",style="dashed", color="red", weight=0];
2811[label="abs (Neg Zero)",fontsize=16,color="magenta"];2811 -> 2826[label="",style="dashed", color="magenta", weight=3];
2812 -> 2804[label="",style="dashed", color="red", weight=0];
2812[label="abs (Pos (Succ vuz160))",fontsize=16,color="magenta"];2812 -> 2827[label="",style="dashed", color="magenta", weight=3];
2862[label="absReal1 (Neg vuz19) (not (compare (Neg vuz19) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2862 -> 2872[label="",style="solid", color="black", weight=3];
2813 -> 2808[label="",style="dashed", color="red", weight=0];
2813[label="abs (Neg Zero)",fontsize=16,color="magenta"];2813 -> 2828[label="",style="dashed", color="magenta", weight=3];
2814 -> 2808[label="",style="dashed", color="red", weight=0];
2814[label="abs (Neg (Succ vuz190))",fontsize=16,color="magenta"];2814 -> 2829[label="",style="dashed", color="magenta", weight=3];
2785 -> 2734[label="",style="dashed", color="red", weight=0];
2785[label="primMinusNatS vuz790 vuz800",fontsize=16,color="magenta"];2785 -> 2830[label="",style="dashed", color="magenta", weight=3];
2785 -> 2831[label="",style="dashed", color="magenta", weight=3];
2786[label="Succ vuz790",fontsize=16,color="green",shape="box"];2787[label="Zero",fontsize=16,color="green",shape="box"];2788[label="Zero",fontsize=16,color="green",shape="box"];2865[label="absReal1 (Pos (Succ vuz840)) (not (primCmpInt (Pos (Succ vuz840)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2865 -> 2875[label="",style="solid", color="black", weight=3];
2866[label="absReal1 (Pos vuz16) (not (primCmpInt (Pos vuz16) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];3374[label="vuz16/Succ vuz160",fontsize=10,color="white",style="solid",shape="box"];2866 -> 3374[label="",style="solid", color="burlywood", weight=9];
3374 -> 2876[label="",style="solid", color="burlywood", weight=3];
3375[label="vuz16/Zero",fontsize=10,color="white",style="solid",shape="box"];2866 -> 3375[label="",style="solid", color="burlywood", weight=9];
3375 -> 2877[label="",style="solid", color="burlywood", weight=3];
2867[label="gcd0Gcd'1 (primEqInt (Pos (Succ vuz8600)) (Pos Zero)) vuz87 (Pos (Succ vuz8600))",fontsize=16,color="black",shape="box"];2867 -> 2878[label="",style="solid", color="black", weight=3];
2868[label="gcd0Gcd'1 (primEqInt (Pos Zero) (Pos Zero)) vuz87 (Pos Zero)",fontsize=16,color="black",shape="box"];2868 -> 2879[label="",style="solid", color="black", weight=3];
2869[label="gcd0Gcd'1 (primEqInt (Neg (Succ vuz8600)) (Pos Zero)) vuz87 (Neg (Succ vuz8600))",fontsize=16,color="black",shape="box"];2869 -> 2880[label="",style="solid", color="black", weight=3];
2870[label="gcd0Gcd'1 (primEqInt (Neg Zero) (Pos Zero)) vuz87 (Neg Zero)",fontsize=16,color="black",shape="box"];2870 -> 2881[label="",style="solid", color="black", weight=3];
2873[label="Zero",fontsize=16,color="green",shape="box"];2874[label="Succ vuz160",fontsize=16,color="green",shape="box"];2871[label="absReal1 (Neg (Succ vuz410)) (not (primCmpInt (Neg (Succ vuz410)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2871 -> 2882[label="",style="solid", color="black", weight=3];
2826[label="Zero",fontsize=16,color="green",shape="box"];2827[label="Succ vuz160",fontsize=16,color="green",shape="box"];2872[label="absReal1 (Neg vuz19) (not (primCmpInt (Neg vuz19) (fromInt (Pos Zero)) == LT))",fontsize=16,color="burlywood",shape="box"];3376[label="vuz19/Succ vuz190",fontsize=10,color="white",style="solid",shape="box"];2872 -> 3376[label="",style="solid", color="burlywood", weight=9];
3376 -> 2883[label="",style="solid", color="burlywood", weight=3];
3377[label="vuz19/Zero",fontsize=10,color="white",style="solid",shape="box"];2872 -> 3377[label="",style="solid", color="burlywood", weight=9];
3377 -> 2884[label="",style="solid", color="burlywood", weight=3];
2828[label="Zero",fontsize=16,color="green",shape="box"];2829[label="Succ vuz190",fontsize=16,color="green",shape="box"];2830[label="vuz800",fontsize=16,color="green",shape="box"];2831[label="vuz790",fontsize=16,color="green",shape="box"];2875[label="absReal1 (Pos (Succ vuz840)) (not (primCmpInt (Pos (Succ vuz840)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];2875 -> 2885[label="",style="solid", color="black", weight=3];
2876[label="absReal1 (Pos (Succ vuz160)) (not (primCmpInt (Pos (Succ vuz160)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2876 -> 2886[label="",style="solid", color="black", weight=3];
2877[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2877 -> 2887[label="",style="solid", color="black", weight=3];
2878[label="gcd0Gcd'1 False vuz87 (Pos (Succ vuz8600))",fontsize=16,color="black",shape="box"];2878 -> 2888[label="",style="solid", color="black", weight=3];
2879[label="gcd0Gcd'1 True vuz87 (Pos Zero)",fontsize=16,color="black",shape="box"];2879 -> 2889[label="",style="solid", color="black", weight=3];
2880[label="gcd0Gcd'1 False vuz87 (Neg (Succ vuz8600))",fontsize=16,color="black",shape="box"];2880 -> 2890[label="",style="solid", color="black", weight=3];
2881[label="gcd0Gcd'1 True vuz87 (Neg Zero)",fontsize=16,color="black",shape="box"];2881 -> 2891[label="",style="solid", color="black", weight=3];
2882[label="absReal1 (Neg (Succ vuz410)) (not (primCmpInt (Neg (Succ vuz410)) (Pos Zero) == LT))",fontsize=16,color="black",shape="triangle"];2882 -> 2892[label="",style="solid", color="black", weight=3];
2883[label="absReal1 (Neg (Succ vuz190)) (not (primCmpInt (Neg (Succ vuz190)) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2883 -> 2893[label="",style="solid", color="black", weight=3];
2884[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (fromInt (Pos Zero)) == LT))",fontsize=16,color="black",shape="box"];2884 -> 2894[label="",style="solid", color="black", weight=3];
2885[label="absReal1 (Pos (Succ vuz840)) (not (primCmpNat (Succ vuz840) Zero == LT))",fontsize=16,color="black",shape="box"];2885 -> 2895[label="",style="solid", color="black", weight=3];
2886 -> 2875[label="",style="dashed", color="red", weight=0];
2886[label="absReal1 (Pos (Succ vuz160)) (not (primCmpInt (Pos (Succ vuz160)) (Pos Zero) == LT))",fontsize=16,color="magenta"];2886 -> 2896[label="",style="dashed", color="magenta", weight=3];
2887[label="absReal1 (Pos Zero) (not (primCmpInt (Pos Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];2887 -> 2897[label="",style="solid", color="black", weight=3];
2888[label="gcd0Gcd'0 vuz87 (Pos (Succ vuz8600))",fontsize=16,color="black",shape="box"];2888 -> 2898[label="",style="solid", color="black", weight=3];
2889[label="vuz87",fontsize=16,color="green",shape="box"];2890[label="gcd0Gcd'0 vuz87 (Neg (Succ vuz8600))",fontsize=16,color="black",shape="box"];2890 -> 2899[label="",style="solid", color="black", weight=3];
2891[label="vuz87",fontsize=16,color="green",shape="box"];2892[label="absReal1 (Neg (Succ vuz410)) (not (LT == LT))",fontsize=16,color="black",shape="box"];2892 -> 2900[label="",style="solid", color="black", weight=3];
2893 -> 2882[label="",style="dashed", color="red", weight=0];
2893[label="absReal1 (Neg (Succ vuz190)) (not (primCmpInt (Neg (Succ vuz190)) (Pos Zero) == LT))",fontsize=16,color="magenta"];2893 -> 2901[label="",style="dashed", color="magenta", weight=3];
2894[label="absReal1 (Neg Zero) (not (primCmpInt (Neg Zero) (Pos Zero) == LT))",fontsize=16,color="black",shape="box"];2894 -> 2902[label="",style="solid", color="black", weight=3];
2895[label="absReal1 (Pos (Succ vuz840)) (not (GT == LT))",fontsize=16,color="black",shape="box"];2895 -> 2903[label="",style="solid", color="black", weight=3];
2896[label="vuz160",fontsize=16,color="green",shape="box"];2897[label="absReal1 (Pos Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];2897 -> 2904[label="",style="solid", color="black", weight=3];
2898 -> 2802[label="",style="dashed", color="red", weight=0];
2898[label="gcd0Gcd' (Pos (Succ vuz8600)) (vuz87 `rem` Pos (Succ vuz8600))",fontsize=16,color="magenta"];2898 -> 2905[label="",style="dashed", color="magenta", weight=3];
2898 -> 2906[label="",style="dashed", color="magenta", weight=3];
2899 -> 2802[label="",style="dashed", color="red", weight=0];
2899[label="gcd0Gcd' (Neg (Succ vuz8600)) (vuz87 `rem` Neg (Succ vuz8600))",fontsize=16,color="magenta"];2899 -> 2907[label="",style="dashed", color="magenta", weight=3];
2899 -> 2908[label="",style="dashed", color="magenta", weight=3];
2900[label="absReal1 (Neg (Succ vuz410)) (not True)",fontsize=16,color="black",shape="box"];2900 -> 2909[label="",style="solid", color="black", weight=3];
2901[label="vuz190",fontsize=16,color="green",shape="box"];2902[label="absReal1 (Neg Zero) (not (EQ == LT))",fontsize=16,color="black",shape="box"];2902 -> 2910[label="",style="solid", color="black", weight=3];
2903[label="absReal1 (Pos (Succ vuz840)) (not False)",fontsize=16,color="black",shape="box"];2903 -> 2911[label="",style="solid", color="black", weight=3];
2904[label="absReal1 (Pos Zero) (not False)",fontsize=16,color="black",shape="box"];2904 -> 2912[label="",style="solid", color="black", weight=3];
2905[label="Pos (Succ vuz8600)",fontsize=16,color="green",shape="box"];2906[label="vuz87 `rem` Pos (Succ vuz8600)",fontsize=16,color="black",shape="box"];2906 -> 2913[label="",style="solid", color="black", weight=3];
2907[label="Neg (Succ vuz8600)",fontsize=16,color="green",shape="box"];2908[label="vuz87 `rem` Neg (Succ vuz8600)",fontsize=16,color="black",shape="box"];2908 -> 2914[label="",style="solid", color="black", weight=3];
2909[label="absReal1 (Neg (Succ vuz410)) False",fontsize=16,color="black",shape="box"];2909 -> 2915[label="",style="solid", color="black", weight=3];
2910[label="absReal1 (Neg Zero) (not False)",fontsize=16,color="black",shape="box"];2910 -> 2916[label="",style="solid", color="black", weight=3];
2911[label="absReal1 (Pos (Succ vuz840)) True",fontsize=16,color="black",shape="box"];2911 -> 2917[label="",style="solid", color="black", weight=3];
2912[label="absReal1 (Pos Zero) True",fontsize=16,color="black",shape="box"];2912 -> 2918[label="",style="solid", color="black", weight=3];
2913[label="primRemInt vuz87 (Pos (Succ vuz8600))",fontsize=16,color="burlywood",shape="box"];3382[label="vuz87/Pos vuz870",fontsize=10,color="white",style="solid",shape="box"];2913 -> 3382[label="",style="solid", color="burlywood", weight=9];
3382 -> 2919[label="",style="solid", color="burlywood", weight=3];
3383[label="vuz87/Neg vuz870",fontsize=10,color="white",style="solid",shape="box"];2913 -> 3383[label="",style="solid", color="burlywood", weight=9];
3383 -> 2920[label="",style="solid", color="burlywood", weight=3];
2914[label="primRemInt vuz87 (Neg (Succ vuz8600))",fontsize=16,color="burlywood",shape="box"];3384[label="vuz87/Pos vuz870",fontsize=10,color="white",style="solid",shape="box"];2914 -> 3384[label="",style="solid", color="burlywood", weight=9];
3384 -> 2921[label="",style="solid", color="burlywood", weight=3];
3385[label="vuz87/Neg vuz870",fontsize=10,color="white",style="solid",shape="box"];2914 -> 3385[label="",style="solid", color="burlywood", weight=9];
3385 -> 2922[label="",style="solid", color="burlywood", weight=3];
2915[label="absReal0 (Neg (Succ vuz410)) otherwise",fontsize=16,color="black",shape="box"];2915 -> 2923[label="",style="solid", color="black", weight=3];
2916[label="absReal1 (Neg Zero) True",fontsize=16,color="black",shape="box"];2916 -> 2924[label="",style="solid", color="black", weight=3];
2917[label="Pos (Succ vuz840)",fontsize=16,color="green",shape="box"];2918[label="Pos Zero",fontsize=16,color="green",shape="box"];2919[label="primRemInt (Pos vuz870) (Pos (Succ vuz8600))",fontsize=16,color="black",shape="box"];2919 -> 2925[label="",style="solid", color="black", weight=3];
2920[label="primRemInt (Neg vuz870) (Pos (Succ vuz8600))",fontsize=16,color="black",shape="box"];2920 -> 2926[label="",style="solid", color="black", weight=3];
2921[label="primRemInt (Pos vuz870) (Neg (Succ vuz8600))",fontsize=16,color="black",shape="box"];2921 -> 2927[label="",style="solid", color="black", weight=3];
2922[label="primRemInt (Neg vuz870) (Neg (Succ vuz8600))",fontsize=16,color="black",shape="box"];2922 -> 2928[label="",style="solid", color="black", weight=3];
2923[label="absReal0 (Neg (Succ vuz410)) True",fontsize=16,color="black",shape="box"];2923 -> 2929[label="",style="solid", color="black", weight=3];
2924[label="Neg Zero",fontsize=16,color="green",shape="box"];2925[label="Pos (primModNatS vuz870 (Succ vuz8600))",fontsize=16,color="green",shape="box"];2925 -> 2930[label="",style="dashed", color="green", weight=3];
2926[label="Neg (primModNatS vuz870 (Succ vuz8600))",fontsize=16,color="green",shape="box"];2926 -> 2931[label="",style="dashed", color="green", weight=3];
2927[label="Pos (primModNatS vuz870 (Succ vuz8600))",fontsize=16,color="green",shape="box"];2927 -> 2932[label="",style="dashed", color="green", weight=3];
2928[label="Neg (primModNatS vuz870 (Succ vuz8600))",fontsize=16,color="green",shape="box"];2928 -> 2933[label="",style="dashed", color="green", weight=3];
2929[label="`negate` Neg (Succ vuz410)",fontsize=16,color="black",shape="box"];2929 -> 2934[label="",style="solid", color="black", weight=3];
2930[label="primModNatS vuz870 (Succ vuz8600)",fontsize=16,color="burlywood",shape="triangle"];3386[label="vuz870/Succ vuz8700",fontsize=10,color="white",style="solid",shape="box"];2930 -> 3386[label="",style="solid", color="burlywood", weight=9];
3386 -> 2935[label="",style="solid", color="burlywood", weight=3];
3387[label="vuz870/Zero",fontsize=10,color="white",style="solid",shape="box"];2930 -> 3387[label="",style="solid", color="burlywood", weight=9];
3387 -> 2936[label="",style="solid", color="burlywood", weight=3];
2931 -> 2930[label="",style="dashed", color="red", weight=0];
2931[label="primModNatS vuz870 (Succ vuz8600)",fontsize=16,color="magenta"];2931 -> 2937[label="",style="dashed", color="magenta", weight=3];
2932 -> 2930[label="",style="dashed", color="red", weight=0];
2932[label="primModNatS vuz870 (Succ vuz8600)",fontsize=16,color="magenta"];2932 -> 2938[label="",style="dashed", color="magenta", weight=3];
2933 -> 2930[label="",style="dashed", color="red", weight=0];
2933[label="primModNatS vuz870 (Succ vuz8600)",fontsize=16,color="magenta"];2933 -> 2939[label="",style="dashed", color="magenta", weight=3];
2933 -> 2940[label="",style="dashed", color="magenta", weight=3];
2934[label="primNegInt (Neg (Succ vuz410))",fontsize=16,color="black",shape="box"];2934 -> 2941[label="",style="solid", color="black", weight=3];
2935[label="primModNatS (Succ vuz8700) (Succ vuz8600)",fontsize=16,color="black",shape="box"];2935 -> 2942[label="",style="solid", color="black", weight=3];
2936[label="primModNatS Zero (Succ vuz8600)",fontsize=16,color="black",shape="box"];2936 -> 2943[label="",style="solid", color="black", weight=3];
2937[label="vuz870",fontsize=16,color="green",shape="box"];2938[label="vuz8600",fontsize=16,color="green",shape="box"];2939[label="vuz870",fontsize=16,color="green",shape="box"];2940[label="vuz8600",fontsize=16,color="green",shape="box"];2941[label="Pos (Succ vuz410)",fontsize=16,color="green",shape="box"];2942[label="primModNatS0 vuz8700 vuz8600 (primGEqNatS vuz8700 vuz8600)",fontsize=16,color="burlywood",shape="box"];3391[label="vuz8700/Succ vuz87000",fontsize=10,color="white",style="solid",shape="box"];2942 -> 3391[label="",style="solid", color="burlywood", weight=9];
3391 -> 2944[label="",style="solid", color="burlywood", weight=3];
3392[label="vuz8700/Zero",fontsize=10,color="white",style="solid",shape="box"];2942 -> 3392[label="",style="solid", color="burlywood", weight=9];
3392 -> 2945[label="",style="solid", color="burlywood", weight=3];
2943[label="Zero",fontsize=16,color="green",shape="box"];2944[label="primModNatS0 (Succ vuz87000) vuz8600 (primGEqNatS (Succ vuz87000) vuz8600)",fontsize=16,color="burlywood",shape="box"];3393[label="vuz8600/Succ vuz86000",fontsize=10,color="white",style="solid",shape="box"];2944 -> 3393[label="",style="solid", color="burlywood", weight=9];
3393 -> 2946[label="",style="solid", color="burlywood", weight=3];
3394[label="vuz8600/Zero",fontsize=10,color="white",style="solid",shape="box"];2944 -> 3394[label="",style="solid", color="burlywood", weight=9];
3394 -> 2947[label="",style="solid", color="burlywood", weight=3];
2945[label="primModNatS0 Zero vuz8600 (primGEqNatS Zero vuz8600)",fontsize=16,color="burlywood",shape="box"];3395[label="vuz8600/Succ vuz86000",fontsize=10,color="white",style="solid",shape="box"];2945 -> 3395[label="",style="solid", color="burlywood", weight=9];
3395 -> 2948[label="",style="solid", color="burlywood", weight=3];
3396[label="vuz8600/Zero",fontsize=10,color="white",style="solid",shape="box"];2945 -> 3396[label="",style="solid", color="burlywood", weight=9];
3396 -> 2949[label="",style="solid", color="burlywood", weight=3];
2946[label="primModNatS0 (Succ vuz87000) (Succ vuz86000) (primGEqNatS (Succ vuz87000) (Succ vuz86000))",fontsize=16,color="black",shape="box"];2946 -> 2950[label="",style="solid", color="black", weight=3];
2947[label="primModNatS0 (Succ vuz87000) Zero (primGEqNatS (Succ vuz87000) Zero)",fontsize=16,color="black",shape="box"];2947 -> 2951[label="",style="solid", color="black", weight=3];
2948[label="primModNatS0 Zero (Succ vuz86000) (primGEqNatS Zero (Succ vuz86000))",fontsize=16,color="black",shape="box"];2948 -> 2952[label="",style="solid", color="black", weight=3];
2949[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2949 -> 2953[label="",style="solid", color="black", weight=3];
2950 -> 3112[label="",style="dashed", color="red", weight=0];
2950[label="primModNatS0 (Succ vuz87000) (Succ vuz86000) (primGEqNatS vuz87000 vuz86000)",fontsize=16,color="magenta"];2950 -> 3113[label="",style="dashed", color="magenta", weight=3];
2950 -> 3114[label="",style="dashed", color="magenta", weight=3];
2950 -> 3115[label="",style="dashed", color="magenta", weight=3];
2950 -> 3116[label="",style="dashed", color="magenta", weight=3];
2951[label="primModNatS0 (Succ vuz87000) Zero True",fontsize=16,color="black",shape="box"];2951 -> 2956[label="",style="solid", color="black", weight=3];
2952[label="primModNatS0 Zero (Succ vuz86000) False",fontsize=16,color="black",shape="box"];2952 -> 2957[label="",style="solid", color="black", weight=3];
2953[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2953 -> 2958[label="",style="solid", color="black", weight=3];
3113[label="vuz86000",fontsize=16,color="green",shape="box"];3114[label="vuz87000",fontsize=16,color="green",shape="box"];3115[label="vuz86000",fontsize=16,color="green",shape="box"];3116[label="vuz87000",fontsize=16,color="green",shape="box"];3112[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS vuz106 vuz107)",fontsize=16,color="burlywood",shape="triangle"];3398[label="vuz106/Succ vuz1060",fontsize=10,color="white",style="solid",shape="box"];3112 -> 3398[label="",style="solid", color="burlywood", weight=9];
3398 -> 3145[label="",style="solid", color="burlywood", weight=3];
3399[label="vuz106/Zero",fontsize=10,color="white",style="solid",shape="box"];3112 -> 3399[label="",style="solid", color="burlywood", weight=9];
3399 -> 3146[label="",style="solid", color="burlywood", weight=3];
2956 -> 2930[label="",style="dashed", color="red", weight=0];
2956[label="primModNatS (primMinusNatS (Succ vuz87000) Zero) (Succ Zero)",fontsize=16,color="magenta"];2956 -> 2963[label="",style="dashed", color="magenta", weight=3];
2956 -> 2964[label="",style="dashed", color="magenta", weight=3];
2957[label="Succ Zero",fontsize=16,color="green",shape="box"];2958 -> 2930[label="",style="dashed", color="red", weight=0];
2958[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2958 -> 2965[label="",style="dashed", color="magenta", weight=3];
2958 -> 2966[label="",style="dashed", color="magenta", weight=3];
3145[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS (Succ vuz1060) vuz107)",fontsize=16,color="burlywood",shape="box"];3402[label="vuz107/Succ vuz1070",fontsize=10,color="white",style="solid",shape="box"];3145 -> 3402[label="",style="solid", color="burlywood", weight=9];
3402 -> 3147[label="",style="solid", color="burlywood", weight=3];
3403[label="vuz107/Zero",fontsize=10,color="white",style="solid",shape="box"];3145 -> 3403[label="",style="solid", color="burlywood", weight=9];
3403 -> 3148[label="",style="solid", color="burlywood", weight=3];
3146[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS Zero vuz107)",fontsize=16,color="burlywood",shape="box"];3404[label="vuz107/Succ vuz1070",fontsize=10,color="white",style="solid",shape="box"];3146 -> 3404[label="",style="solid", color="burlywood", weight=9];
3404 -> 3149[label="",style="solid", color="burlywood", weight=3];
3405[label="vuz107/Zero",fontsize=10,color="white",style="solid",shape="box"];3146 -> 3405[label="",style="solid", color="burlywood", weight=9];
3405 -> 3150[label="",style="solid", color="burlywood", weight=3];
2963 -> 2734[label="",style="dashed", color="red", weight=0];
2963[label="primMinusNatS (Succ vuz87000) Zero",fontsize=16,color="magenta"];2963 -> 2971[label="",style="dashed", color="magenta", weight=3];
2963 -> 2972[label="",style="dashed", color="magenta", weight=3];
2964[label="Zero",fontsize=16,color="green",shape="box"];2965 -> 2734[label="",style="dashed", color="red", weight=0];
2965[label="primMinusNatS Zero Zero",fontsize=16,color="magenta"];2965 -> 2973[label="",style="dashed", color="magenta", weight=3];
2965 -> 2974[label="",style="dashed", color="magenta", weight=3];
2966[label="Zero",fontsize=16,color="green",shape="box"];3147[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS (Succ vuz1060) (Succ vuz1070))",fontsize=16,color="black",shape="box"];3147 -> 3151[label="",style="solid", color="black", weight=3];
3148[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS (Succ vuz1060) Zero)",fontsize=16,color="black",shape="box"];3148 -> 3152[label="",style="solid", color="black", weight=3];
3149[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS Zero (Succ vuz1070))",fontsize=16,color="black",shape="box"];3149 -> 3153[label="",style="solid", color="black", weight=3];
3150[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];3150 -> 3154[label="",style="solid", color="black", weight=3];
2971[label="Zero",fontsize=16,color="green",shape="box"];2972[label="Succ vuz87000",fontsize=16,color="green",shape="box"];2973[label="Zero",fontsize=16,color="green",shape="box"];2974[label="Zero",fontsize=16,color="green",shape="box"];3151 -> 3112[label="",style="dashed", color="red", weight=0];
3151[label="primModNatS0 (Succ vuz104) (Succ vuz105) (primGEqNatS vuz1060 vuz1070)",fontsize=16,color="magenta"];3151 -> 3155[label="",style="dashed", color="magenta", weight=3];
3151 -> 3156[label="",style="dashed", color="magenta", weight=3];
3152[label="primModNatS0 (Succ vuz104) (Succ vuz105) True",fontsize=16,color="black",shape="triangle"];3152 -> 3157[label="",style="solid", color="black", weight=3];
3153[label="primModNatS0 (Succ vuz104) (Succ vuz105) False",fontsize=16,color="black",shape="box"];3153 -> 3158[label="",style="solid", color="black", weight=3];
3154 -> 3152[label="",style="dashed", color="red", weight=0];
3154[label="primModNatS0 (Succ vuz104) (Succ vuz105) True",fontsize=16,color="magenta"];3155[label="vuz1070",fontsize=16,color="green",shape="box"];3156[label="vuz1060",fontsize=16,color="green",shape="box"];3157 -> 2930[label="",style="dashed", color="red", weight=0];
3157[label="primModNatS (primMinusNatS (Succ vuz104) (Succ vuz105)) (Succ (Succ vuz105))",fontsize=16,color="magenta"];3157 -> 3159[label="",style="dashed", color="magenta", weight=3];
3157 -> 3160[label="",style="dashed", color="magenta", weight=3];
3158[label="Succ (Succ vuz104)",fontsize=16,color="green",shape="box"];3159 -> 2734[label="",style="dashed", color="red", weight=0];
3159[label="primMinusNatS (Succ vuz104) (Succ vuz105)",fontsize=16,color="magenta"];3159 -> 3161[label="",style="dashed", color="magenta", weight=3];
3159 -> 3162[label="",style="dashed", color="magenta", weight=3];
3160[label="Succ vuz105",fontsize=16,color="green",shape="box"];3161[label="Succ vuz105",fontsize=16,color="green",shape="box"];3162[label="Succ vuz104",fontsize=16,color="green",shape="box"];}

↳ 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_primPlusNat(Succ(vuz2100), Succ(vuz41000)) → new_primPlusNat(vuz2100, vuz41000)

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_primPlusNat(Succ(vuz2100), Succ(vuz41000)) → new_primPlusNat(vuz2100, vuz41000)
The graph contains the following edges 1 > 1, 2 > 2

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                            ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primMulNat(Succ(vuz3100), Succ(vuz4100)) → new_primMulNat(vuz3100, Succ(vuz4100))

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

new_primMulNat(Succ(vuz3100), Succ(vuz4100)) → new_primMulNat(vuz3100, Succ(vuz4100))
The graph contains the following edges 1 > 1, 2 >= 2

↳ 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_primMinusNatS(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS(vuz790, vuz800)

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

new_primMinusNatS(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS(vuz790, vuz800)
The graph contains the following edges 1 > 1, 2 > 2

↳ 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_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS0(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS(Succ(Zero), Zero) → new_primModNatS(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS(Succ(Succ(vuz87000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS0(vuz104, vuz105, Zero, Zero) → new_primModNatS00(vuz104, vuz105)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS(Succ(Succ(vuz87000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ RuleRemovalProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS(Succ(Succ(vuz87000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By using the rule removal processor [15] with the following polynomial ordering [25], at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.
Strictly oriented dependency pairs:

new_primModNatS(Succ(Succ(vuz87000)), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

Strictly oriented rules of the TRS R:

new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

Used ordering: POLO with Polynomial interpretation [25]:

POL(Succ(x₁)) = 2 + 2·x₁
POL(Zero) = 0
POL(new_primMinusNatS0(x₁, x₂)) = 1 + 2·x₁ + x₂
POL(new_primModNatS(x₁, x₂)) = x₁ + x₂

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ RuleRemovalProof

                                        ↳ QDP

                                          ↳ PisEmptyProof

                                ↳ QDP

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

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

We have to consider all minimal (P,Q,R)-chains.
The TRS P is empty. Hence, there is no (P,Q,R) chain.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS0(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS0(vuz104, vuz105, Zero, Zero) → new_primModNatS00(vuz104, vuz105)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105)) at position [0] we obtained the following new rules:

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS0(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))
new_primModNatS0(vuz104, vuz105, Zero, Zero) → new_primModNatS00(vuz104, vuz105)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105)) at position [0] we obtained the following new rules:

new_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))
new_primModNatS(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS0(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS0(vuz104, vuz105, Zero, Zero) → new_primModNatS00(vuz104, vuz105)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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_primModNatS00(vuz104, vuz105) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))
new_primModNatS(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS0(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS(new_primMinusNatS0(vuz104, vuz105), Succ(vuz105))

The remaining pairs can at least be oriented weakly.

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS0(vuz104, vuz105, Zero, Zero) → new_primModNatS00(vuz104, vuz105)

Used ordering: Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + x₁
POL(Zero) = 0
POL(new_primMinusNatS0(x₁, x₂)) = x₁
POL(new_primModNatS(x₁, x₂)) = x₁
POL(new_primModNatS0(x₁, x₂, x₃, x₄)) = 1 + x₁
POL(new_primModNatS00(x₁, x₂)) = 1 + x₁

The following usable rules [17] were oriented:

new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz104, vuz105, Zero, Zero) → new_primModNatS00(vuz104, vuz105)
new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ Rewriting

                                    ↳ QDP

                                      ↳ Rewriting

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                                                        ↳ QDP

                                                          ↳ QDPSizeChangeProof

                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)

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

new_primModNatS0(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS0(vuz104, vuz105, vuz1060, vuz1070)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz87, Neg(Succ(vuz8600))) → new_gcd0Gcd'(Neg(Succ(vuz8600)), new_primRemInt0(vuz87, vuz8600))
new_gcd0Gcd'(vuz87, Pos(Succ(vuz8600))) → new_gcd0Gcd'(Pos(Succ(vuz8600)), new_primRemInt(vuz87, vuz8600))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primRemInt0(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt0(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Zero) → Zero
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

The set Q consists of the following terms:

new_primRemInt0(Pos(x0), x1)
new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primRemInt0(Neg(x0), x1)
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_gcd0Gcd'(vuz87, Neg(Succ(vuz8600))) → new_gcd0Gcd'(Neg(Succ(vuz8600)), new_primRemInt0(vuz87, vuz8600)) at position [1] we obtained the following new rules:

new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz87, Pos(Succ(vuz8600))) → new_gcd0Gcd'(Pos(Succ(vuz8600)), new_primRemInt(vuz87, vuz8600))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primRemInt0(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt0(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Zero) → Zero
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

The set Q consists of the following terms:

new_primRemInt0(Pos(x0), x1)
new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primRemInt0(Neg(x0), x1)
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                    ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primRemInt0(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt0(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Zero) → Zero
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

The set Q consists of the following terms:

new_primRemInt0(Pos(x0), x1)
new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primRemInt0(Neg(x0), x1)
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                    ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primRemInt0(Pos(x0), x1)
new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primRemInt0(Neg(x0), x1)
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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_primRemInt0(Pos(x0), x1)
new_primRemInt(Pos(x0), x1)
new_primRemInt0(Neg(x0), x1)
new_primRemInt(Neg(x0), x1)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Instantiation

                                    ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'(Neg(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(x0, x1))) we obtained the following new rules:

new_gcd0Gcd'(Neg(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(Succ(z1), x1)))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Instantiation

                                                ↳ QDP

                                                  ↳ MNOCProof

                                    ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Instantiation

                                                ↳ QDP

                                                  ↳ MNOCProof

                                                    ↳ QDP

                                    ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Neg(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz87, Pos(Succ(vuz8600))) → new_gcd0Gcd'(Pos(Succ(vuz8600)), new_primRemInt(vuz87, vuz8600))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primRemInt0(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt0(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Zero) → Zero
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)

The set Q consists of the following terms:

new_primRemInt0(Pos(x0), x1)
new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primRemInt0(Neg(x0), x1)
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz87, Pos(Succ(vuz8600))) → new_gcd0Gcd'(Pos(Succ(vuz8600)), new_primRemInt(vuz87, vuz8600))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))

The set Q consists of the following terms:

new_primRemInt0(Pos(x0), x1)
new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primRemInt0(Neg(x0), x1)
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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_primRemInt0(Pos(x0), x1)
new_primRemInt0(Neg(x0), x1)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(vuz87, Pos(Succ(vuz8600))) → new_gcd0Gcd'(Pos(Succ(vuz8600)), new_primRemInt(vuz87, vuz8600))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

We have to consider all minimal (P,Q,R)-chains.
By narrowing [15] the rule new_gcd0Gcd'(vuz87, Pos(Succ(vuz8600))) → new_gcd0Gcd'(Pos(Succ(vuz8600)), new_primRemInt(vuz87, vuz8600)) at position [1] we obtained the following new rules:

new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                      ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                      ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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_primRemInt(Pos(x0), x1)
new_primRemInt(Neg(x0), x1)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                      ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'(Pos(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(x0, x1))) we obtained the following new rules:

new_gcd0Gcd'(Pos(Succ(z1)), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ MNOCProof

                                                      ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(Succ(z1)), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ MNOCProof

                                                                      ↳ QDP

                                                      ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(Succ(z1)), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primRemInt(Neg(vuz870), vuz8600) → Neg(new_primModNatS1(vuz870, vuz8600))
new_primRemInt(Pos(vuz870), vuz8600) → Pos(new_primModNatS1(vuz870, vuz8600))

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primRemInt(Pos(x0), x1)
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primRemInt(Neg(x0), x1)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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_primRemInt(Pos(x0), x1)
new_primRemInt(Neg(x0), x1)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'(Pos(x0), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(x0, x1))) we obtained the following new rules:

new_gcd0Gcd'(Pos(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1)))
new_gcd0Gcd'(Pos(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_gcd0Gcd'(Neg(x0), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(x0, x1))) we obtained the following new rules:

new_gcd0Gcd'(Neg(Succ(z1)), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(Succ(z1), x1)))

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                                                                      ↳ QDP

                                                                        ↳ MNOCProof

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Neg(Succ(z1)), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(Succ(z1), x1)))
new_gcd0Gcd'(Pos(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

new_primModNatS01(x0, x1, Succ(x2), Zero)
new_primModNatS1(Succ(Succ(x0)), Succ(x1))
new_primMinusNatS0(Zero, Succ(x0))
new_primModNatS1(Zero, x0)
new_primModNatS1(Succ(Succ(x0)), Zero)
new_primModNatS02(x0, x1)
new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
new_primModNatS1(Succ(Zero), Succ(x0))
new_primModNatS01(x0, x1, Zero, Zero)
new_primMinusNatS0(Succ(x0), Succ(x1))
new_primModNatS01(x0, x1, Zero, Succ(x2))
new_primModNatS1(Succ(Zero), Zero)
new_primMinusNatS0(Succ(x0), Zero)
new_primMinusNatS0(Zero, Zero)

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ Narrowing

                              ↳ QDP

                                ↳ DependencyGraphProof

                                  ↳ AND

                                    ↳ QDP

                                    ↳ QDP

                                      ↳ UsableRulesProof

                                        ↳ QDP

                                          ↳ QReductionProof

                                            ↳ QDP

                                              ↳ Narrowing

                                                ↳ QDP

                                                  ↳ DependencyGraphProof

                                                    ↳ AND

                                                      ↳ QDP

                                                      ↳ QDP

                                                        ↳ UsableRulesProof

                                                          ↳ QDP

                                                            ↳ QReductionProof

                                                              ↳ QDP

                                                                ↳ Instantiation

                                                                  ↳ QDP

                                                                    ↳ Instantiation

                                                                      ↳ QDP

                                                                        ↳ MNOCProof

                                                                          ↳ QDP

                          ↳ QDP

                      ↳ Narrow

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

new_gcd0Gcd'(Pos(Succ(z1)), Neg(Succ(x1))) → new_gcd0Gcd'(Neg(Succ(x1)), Pos(new_primModNatS1(Succ(z1), x1)))
new_gcd0Gcd'(Neg(Succ(z1)), Pos(Succ(x1))) → new_gcd0Gcd'(Pos(Succ(x1)), Neg(new_primModNatS1(Succ(z1), x1)))

The TRS R consists of the following rules:

new_primModNatS1(Succ(Zero), Zero) → new_primModNatS1(new_primMinusNatS0(Zero, Zero), Zero)
new_primModNatS1(Succ(Succ(vuz87000)), Zero) → new_primModNatS1(new_primMinusNatS0(Succ(vuz87000), Zero), Zero)
new_primModNatS1(Succ(Zero), Succ(vuz86000)) → Succ(Zero)
new_primModNatS1(Zero, vuz8600) → Zero
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Succ(vuz1070)) → new_primModNatS01(vuz104, vuz105, vuz1060, vuz1070)
new_primModNatS02(vuz104, vuz105) → new_primModNatS1(new_primMinusNatS0(Succ(vuz104), Succ(vuz105)), Succ(vuz105))
new_primModNatS1(Succ(Succ(vuz87000)), Succ(vuz86000)) → new_primModNatS01(vuz87000, vuz86000, vuz87000, vuz86000)
new_primModNatS01(vuz104, vuz105, Zero, Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Succ(vuz1060), Zero) → new_primModNatS02(vuz104, vuz105)
new_primModNatS01(vuz104, vuz105, Zero, Succ(vuz1070)) → Succ(Succ(vuz104))
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Zero, Zero) → new_primDivNatS00(vuz79, vuz80)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)
new_primDivNatS00(vuz79, vuz80) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))
new_primDivNatS(Succ(Succ(vuz3900)), Succ(vuz40000)) → new_primDivNatS0(vuz3900, vuz40000, vuz3900, vuz40000)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Zero) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))
new_primDivNatS(Succ(Zero), Zero) → new_primDivNatS(new_primMinusNatS2, Zero)
new_primDivNatS(Succ(Succ(vuz3900)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz3900), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS1(vuz3900) → Succ(vuz3900)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primMinusNatS2 → Zero

The set Q consists of the following terms:

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

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(Succ(vuz3900)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz3900), Zero)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS1(vuz3900) → Succ(vuz3900)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primMinusNatS2 → Zero

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(Succ(vuz3900)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz3900), Zero)

The TRS R consists of the following rules:

new_primMinusNatS1(vuz3900) → Succ(vuz3900)

The set Q consists of the following terms:

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ RuleRemovalProof

                                ↳ QDP

                      ↳ Narrow

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

new_primDivNatS(Succ(Succ(vuz3900)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz3900), Zero)

The TRS R consists of the following rules:

new_primMinusNatS1(vuz3900) → Succ(vuz3900)

The set Q consists of the following terms:

new_primMinusNatS1(x0)

new_primDivNatS(Succ(Succ(vuz3900)), Zero) → new_primDivNatS(new_primMinusNatS1(vuz3900), Zero)

Strictly oriented rules of the TRS R:

new_primMinusNatS1(vuz3900) → Succ(vuz3900)

Used ordering: POLO with Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + 2·x₁
POL(Zero) = 0
POL(new_primDivNatS(x₁, x₂)) = x₁ + x₂
POL(new_primMinusNatS1(x₁)) = 2 + 2·x₁

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ RuleRemovalProof

                                            ↳ QDP

                                              ↳ PisEmptyProof

                                ↳ QDP

                      ↳ Narrow

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

new_primMinusNatS1(x0)

We have to consider all minimal (P,Q,R)-chains.
The TRS P is empty. Hence, there is no (P,Q,R) chain.

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Zero, Zero) → new_primDivNatS00(vuz79, vuz80)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)
new_primDivNatS(Succ(Succ(vuz3900)), Succ(vuz40000)) → new_primDivNatS0(vuz3900, vuz40000, vuz3900, vuz40000)
new_primDivNatS00(vuz79, vuz80) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Zero) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS1(vuz3900) → Succ(vuz3900)
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primMinusNatS2 → Zero

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Zero, Zero) → new_primDivNatS00(vuz79, vuz80)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)
new_primDivNatS(Succ(Succ(vuz3900)), Succ(vuz40000)) → new_primDivNatS0(vuz3900, vuz40000, vuz3900, vuz40000)
new_primDivNatS00(vuz79, vuz80) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Zero) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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
new_primMinusNatS1(x0)

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Zero, Zero) → new_primDivNatS00(vuz79, vuz80)
new_primDivNatS00(vuz79, vuz80) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))
new_primDivNatS(Succ(Succ(vuz3900)), Succ(vuz40000)) → new_primDivNatS0(vuz3900, vuz40000, vuz3900, vuz40000)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Zero) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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_primDivNatS00(vuz79, vuz80) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))
new_primDivNatS(Succ(Succ(vuz3900)), Succ(vuz40000)) → new_primDivNatS0(vuz3900, vuz40000, vuz3900, vuz40000)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Zero) → new_primDivNatS(new_primMinusNatS0(vuz79, vuz80), Succ(vuz80))

The remaining pairs can at least be oriented weakly.

new_primDivNatS0(vuz79, vuz80, Zero, Zero) → new_primDivNatS00(vuz79, vuz80)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)

Used ordering: Polynomial interpretation [25]:

POL(Succ(x₁)) = 1 + x₁
POL(Zero) = 0
POL(new_primDivNatS(x₁, x₂)) = x₁
POL(new_primDivNatS0(x₁, x₂, x₃, x₄)) = 1 + x₁
POL(new_primDivNatS00(x₁, x₂)) = 1 + x₁
POL(new_primMinusNatS0(x₁, x₂)) = x₁

The following usable rules [17] were oriented:

new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Zero, Succ(vuz800)) → Zero

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Zero, Zero) → new_primDivNatS00(vuz79, vuz80)
new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

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

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)

The TRS R consists of the following rules:

new_primMinusNatS0(Zero, Succ(vuz800)) → Zero
new_primMinusNatS0(Zero, Zero) → Zero
new_primMinusNatS0(Succ(vuz790), Succ(vuz800)) → new_primMinusNatS0(vuz790, vuz800)
new_primMinusNatS0(Succ(vuz790), Zero) → Succ(vuz790)

The set Q consists of the following terms:

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)

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

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

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

↳ HASKELL

  ↳ IFR

    ↳ HASKELL

      ↳ BR

        ↳ HASKELL

          ↳ COR

            ↳ HASKELL

              ↳ LetRed

                ↳ HASKELL

                  ↳ NumRed

                    ↳ HASKELL

                      ↳ Narrow

                        ↳ AND

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                          ↳ QDP

                            ↳ DependencyGraphProof

                              ↳ AND

                                ↳ QDP

                                ↳ QDP

                                  ↳ UsableRulesProof

                                    ↳ QDP

                                      ↳ QReductionProof

                                        ↳ QDP

                                          ↳ QDPOrderProof

                                            ↳ QDP

                                              ↳ DependencyGraphProof

                                                ↳ QDP

                                                  ↳ UsableRulesProof

                                                    ↳ QDP

                                                      ↳ QReductionProof

                                                        ↳ QDP

                                                          ↳ QDPSizeChangeProof

                      ↳ Narrow

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

new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)

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

new_primDivNatS0(vuz79, vuz80, Succ(vuz810), Succ(vuz820)) → new_primDivNatS0(vuz79, vuz80, vuz810, vuz820)
The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4

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

gcd2	True yz zu	= gcd1 (zu == 0) yz zu
gcd2	zy zz vuu	= gcd0 zz vuu

reduce2Reduce1	vux vuy x y True	= error []
reduce2Reduce1	vux vuy x y False	= reduce2Reduce0 vux vuy x y otherwise

gcd0Gcd'2	x xz	= gcd0Gcd'1 (xz == 0) x xz
gcd0Gcd'2	yx yy	= gcd0Gcd'0 yx yy